Composable free-space continuous-variable quantum key distribution using discrete modulation

Kevin Jaksch, Thomas Dirmeier, Yannick Weiser, Stefan Richter, Oemer Bayraktar, Bastian Hacker, Conrad Rösler, Imran Khan, Stefan Petscharning, et al.

Continuous-variable (CV) quantum key distribution (QKD) allows for quantum secure communication with the benefit of being close to existing classical coherent communication. In recent years, CV QKD protocols using a discrete number of displaced coherent states have been studied intensively, as the modulation can be directly implemented with real devices with a finite digital resolution. However, the experimental demonstrations until now only calculated key rates in the asymptotic regime. To be used in cryptographic applications, a QKD system has to generate keys with composable security in the finite-size regime. In this paper, we present a CV QKD system using discrete modulation that is especially designed for urban atmospheric channels. For this, we use polarization encoding to cope with the turbulent but non-birefringent atmosphere. This will allow to expand CV QKD networks beyond the existing fiber backbone. In a first laboratory demonstration, we implemented a novel type of security proof allowing to calculate composable finite-size key rates against i.i.d. collective attacks without any Gaussian assumptions. We applied the full QKD protocol including a QRNG, error correction and privacy amplification to extract secret keys. In particular, we studied the impact of frame errors on the actual key generation.

Covariant operator bases for continuous variables

Aaron Z. Goldberg, Andrei B. Klimov, Gerd Leuchs, Luis Sanchez-Soto

Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations. This basis is the analogue of the irreducible tensors widely used in the context of SU(2) symmetry. Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit. We use these quantities to assess properties such as quantumness or Gaussianity and to furnish direct connections between tomographic measurements and quasiprobability distribution reconstructions.

Quantum squeezing via self-induced transparency in a photonic crystal fiber

Mojdeh S. Najafabadi, Luis Sanchez-Soto, J. F. Corney, Nikolay Kalinin, A. A. Sorokin, Gerd Leuchs

We study the quantum squeezing produced in self-induced transparency in a photonic crystal fiber by performing a fully quantum simulation based on the positive P representation. The amplitude squeezing depends on the area of the initial pulse: When the area is 2 pi, there is no energy absorption and no amplitude squeezing. However, when the area is between 2 pi and 3 pi, one observes amplitude-dependent energy absorption and a significant amount of squeezing. We also investigate the effect of damping, detuning, and temperature: The results indicate that a heightened atom-pulse coupling, caused by an increase in the spontaneous emission ratio, reduces the amplitude squeezing.

Multipoles from Majorana constellations

J. L. Romero, A. B. Klimov, A. Z. Goldberg, Gerd Leuchs, Luis Sanchez-Soto

Majorana stars, the 2S spin coherent states that are orthogonal to a spin-S state, offer an elegant method to visualize quantum states, disclosing their intrinsic symmetries. These states are naturally described by the corresponding multipoles. These quantities can be experimentally determined and allow for an SU(2)-invariant analysis. We investigate the relationship between Majorana constellations and state multipoles, thus providing insights into the underlying symmetries of the system. We illustrate our approach with some relevant and informative examples.

Quantum-enhanced interferometer using Kerr squeezing

Nikolay Kalinin, Thomas Dirmeier, Arseny A. Sorokin, Elena A. Anashkina, Luis Sanchez-Soto, Joel F. Corney, Gerd Leuchs, Alexey V. Andrianov

One of the prime applications of squeezed light is enhancing the sensitivity of an interferometer below the quantum shot-noise limit, but so far, no such experimental demonstration was reported when using the optical Kerr effect. In prior setups involving Kerr-squeezed light, the role of the interferometer was merely to characterize the noise pattern. The lack of such a demonstration was largely due to the cumbersome tilting of the squeezed ellipse in phase space. Here, we present the first experimental observation of phase-sensitivity enhancement in an interferometer using Kerr squeezing.

Superresolution Enhancement in Biphoton Spatial-Mode Demultiplexing

Florence Grenapin, Dilip Paneru, Alessio D'Errico, Vincenzo Grillo, Gerd Leuchs, Ebrahim Karimi

Imaging systems measuring intensity in the far field succumb to Rayleigh's curse, a resolution limitation dictated by the finite aperture of the optical system. Many proof-of-principle and some two-dimensional imaging experiments have shown that, by using spatial mode demultiplexing (SPADE), the field information collected is maximal, and, thus, the resolution increases beyond the Rayleigh criterion. Hitherto, the SPADE approaches are based on resolving the lateral splitting of a Gaussian wave function. Here, we consider the case in which the light field originates from a biphoton source, i.e., spontaneous parametric down-conversion, and a horizontal separation is introduced in one of the two photons. We show that a separation induced in the signal photon arm can be superresolved using coincidence measurements after projecting both photons on Hermite-Gauss modes. Remarkably, the Fisher information associated with the measurement is enhanced compared to the ordinary SPADE techniques by root K, where K is the Schmidt number of the two-photon state that quantifies the amount of spatial entanglement between the two photons.

All-in-One Photoactivated Inhibition of Butyrylcholinesterase Combined with Luminescence as an Activation and Localization Indicator: Carbon Quantum Dots@Phosphonate Hybrids

Gulia Bikbaeva, Anna Pilip, Anastasia Egorova, Ilya Kolesnikov, Dmitrii Pankin, Kirill Laptinskiy, Alexey Vervald, Tatiana Dolenko, Gerd Leuchs, et al.

Photopharmacology is a booming research area requiring a new generation of agents possessing simultaneous functions of photoswitching and pharmacophore. It is important that any practical implementation of photopharmacology ideally requires spatial control of the medicinal treatment zone. Thus, advances in the study of substances meeting all the listed requirements will lead to breakthrough research in the coming years. In this study, CQDs@phosphonate nanohybrids are presented for the first time and combine biocompatible and nontoxic luminescent carbon quantum dots (CQDs) with photoactive phosphonate enabling inhibition of butyrylcholinesterase (BChE), which is a prognostic marker of numerous diseases. The conjunction of these components in hybrids maintains photoswitching and provides enhancement of BChE inhibition. After laser irradiation with a wavelength of 266 nm, CQDs@phosphonate hybrids demonstrate a drastic increase of butyrylcholinesterase inhibition from 38% up to almost 100% and a simultaneous luminescence decrease. All the listed hybrid properties are demonstrated not only for in vitro experiments but also for complex biological samples, i.e., chicken breast. Thus, the most important achievement is the demonstration of hybrids characterized by a remarkable combination of all-in-one properties important for photopharmacology: (i) bioactivity toward butyrylcholinesterase inhibition, (ii) strong change of inhibition degree as a result of laser irradiation, luminescence as an indicator of (iii) bioactivity state, and of (iv) spatial localization on the surface of a sample.

Sensing Rotations with Multiplane Light Conversion

M. Eriksson, A. Z. Goldberg, M. Hiekkamaki, F. Bouchard, J. Rehacek, Z. Hradil, Gerd Leuchs, R. Fickler, Luis Sanchez-Soto

We report an experiment estimating the three parameters of a general rotation. The scheme uses quantum states attaining the ultimate precision dictated by the quantum Cramer-Rao bound. We realize the states experimentally using the orbital angular momentum of light and implement the rotations with a multiplane light-conversion setup, which allows one to perform arbitrary unitary transformations on a finite set of spatial modes. The observed performance suggests a range of potential applications in the next generation of rotation sensors.

Collectively Enhanced Giant Circular Dichroism of Germanium Nanohelix Square Lattice Arrays

Günter Ellrott, Paul Beck, Vitaliy Sultanov, Sergej Rothau, Norbert Lindlein, Maria Chekhova, Vojislav Kristic

Circular dichroism is a unique chiroptical signature of the chirality of a system and is a prevalent way to characterize and distinguish systems on a fundamental level and for their technological applicability. Thus, engineering and maximizing the chiroptical response of a single chiral object or a metasurface composed of chiral entities is a formidable task. Current efforts strongly focus on individual metallic nanostructures and their periodic ensembles to harvest on (resonant) plasmonic properties and interactions. This route, however, waives the advantages of high-refractive-index nanoscale materials embracing low dissipative losses at optical wavelengths and electromagnetic fields penetrating and propagating in such materials. Herein, a strong circular dichroism is demonstrated in square lattices of nanohelices made of the high-refractive-index semiconductor germanium, with dissymmetry factors outperforming metal-based ensembles. The observation of a much higher dissymmetry emerges for illumination with spatially coherent light, in comparison to spatially incoherent light. High dissymmetry is attributed to cooperative coupling between single helices, resulting from the combination of dielectric resonances of both the individual helical building blocks and the highly ordered lattice.

Quasiclassical approach to the nonlinear Kerr dynamics

Mojdeh S. Najafabadi, Andrei B. Klimov, Luis Sanchez-Soto, Gerd Leuchs

We examine the quasiclassical approximation to the self-Kerr nonlinear effect. The corresponding dynamics appears as classical trajectories, with the quantumness of the state included via its Wigner function. We obtain analytical estimates of the optimal squeezing attainable that compare fairly well with the numerical quantum solution. We delimit the range of parameters for which the quasiclassical solution retains relevant quantum features.<br><br>

Fiber-Optical Sources of Quantum Squeezed Light

A. V. Andrianov, Nikolay Kalinin, A. A. Sorokin, E. A. Anashkina, Gerd Leuchs

Quantum squeezed states of light characterized by a reduced quantum uncertainty with respect to one of the quadrature variables smaller than the uncertainty of the vacuum state (the standard quantum limit) play an important role in the current fundamental and applied research. The main information concerning the proprieties and manifestations of the squeezed states are presented. A concise review of the methods for obtaining and detecting the quantum squeezed light is performed; at that, a special attention is payed to fiber-optical schemas. The Kerr mechanism of squeezed state generation that is realized in various variants of fiber-optic systems is considered in detail. An experimental scheme of generation of polarization-squeezed states based on a nonlinear polarization-maintaining fiber is presented. Different factors that limit squeezing are considered.

Protecting Quantum Modes in Optical Fibers

Muhammad Abdullah Butt, Paul Roth, Gordon Wong, Michael Frosz, Luis Sanchez-Soto, E. A. Anashkina, A. V. Andrianov, Peter Banzer, Philip Russell, et al.

Polarization-preserving fibers maintain the two polarization states of an orthogonal basis. Quantum communication, however, requires sending at least two nonorthogonal states and these cannot both be preserved. We present an alternative scheme that allows for using polarization encoding in a fiber not only in the discrete, but also in the continuous-variable regime. For the example of a helically twisted photonic crystal fiber, we experimentally demonstrate that using appropriate nonorthogonal modes, the polarization-preserving fiber does not fully scramble these modes over the full Poincaré sphere, but that the output polarization will stay on a great circle; that is, within a one-dimensional protected subspace, which can be parametrized by a single variable. This allows for more efficient measurements of quantum excitations in nonorthogonal modes.

Influence of Initial Surface Roughness on LIPSS Formation and Its Consecutive Impact on Cell/Bacteria Attachment for TiAl6V4 Surfaces

Lamborghini Sotelo, Tommaso Fontanot, Sanjana Vig, Patrick Herre, Peyman Yousefi, Maria Helena Fernandes, George Sarau, Gerd Leuchs, Silke Christiansen

The influence of the initial surface roughness of TiAl6V4 samples on the orientation and periodicity of the resulting laser-induced periodic surface structures (LIPSS), as well as the surface wettability and chemistry is reported here. Before LIPSS fabrication, initial sample surface roughness is adjusted by variations of finial polishing steps with polishing grain sizes of 18.3, 8.4, 5, and 0.5 mu m. A 3 x 3 irradiation matrix was defined and lasered on all samples by changing the laser power and distance between consecutive laser scans. The resulting structures were characterized by scanning electron microscopy (SEM), atomic force microscopy, Raman spectroscopy, and contact angle measurements. As a further step, three representative generated structures were chosen to explore their bone implant viability by resazurin assays, alkaline phosphatase activity, and direct SEM imaging of the induced cells (MG63) and bacteria (Escherichia coli and Staphylococcus aureus). Results show that initial surface roughness has big influence on the wettability of the resulting surface, as well as inducing small variations on the orientation of the generated LIPSS. Structures generated with a higher integrated fluence have also shown to enhance cell differentiation while reducing bacterial activity, making them a great candidate for improved bone implant compatibility and durability.

3D Nanocomposite with High Aspect Ratio Based on Polyaniline Decorated with Silver NPs: Synthesis and Application as Electrochemical Glucose Sensor

Anna A. Vasileva, Daria V. Mamonova, Vladimir Mikhailovskii, Yuri V. Petrov, Yana G. Toropova, Ilya E. Kolesnikov, Gerd Leuchs, Alina A. Manshina

In this paper, we present a new methodology for creating 3D ordered porous nanocomposites based on anodic aluminum oxide template with polyaniline (PANI) and silver NPs. The approach includes in situ synthesis of polyaniline on templates of anodic aluminum oxide nanomembranes and laser-induced deposition (LID) of Ag NPs directly on the pore walls. The proposed method allows for the formation of structures with a high aspect ratio of the pores, topological ordering and uniformity of properties throughout the sample, and a high specific surface area. For the developed structures, we demonstrated their effectiveness as non-enzymatic electrochemical sensors on glucose in a concentration range crucial for medical applications. The obtained systems possess high potential for miniaturization and were applied to glucose detection in real objects-laboratory rat blood plasma.

Near single-photon imaging in the shortwave infrared using homodyne detection

O. Wolley, S. Mekhail, P. -A Moreau, T. Gregory, G. Gibson, Gerd Leuchs, M. J. Padgett

Low-light imaging is challenging in regimes where low-noise detectors are not yet available. One such regime is the shortwave infrared where even the best multipixel detector arrays typically have a noise floor in excess of 100 photons per pixel per frame. We present a homodyne imaging system capable of recovering both intensity and phase images of an object from a single frame despite an illumination intensity of ??? 1 photon per pixel. We interfere this weak signal which is below the noise floor of the detector with a reference beam that is ??? 300, 000 times brighter, record the resulting interference pattern in the spatial domain on a detector array, and use Fourier techniques to extract the intensity and phase images. We believe our approach could vastly extend the range of applications for low-light imaging by accessing domains where low-noise cameras are not currently available and for which low-intensity illumination is required.

Local sampling of the SU(1,1) Wigner function

Nicolas Fabre, Andrei B. Klimov, Gerd Leuchs, Luis Sanchez-Soto

Despite its indisputable merits, the Wigner phase-space formulation has not been widely explored for systems with SU(1,1) symmetry, as a simple operational definition of the Wigner function has proved elusive in this case. We capitalize on unique properties of the parity operator, to derive in a consistent way a bona fide SU(1,1) Wigner function that faithfully parallels the structure of its continuous-variable counterpart. We propose an optical scheme, involving a squeezer and photon-number-resolving detectors, that allows for direct point-by-point sampling of that Wigner function. This provides an adequate framework to represent SU(1,1) states satisfactorily.

Physical Mechanisms Underpinning the Vacuum Permittivity

Gerd Leuchs, Margaret Hawton, Luis Sanchez-Soto

The debate about the emptiness of space goes back to the prehistory of science and is epitomized by the Aristotelian 'horror vacui', which can be seen as the precursor of the ether, whose modern version is the dynamical quantum vacuum. In this paper, we suggest to change a common view to 'gaudium vacui' and discuss how the vacuum fluctuations fix the value of the permittivity, e(0), and permeability, mu(0), by modelling their dynamical response by three-dimensional harmonic oscillators.

Observation of Robust Polarization Squeezing via the Kerr Nonlinearity in an Optical Fiber

Nikolay Kalinin, Thomas Dirmeier, Arseny A. Sorokin, Elena A. Anashkina, Luis Sanchez-Soto, Joel F. Corney, Gerd Leuchs, Alexey V. Andrianov

Squeezed light is one of the resources of photonic quantum technology. Among the various nonlinear interactions capable of generating squeezing, the optical Kerr effect is particularly easy-to-use. A popular venue is to generate polarization squeezing, which is a special self-referencing variant of two-mode squeezing. To date, polarization squeezing generation setups have been very sensitive to fluctuations of external factors and have required careful tuning. In this work, a development of a new all-fiber setup for polarization squeezing generation is reported. The setup consists of passive elements only and is simple, robust, and stable. More than 5 dB of directly measured squeezing is obtained over long periods of time without any need for adjustments. Thus, the new scheme provides a robust and easy-to-set-up way of obtaining squeezed light applicable to different applications. The impact of pulse duration and pulse power on the degree of squeezing is investigated.

Laser-Induced Synthesis of Electrocatalytically Active Ag, Pt, and AgPt/Polyaniline Nanocomposites for Hydrogen Evolution Reactions

Anna A. A. Vasileva, Daria V. V. Mamonova, Yuri V. V. Petrov, Ilya E. E. Kolesnikov, Gerd Leuchs, Alina A. A. Manshina

We present an efficient and easily implemented approach for creating stable electrocatalytically active nanocomposites based on polyaniline (PANI) with metal NPs. The approach combines in situ synthesis of polyaniline followed by laser-induced deposition (LID) of Ag, Pt, and AgPt NPs. The observed peculiarity of LID of PANI is the role of the substrate during the formation of multi-metallic nanoparticles (MNP). This allows us to solve the problem of losing catalytically active particles from the electrode's surface in electrochemical use. The synthesized PANI/Ag, PANI/Pt, and PANI/AgPt composites were studied with different techniques, such as SEM, EDX, Raman spectroscopy, and XPS. These suggested a mechanism for the formation of MNP on PANI. The MNP-PANI interaction was demonstrated, and the functionality of the nanocomposites was studied through the electrocatalysis of the hydrogen evolution reaction. The PANI/AgPt nanocomposites demonstrated both the best activity and the most stable metal component in this process. The suggested approach can be considered as universal, since it can be extended to the creation of electrocatalytically active nanocomposites with various mono- and multi-metallic NPs.

Optimizing the generation of polarization squeezed light in nonlinear optical fibers driven by femtosecond pulses

A. Andrianov V, Nikolay Kalinin, A. A. Sorokin, E. A. Anashkina, Luis Sanchez-Soto, J. F. Corney, Gerd Leuchs

Bright squeezed light can be generated in optical fibers utilizing the Kerr effect for ultrashort laser pulses. However, pulse propagation in a fiber is subject to nonconservative effects that deteriorate the squeezing. Here, we analyze two-mode polarization squeezing, which is SU(2)-invariant, robust against technical perturbations, and can be generated in a polarization-maintaining fiber. We perform a rigorous numerical optimization of the process and the pulse parameters using our advanced model of quantum pulse evolution in the fiber that includes various nonconservative effects and real fiber data. Numerical results are consistent with experimental results. (c) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Anticaustics in a Fabry-Perot interferometer

Luis Sanchez-Soto, Juan J. Monzon, Gerd Leuchs

We address the response of a Fabry-Perot interferometer to a monochromatic point source. We calculate the anti -caustics (that is, the virtual wavefronts of null path difference) resulting from the successive internal reflections occurring in the system. They turn out to be a family of ellipsoids (or hyperboloids) of revolution, which allows us to reinterpret the operation of the Fabry-Perot interferometer from a geometrical point of view that facilitates comparison with other apparently disparate arrangements, such as Young's double slit. (c) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Towards Quantum Noise Squeezing for 2-Micron Light with Tellurite and Chalcogenide Fibers with Large Kerr Nonlinearity

Arseny A. Sorokin, Gerd Leuchs, Joel F. Corney, Nikolay Kalinin, Elena A. Anashkina, Alexey Andrianov V

Squeezed light-nonclassical multiphoton states with fluctuations in one of the quadrature field components below the vacuum level-has found applications in quantum light spectroscopy, quantum telecommunications, quantum computing, precision quantum metrology, detecting gravitational waves, and biological measurements. At present, quantum noise squeezing with optical fiber systems operating in the range near 1.5 mu m has been mastered relatively well, but there are no fiber sources of nonclassical squeezed light beyond this range. Silica fibers are not suitable for strong noise suppression for 2 mu m continuous-wave (CW) light since their losses dramatically deteriorate the squeezed state of required lengths longer than 100 m. We propose the generation multiphoton states of 2-micron 10-W class CW light with squeezed quantum fluctuations stronger than -15 dB in chalcogenide and tellurite soft glass fibers with large Kerr nonlinearities. Using a realistic theoretical model, we numerically study squeezing for 2-micron light in step-index soft glass fibers by taking into account Kerr nonlinearity, distributed losses, and inelastic light scattering processes. Quantum noise squeezing stronger than -20 dB is numerically attained for a customized As2Se3 fibers with realistic parameters for the optimal fiber lengths shorter than 1 m. For commercial As2S3 and customized tellurite glass fibers, the expected squeezing in the -20--15 dB range can be reached for fiber lengths of the order of 1 m.

Formation of Non-Classical Multiphoton States of Light with Squeezed Quantum Fluctuations in Bismuth-Modified Tellurite Glass Fibers

A. A. Sorokin, V. V. Dorofeev, S. E. Motorin, I Lyashuk, J. Porins, Gerd Leuchs, V Bobrovs

An optical fiber with a high Kerr nonlinearity coefficient has been proposed and manufactured from bismuth-modified tellurite glass for creation of non-classical multiphoton states of light. Specifically, we have proposed to use these fibers to squeeze the quantum fluctuations of one of the quadratures of light in the 20 W signal significantly below -10 dB compared to the standard quantum noise limit, which is important for various practical applications. Using numerical simulation based on the stochastic nonlinear Schrodinger equation, we have demonstrated noise squeezing stronger than -16 dB at tellurite fiber lengths of 6-14 m, while in squeezing of -14 dB is expected in silica glass fibers having lengths of 120-300 m. Analytical formulas were used to analyze the physical factors that limit the achievable squeezing.

Vacuum breakdown in magnetic dipole wave by 10-PW class lasers

E. S. Efimenko, A. Bashinov V, A. A. Muraviev, V. D. Volokitin, I. B. Meyerov, Gerd Leuchs, A. M. Sergeev, A. Kim V

The vacuum breakdown by 10-PW-class lasers is studied in the optimal configuration of laser beams in the form of an m-dipole wave, which maximizes the magnetic field. Using 3D PIC simulations we calculated the threshold of vacuum breakdown, which is about 10 PW. We examined in detail the dynamics of particles and identified particle trajectories which contribute the most to vacuum breakdown in such highly inhomogeneous fields. We analyzed the dynamics of the electron-positron plasma distribution on the avalanche stage. It is shown that the forming plasma structures represent concentric toroidal layers and the interplay between particle ensembles from different spatial regions favors vacuum breakdown. Based on the angular distribution of charged particles and gamma photons a way to experimentally identify the process of vacuum breakdown is proposed.

Single-Step Process for Titanium Surface Micro- and Nano-Structuring and In Situ Silver Nanoparticles Formation by Ultra-Short Laser Patterning

Dante Maria Aceti, Emil Filipov, Liliya Angelova, Lamborghini Sotelo, Tommaso Fontanot, Peyman Yousefi, Silke Christiansen, Gerd Leuchs, Stanislav Stanimirov, et al.

Ultra-short laser (USL)-induced surface structuring combined with nanoparticles synthesis by multiphoton photoreduction represents a novel single-step approach for commercially pure titanium (cp-Ti) surface enhancement. Such a combination leads to the formation of distinct topographical features covered by nanoparticles. The USL processing of cp-Ti in an aqueous solution of silver nitrate (AgNO3) induces the formation of micron-sized spikes surmounted by silver nanoparticles (AgNPs). The proposed approach combines the structuring and oxidation of the Ti surface and the synthesis of AgNPs in a one-step process, without the use of additional chemicals or a complex apparatus. Such a process is easy to implement, versatile and sustainable compared to alternative methodologies capable of obtaining comparable results. Antimicrobial surfaces on medical devices (e.g., surgical tools or implants), for which titanium is widely used, can be realized due to the simultaneous presence of AgNPs and micro/nano-structured surface topography. The processed surfaces were examined by means of a scanning electron microscope (SEM), energy-dispersive X-ray spectroscopy (EDX), atomic force microscopy (AFM) and Raman spectroscopy. The surface morphology and the oxidation, quality and quantity of AgNPs were analyzed in relation to process parameters (laser scanning speed and AgNO3 concentration), as well as the effect of AgNPs on the Raman signal of Titanium oxide.

Particle trajectories, gamma-ray emission, and anomalous radiative trapping effects in magnetic dipole wave

A. Bashinov V, E. S. Efimenko, A. A. Muraviev, V. D. Volokitin, I. B. Meyerov, Gerd Leuchs, A. M. Sergeev, A. Kim V

In studies of interaction of matter with laser fields of extreme intensity there are two limiting cases of a multibeam setup maximizing either the electric field or the magnetic field. In this work attention is paid to the optimal configuration of laser beams in the form of an m-dipole wave, which maximizes the magnetic field. We consider in such highly inhomogeneous fields the advantages and specific features of laser-matter interaction, which stem from individual particle trajectories that are strongly affected by gamma photon emission. It is shown that in this field mode qualitatively different scenarios of particle dynamics take place in comparison with the mode that maximizes the electric field. A detailed map of possible regimes of particle motion (ponderomotive trapping, normal radiative trapping, radial, and axial anomalous radiative trapping), as well as angular and energy distributions of particles and gamma photons, is obtained in a wide range of laser powers up to 300 PW, and it reveals signatures of radiation losses experimentally detectable even with subpetawatt lasers.

Extreme Concentration and Nanoscale Interaction of Light

Gerd Leuchs, Alexey Andrianov V, Elena A. Anashkina, Alina A. Manshina, Peter Banzer, Markus Sondermann

Concentrating light strongly calls for appropriate polarization patterns of the focused light beam and for up to a full 4 pi solid angle geometry. Focusing on the extreme requires efficient coupling to nanostructures of one kind or another via cylindrical vector beams having such patterns, the details of which depend on the geometry and property of the respective nanostructure. Cylindrical vector beams can not only be used to study a nanostructure, but also vice versa. Closely related is the discussion of topics such as the ultimate diffraction limit, a resonant field enhancement near nanoscopic absorbers, as well as speculations about nonresonant field enhancement, which, if it exists, might be relevant to pair production in vacuum. These cases do require further rigorous simulations and more decisive experiments. While there is a wide diversity of scenarios, there are also conceptually very different models offering helpful intuitive pictures despite this diversity.

Quantumness beyond entanglement: The case of symmetric states

Aaron Z. Goldberg, Markus Grassl, Gerd Leuchs, Luis L. Sanchez-Soto

Nowadays, it is accepted that truly quantum correlations can exist even in the absence of entanglement. For the case of symmetric states, a physically trivial unitary transformation can alter a state from entangled to separable, and vice versa. We propose to certify the presence of quantumness via an average of a state's bipartite entanglement properties over all physically relevant modal decompositions. We investigate extremal states for such a measure: SU(2)-coherent states possess the least quantumness, whereas the opposite extreme is inhabited by states with maximally spread Majorana constellations.

Quantum Noise Squeezing for Optical Signals in Zinc-Tellurite Fibers

A. A. Sorokin, V. V. Dorofeev, S. E. Motorin, Gerd Leuchs

Nonclassical multiphoton states of light with squeezed quantum fluctuations are in demand for various ultrahigh-accuracy measurements. In this study, we propose to use fiber of bismuth-modified zinc-tellurite glass with high Kerr nonlinearity to squeeze quantum noise of optical signals. We experimentally fabricated such fiber and, using numerical simulation of the nonlinear evolution of cw laser signal taking into account fiber characteristics for optimum parameters, theoretically demonstrated noise squeezing better than -15 dB.

From polarization multipoles to higher-order coherences

Aaron Z. Goldberg, Andrei B. Klimov, Hubert DeGuise, Gerd Leuchs, Girish S. Agarwal, Luis Sanchez-Soto

We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the natural variables to deal with a number of problems in the quantum domain. In the case of polarization, the moments are measured after the light has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific values of the angles of the wave plates. For more general two-mode problems, equivalent measurements can be performed. (C) 2022 Optical Society of America

Lenslet array-free efficient coherent combining of broadband pulses at the output of a multicore fiber with a square core grid

Nikolay Kalinin, Elena A. Anashkina, Gerd Leuchs, Alexey Andrianov V

An efficient optical scheme for coherent combining of radiation from the output of a multicore fiber (MCF) with a square array of cores in the out-of-phase supermode is proposed. The scheme uses only simple optical elements and is suitable for an arbitrary number of MCF cores. In a proof-of-concept experiment broadband pulses transmitted through a 25-core fiber were combined with 81% efficiency and good beam quality. In numerical modeling a close to unity efficiency is obtained for a large number of cores. The proposed scheme can be used in a reverse direction for efficient beam splitting and launching the out-of-phase supermode into the MCF. (C) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Ultra-Short Laser Surface Properties Optimization of Biocompatibility Characteristics of 3D Poly-ε-Caprolactone and Hydroxyapatite Composite Scaffolds

Albena Daskalova, Emil Filipov, Liliya Angelova, Radostin Stefanov, Dragomir Tatchev, Georgi Avdeev, Lamborghini Sotelo, Silke Christiansen, George Sarau, et al.

The use of laser processing for the creation of diverse morphological patterns onto the surface of polymer scaffolds represents a method for overcoming bacterial biofilm formation and inducing enhanced cellular dynamics. We have investigated the influence of ultra-short laser parameters on 3D-printed poly-epsilon-caprolactone (PCL) and poly-epsilon-caprolactone/hydroxyapatite (PCL/HA) scaffolds with the aim of creating submicron geometrical features to improve the matrix biocompatibility properties. Specifically, the present research was focused on monitoring the effect of the laser fluence (F) and the number of applied pulses (N) on the morphological, chemical and mechanical properties of the scaffolds. SEM analysis revealed that the femtosecond laser treatment of the scaffolds led to the formation of two distinct surface geometrical patterns, microchannels and single microprotrusions, without triggering collateral damage to the surrounding zones. We found that the microchannel structures favor the hydrophilicity properties. As demonstrated by the computer tomography results, surface roughness of the modified zones increases compared to the non-modified surface, without influencing the mechanical stability of the 3D matrices. The X-ray diffraction analysis confirmed that the laser structuring of the matrices did not lead to a change in the semi-crystalline phase of the PCL. The combinations of two types of geometrical designs-wood pile and snowflake-with laser-induced morphologies in the form of channels and columns are considered for optimizing the conditions for establishing an ideal scaffold, namely, precise dimensional form, mechanical stability, improved cytocompatibility and antibacterial behavior.

Dispersion Tailoring and Four-Wave Mixing in Silica Microspheres with Germanosilicate Coating

Maria P. Marisova, Alexey Andrianov V, Gerd Leuchs, Elena A. Anashkina

Optical whispering gallery mode microresonators with controllable parameters in the telecommunication range are demanded for diverse applications. Controlling group velocity dispersion (GVD) in microresonators is an important problem, as near-zero GVD in a broad wavelength range could contribute to the development of new microresonator-based light sources. We demon-strated theoretically near-zero dispersion tailoring in the SCL-band in combination with free-spectral range (FSR) optimization for FSR = 200 GHz and 300 GHz in silica glass microspheres with micronscale germanosilicate coating. As an illustration of a possible application of such a GVD, we also performed a theoretical study of degenerate four-wave mixing (FWM) processes in the proposed microresonators for pumping in the SCL-band. We found that in some cases the generation of two or even three pairs of waves-satellites in a FWM process is possible in principle due to the specific GVD features. We also determined optimal microresonator configurations for achieving gradual change in the satellite frequency shift for the pump wavelengths in the SCL-, S-, CL-, C-, and L-bands. The maximum obtained FWM satellite tunability span was similar to 78 THz for a pump wavelength change of similar to 30 nm, which greatly exceeds the results for a regular silica microsphere without coating.

Benchmarking quantum tomography completeness and fidelity with machine learning

Yong Siah Teo, Seongwook Shin, Hyunseok Jeong, Yosep Kim, Yoon-Ho Kim, Gleb Struchalin I, Egor Kovlakov V, Stanislav S. Straupe, Sergei P. Kulik, et al.

We train convolutional neural networks to predict whether or not a set of measurements is informationally complete to uniquely reconstruct any given quantum state with no prior information. In addition, we perform fidelity benchmarking based on this measurement set without explicitly carrying out state tomography. The networks are trained to recognize the fidelity and a reliable measure for informational completeness. By gradually accumulating measurements and data, these trained convolutional networks can efficiently establish a compressive quantum-state characterization scheme by accelerating runtime computation and greatly reducing systematic drifts in experiments. We confirm the potential of this machine-learning approach by presenting experimental results for both spatial-mode and multiphoton systems of large dimensions. These predictions are further shown to improve when the networks are trained with additional bootstrapped training sets from real experimental data. Using a realistic beam-profile displacement error model for Hermite-Gaussian sources, we further demonstrate numerically that the orders-of-magnitude reduction in certification time with trained networks greatly increases the computation yield of a large-scale quantum processor using these sources, before state fidelity deteriorates significantly.

Quantum noise squeezing of CW light in tellurite glass fibres

E. A. Anashkina, A. A. Sorokin, Gerd Leuchs, A. V. Andrianov

Light with suppressed quantum fluctuations is desirable for a lot of applications. There are several approaches to suppress a noise including Kerr squeezing in optical fibres. Silica fibres are commonly used for this purpose. Here we propose to use highly nonlinear tellurite glass fibres for Kerr squeezing of CW laser field and demonstrate by simulations in the framework of the stochastic generalized nonlinear Schrodinger equation the possibility of -20 dB noise suppression. In simulations, Raman terms and losses are switched on and switched off to find their contributions to the limits of squeezing. The analytical estimates without loss and with lumped loss are also given.

Optical Frequency Combs Generated in Silica Microspheres in the Telecommunication C-, U-, and E-Bands

Elena A. Anashkina, Maria P. Marisova, Toms Salgals, Janis Alnis, Ilya Lyashuk, Gerd Leuchs, Sandis Spolitis, Vjaceslavs Bobrovs, Alexey V. Andrianov

Optical frequency combs (OFCs) generated in microresonators with whispering gallery modes are demanded for different applications including telecommunications. Extending operating spectral ranges is an important problem for wavelength-division multiplexing systems based on microresonators. We demonstrate experimentally three spectrally separated OFCs in the C-, U-, and E-bands in silica microspheres which, in principle, can be used for telecommunication applications. For qualitative explanation of the OFC generation in the sidebands, we calculated gain coefficients and gain bandwidths for degenerate four-wave mixing (FWM) processes. We also attained a regime when the pump frequency was in the normal dispersion range and only two OFCs were generated. The first OFC was near the pump frequency and the second Raman-assisted OFC with a soliton-like spectrum was in the U-band. Numerical simulation based on the Lugiato-Lefever equation was performed to support this result and demonstrate that the Raman-assisted OFC may be a soliton.

Laser-induced switching of the biological activity of phosphonate molecules

Ilya Kolesnikov, Anastasia Khokhlova, Dmitry Pankin, Anna Pilip, Anastasia Egorova, Vladislav Zigel, Maxim Gureev, Gerd Leuchs, Alina Manshina

Butyrylcholinesterase inhibition and its enhancement as a result of laser irradiation are demonstrated for the first time for a series of phosphorylated arylaminomalonates. The effect of substituents in the phenyl group on butyrylcholinesterase inhibition and its laser-activated enhancement is revealed experimentally and confirmed by molecular dynamics and docking modelling.

Effects of coherence on temporal resolution

Syamsundar De, Jano Gil-Lopez, Benjamin Brecht, Christine Silberhorn, Luis Sanchez-Soto, Zdeněk Hradil, Jaroslav Řeháček

Measuring small separations between two optical sources, either in space or in time, constitutes an important metrological challenge as standard intensity-only measurements fail for vanishing separations. Contrarily, it has been established that appropriate coherent mode projections can appraise arbitrarily small separations with quantum-limited precision. However, the question of whether the optical coherence brings any metrological advantage to mode projections is still a point of debate. Here, we elucidate this problem by experimentally investigating the effect of varying coherence on estimating the temporal separation between two single-photon pulses. We show that, for an accurate interpretation, special attention must be paid to properly normalize the quantum Fisher information to account for the strength of the signal.

Thermal noise in electro-optic devices at cryogenic temperatures

Sonia Mobassem, Nicholas J. Lambert, Alfredo Rueda, Johannes M. Fink, Gerd Leuchs, Harald G. L. Schwefel

The quantum bits (qubits) on which superconducting quantum computers are based have energy scales corresponding to photons with GHz frequencies. The energy of photons in the gigahertz domain is too low to allow transmission through the noisy room-temperature environment, where the signal would be lost in thermal noise. Optical photons, on the other hand, have much higher energies, and signals can be detected using highly efficient single-photon detectors. Transduction from microwave to optical frequencies is therefore a potential enabling technology for quantum devices. However, in such a device the optical pump can be a source of thermal noise and thus degrade the fidelity; the similarity of input microwave state to the output optical state. In order to investigate the magnitude of this effect we model the sub-Kelvin thermal behavior of an electro-optic transducer based on a lithium niobate whispering gallery mode resonator. We find that there is an optimum power level for a continuous pump, whilst pulsed operation of the pump increases the fidelity of the conversion.

Numerical Simulations on Polarization Quantum Noise Squeezing for Ultrashort Solitons in Optical Fiber with Enlarged Mode Field Area

Arseny A. Sorokin, Elena A. Anashkina, Joel F. Corney, Vjaceslavs Bobrovs, Gerd Leuchs, Alexey Andrianov V

Broadband quantum noise suppression of light is required for many applications, including detection of gravitational waves, quantum sensing, and quantum communication. Here, using numerical simulations, we investigate the possibility of polarization squeezing of ultrashort soliton pulses in an optical fiber with an enlarged mode field area, such as large-mode area or multicore fibers (to scale up the pulse energy). Our model includes the second-order dispersion, Kerr and Raman effects, quantum noise, and optical losses. In simulations, we switch on and switch off Raman effects and losses to find their contribution to squeezing of optical pulses with different durations (0.1-1 ps). For longer solitons, the peak power is lower and a longer fiber is required to attain the same squeezing as for shorter solitons, when Raman effects and losses are neglected. In the full model, we demonstrate optimal pulse duration (similar to 0.4 ps) since losses limit squeezing of longer pulses and Raman effects limit squeezing of shorter pulses.

IM/DD WDM-PON Communication System Based on Optical Frequency Comb Generated in Silica Whispering Gallery Mode Resonator

Sandis Spolitis, Rihards Murnieks, Laura Skladova, Toms Salgals, Alexey V. Andrianov, Maria P. Marisova, Gerd Leuchs, Elena A. Anashkina, Vjaceslavs Bobrovs

This article reports an implementation of a microsphere-based optical frequency comb (OFC) generator for substitution of individual laser arrays and simulates wavelength division multiplexed passive optical network (WDM-PON) based on this OFC generator. Our proposed generator is built based on silica microsphere, barely studied for fiber optical communication systems, and is a promising solution with photonic integration capability. Kerr OFC as a multiple light source containing more than 20 spectral carriers in the fundamental mode family in the C-band and beyond is demonstrated experimentally. Four of these OFC generator carriers with the highest peak power are studied in simulated 4-channel 393 GHz spaced WDM-PON. Additionally, we show this OFC as a source of optical carriers capable of providing data transmission over most utilized fiber types in modern optical communication systems, namely, single-mode fiber (SMF), non-zero dispersion-shifted fiber (NZ-DSF), and cut-off shifted fiber (CSF). We show through the simulations that error-free data transmission is possible, providing a total transmission capacity of 40 Gbit/s by using four OFC generated carriers.

Microsphere kinematics from the polarization of tightly focused nonseparable light

Stefan Berg-Johansen, Martin Neugebauer, Andrea Aiello, Gerd Leuchs, Peter Banzer, Christoph Marquardt

Recently, it was shown that vector beams can be utilized for fast kinematic sensing via measurements of their global polarization state [Optica 2, 864 (2015)]. The method relies on correlations between the spatial and polarization degrees of freedom of the illuminating field which result from its nonseparable mode structure. Here, we extend the method to the nonparaxial regime. We study experimentally and theoretically the far-field polarization state generated by the scattering of a dielectric microsphere in a tightly focused vector beam as a function of the particle position. Using polarization measurements only, we demonstrate position sensing of a Mie particle in three dimensions. Our work extends the concept of back focal plane interferometry and highlights the potential of polarization analysis in optical tweezers employing structured light.

Rotation sensing at the ultimate limit

Aaron Z Goldberg, Andrei B Klimov, Gerd Leuchs, Luis Sanchez-Soto

Conventional classical sensors are approaching their maximum sensitivity levels in many areas. Yet these levels are still far from the ultimate limits dictated by quantum mechanics. Quantum sensors promise a substantial step ahead by taking advantage of the salient sensitivity of quantum states to the environment. Here, we focus on sensing rotations, a topic of broad application. By resorting to the basic tools of estimation theory, we derive states that achieve the ultimate sensitivities in estimating both the orientation of an unknown rotation axis and the angle rotated about it. The critical enhancement obtained with these optimal states should make of them an indispensable ingredient in the next generation of rotation sensors that is now blossoming.

Axial superlocalization with vortex beams

D. Koutny, Z. Hradil, J. Rehacek, Luis Sanchez-Soto

Improving axial resolution is of paramount importance for three-dimensional optical imaging systems. Here, we investigate the ultimate precision in axial<br>localization using vortex beams. For Laguerre-Gauss beams, this limit can be achieved with just an intensity scan. The same is not true for superpositions<br>of Laguerre-Gauss beams, in particular for those with intensity profiles that rotate on defocusing. Microscopy methods based on rotating vortex beams may thus benefit from replacing traditional intensity sensors with advanced mode-sorting techniques.

Polarization of Light: In Classical, Quantum, and Nonlinear Optics

Maria V. Chekhova, Peter Banzer

This book starts with the description of polarization in classical optics, including also a chapter on crystal optics, which is necessary to understand the use of nonlinear crystals. In addition, spatially non-uniform polarization states are introduced and described. Further, the role of polarization in nonlinear optics is discussed. The final chapters are devoted to the description and applications of polarization in quantum optics and quantum technologies.

Compensation-free high-dimensional free-space optical communication using turbulence-resilient vector beams

Ziyi Zhu, Molly Janasik, Alexander Fyffe, Darrick Hay, Yiyu Zhou, Brian Kantor, Taylor Winder, Robert W. Boyd, Gerd Leuchs, et al.

Free-space optical communication is a promising means to establish versatile, secure and high-bandwidth communication between mobile nodes for many critical applications. While the spatial modes of light offer a degree of freedom to increase the information capacity of an optical link, atmospheric turbulence can introduce severe distortion to the spatial modes and lead to data degradation. Here, we demonstrate experimentally a vector-beam-based, turbulence-resilient communication protocol, namely spatial polarization differential phase shift keying (SPDPSK), that can reliably transmit high-dimensional information through a turbulent channel without the need of any adaptive optics for beam compensation. In a proof-of-principle experiment with a controllable turbulence cell, we measure a channel capacity of 4.84 bits per pulse using 34 vector modes through a turbulent channel with a scintillation index of 1.09, and 4.02 bits per pulse using 18 vector modes through even stronger turbulence corresponding to a scintillation index of 1.54. Resistance to turbulence is an ongoing challenge for point-to-point freespace communications. Here the authors present a protocol for encoding a large amount of information in vector beams that are transmittable through a moderately strong turbulent channel without adaptive beam compensation.

Quantum concepts in optical polarization

Aaron Z. Goldberg, Pablo De La Hoz, Gunnar Bjork, Andrei B. Klimov, Markus Grassl, Gerd Leuchs, Luis Sanchez-Soto

We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincare sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincare space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored, and their potential applications in quantum technologies are discussed. (C) 2021 Optical Society of America.

Agile and versatile quantum communication: Signatures and secrets

Stefan Richter, Matthew Thornton, Imran Khan, Hamish Scott, Kevin Jaksch, Ulrich Vogl, Birgit Stiller, Gerd Leuchs, Christoph Marquardt, et al.

Agile cryptography allows for a resource-efficient swap of a cryptographic core in case the security of an underlying classical cryptographic algorithm becomes compromised. Conversely, versatile cryptography allows the user to switch the cryptographic task without requiring any knowledge of its inner workings.<br>In this paper, we suggest how these related principles can be applied to the field of quantum cryptography by explicitly demonstrating two quantum cryptographic protocols, quantum digital signatures (QDS) and quantum secret sharing (QSS), on the same hardware sender and receiver platform. Crucially, the protocols differ only in their classical postprocessing. The system is also suitable for quantum key distribution (QKD) and is highly compatible with deployed telecommunication infrastructures, since it uses standard quadrature phase-shift keying encoding and heterodyne detection. For the first time, QDS protocols are modified to allow for postselection at the receiver, enhancing protocol performance. The cryptographic primitives QDS and QSS are inherently multipartite, and we prove that they are secure not only when a player internal to the task is dishonest, but also when (external) eavesdropping on the quantum channel is allowed. In our first proof-of-principle demonstration of an agile and versatile quantum communication system, the quantum states are distributed at GHz rates. A 1-bit message may be securely signed using our QDS protocols in less than 0.05 ms over a 2-km fiber link and in less than 0.2 s over a 20-km fiber link. To our knowledge, this also marks the first demonstration of a continuous-variable direct QSS protocol.

SU(1, 1) covariant s-parametrized maps

Andrei B. Klimov, Ulrich Seyfarth, Hubert de Guise, Luis Sanchez-Soto

We propose a practical recipe to compute the s-parametrized maps for systems with SU(1, 1) symmetry using a connection between the Q- and P-symbols through the action of an operator invariant under the group. This establishes equivalence relations between s-parametrized SU(1, 1)-covariant maps. The particular case of the self-dual (Wigner) phase-space functions, defined on the upper sheet of the two-sheet hyperboloid (or, equivalently, inside the Poincaré disc) are analysed.

Achieving the ultimate quantum timing resolution

Vahid Ansari, Benjamin Brecht, Jano Gil-López, John M. Donohue, Jaroslav Řeháček, Zdeněk Hradil, Luis Sanchez-Soto, Christine Silberhorn

Accurate time-delay measurement is at the core of many modern technologies.<br>Here, we present a temporal-mode demultiplexing scheme that achieves the<br>ultimate quantum precision for the simultaneous estimation of the temporal<br>centroid, the time offset, and the relative intensities of an incoherent<br>mixture of ultrashort pulses at the single-photon level. We experimentally<br>resolve temporal separations ten times smaller than the pulse duration, as well<br>as imbalanced intensities differing by a factor of 10^2. This represents an<br>improvement of more than an order of magnitude over the best standard methods<br>based on intensity detection.<br>

Double-Sided Graphene-Enhanced Raman Scattering and Fluorescence Quenching in Hybrid Biological Structures

George Sarau, Christoph Daniel, Martin Heilmann, Gerd Leuchs, Kerstin Amann, Silke H. Christiansen

Due to their large contact and loading surfaces as well as high sensitivities to chemical changes, graphene-based materials (GBMs) are increasingly being employed into novel nanomedicine technologies. Here biomolecule-monolayer graphene-kidney tissue hybrid structures are studied using mapping micro-Raman and fluorescence spectroscopies. Because in this configuration graphene interacts with molecules on both sides, a double-sided graphene-enhanced Raman scattering (GERS) effect up to approximate to 10.1 is found for biomolecules adsorbed on graphene and amino acids in the kidney tissue below graphene. Moreover, graphene causes an efficient autofluorescence quenching (FLQ) up to approximate to 20% emitted by the kidney tissue. Despite the complexity of such layered materials, the intriguing simultaneous occurrence of double-sided GERS (a new development of GERS) and FLQ phenomena can be well explained by suitable molecular structure and energy level alignment between molecules and graphene. These result in effective charge transfer mediated by non-covalent interactions as indicated by correlative strain, doping, and defect analyses in graphene based on the Raman data and energy level calculations. Last, the advantages of using graphene over standard photobleaching are demonstrated. This work can be extended to other macromolecular entities toward integrating GBMs in versatile drug delivery, imaging, and sensing devices.

Transverse spinning of unpolarized light

Jörg Eismann, L.H Nicholls, D. J. Roth, M. A. Alonso, Peter Banzer, F. J. Rodríguez-Fortuño, A. V. Zayats, F. Nori, K. Y. Bliokh

It is well known that spin angular momentum of light, and therefore that of<br>photons, is directly related to their circular polarization. Naturally, for<br>totally unpolarized light, polarization is undefined and the spin vanishes.<br>However, for nonparaxial light, the recently discovered transverse spin<br>component, orthogonal to the main propagation direction, is largely independent<br>of the polarization state of the wave. Here we demonstrate, both theoretically<br>and experimentally, that this transverse spin survives even in nonparaxial<br>fields (e.g., tightly focused or evanescent) generated from a totally<br>unpolarized light source. This counterintuitive phenomenon is closely related<br>to the fundamental difference between the degrees of polarization for 2D<br>paraxial and 3D nonparaxial fields. Our results open an avenue for studies of<br>spin-related phenomena and optical manipulation using unpolarized light.<br>

Toward a Corrected Knife-Edge-Based Reconstruction of Tightly Focused Higher Order Beams

Sergejus Orlovas, Christian Huber, Pavel Marchenko, Peter Banzer, Gerd Leuchs

The knife-edge method is an established technique for profiling of even tightly focused light beams. However, the straightforward implementation of this method fails if the materials and geometry of the knife-edges are not chosen carefully or, in particular, if knife-edges are used that are made of pure materials. Artifacts are introduced in these cases in the shape and position of the reconstructed beam profile due to the interaction of the light beam under study with the knife. Hence, corrections to the standard knife-edge evaluation method are required. Here we investigate the knife-edge method for highly focused radially and azimuthally polarized beams and their linearly polarized constituents. We introduce relative shifts for those constituents and report on the consistency with the case of a linearly polarized fundamental Gaussian beam. An adapted knife-edge reconstruction technique is presented and proof-of-concept tests are shown, demonstrating the reconstruction of beam profiles.

Extremal quantum states

Aaron Z. Goldberg, Andrei B. Klimov, Markus Grassl, Gerd Leuchs, Luis Sanchez-Soto

The striking differences between quantum and classical systems predicate disruptive quantum technologies. We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations because they can be applied beyond particular symmetry groups. The symmetry-transcending properties of the Husimi Q function make it our basic tool. In terms of the latter, we examine quantities such as the Wehrl entropy, inverse participation ratio, cumulative multipolar distribution, and metrological power, which are linked to the intrinsic properties of any quantum state. We use these quantities to formulate extremal principles and determine in this way which states are the most and least "quantum"; the corresponding properties and potential usefulness of each extremal principle are explored in detail. While the extrema largely coincide for continuous-variable systems, our analysis of spin systems shows that care must be taken when applying an extremal principle to new contexts.

Quantum Fisher Information with Coherence

Zdeněk Hradil, Jaroslav Řeháček, Luis Sanchez-Soto, Berthold-Georg Englert

In recent proposals for achieving optical super-resolution, variants of the<br>Quantum Fisher Information (QFI) quantify the attainable precision. We find<br>that claims about a strong enhancement of the resolution resulting from<br>coherence effects are questionable because they refer to very small subsets of<br>the data without proper normalization. When the QFI is normalized, accounting<br>for the strength of the signal, there is no advantage of coherent sources over<br>incoherent ones. Our findings have a bearing on further studies of the<br>achievable precision of optical instruments.<br>

Compressively certifying quantum measurements

I. Gianani, Y. S. Teo, V. Cimini, H. Jeong, Gerd Leuchs, M. Barbieri, Luis Sanchez-Soto

We introduce a reliable compressive procedure to uniquely characterize any<br>given low-rank quantum measurement using a minimal set of probe states that is<br>based solely on data collected from the unknown measurement itself. The<br>procedure is most compressive when the measurement constitutes pure detection<br>outcomes, requiring only an informationally complete number of probe states<br>that scales linearly with the system dimension. We argue and provide numerical<br>evidence showing that the minimal number of probe states needed is even<br>generally below the numbers known in the closely-related classical<br>phase-retrieval problem because of the quantum constraint. We also present<br>affirmative results with polarization experiments that illustrate significant<br>compressive behaviors for both two- and four-qubit detectors just by using<br>random product probe states.<br>

Distillation of squeezing using an engineered pulsed parametric down-conversion source

Thomas Dirmeier, Johannes Tiedau, Imran Khan, Vahid Ansari, Christian R. Müller, Christine Silberhorn, Christoph Marquardt, Gerd Leuchs

Hybrid quantum information processing combines the advantages of discrete and continues variable protocols by realizing protocols consisting of photon counting and homodyne measurements. However, the mode structure of pulsed sources and the properties of the detection schemes often require the use of optical filters in order to combine both detection methods in a common experiment. This limits the efficiency and the overall achievable squeezing of the experiment. In our work, we use photon subtraction to implement the distillation of pulsed squeezed states originating from a genuinely spatially and temporally single-mode parametric down-conversion source in non-linear waveguides. Due to the distillation, we witness an improvement of 0.17 dB from an initial squeezing value of −1.648 ± 0.002 dB, while achieving a purity of 0.58, and confirm the non-Gaussianity of the distilled state via the higher-order cumulants. With this, we demonstrate the source’s suitability for scalable hybrid quantum network applications with pulsed quantum light.

Ultrafast spinning twisted ribbons of confined electric fields

Thomas Bauer, Svetlana N. Khonina, Ilya Golub, Gerd Leuchs, Peter Banzer

Topological properties of light attract tremendous attention in the optics communities and beyond. For instance, light beams gain robustness against certain deformations when carrying topological features, enabling intriguing applications. We report on the observation of a topological structure contained in an optical beam, i.e., a twisted ribbon formed by the electric field vector per se, in stark contrast to recently reported studies dealing with topological structures based on the distribution of the time averaged polarization ellipse. Moreover, our ribbons are spinning in time at a frequency given by the optical frequency divided by the total angular momentum of the incoming beam. The number of full twists of the ribbon is equal to the orbital angular momentum of the longitudinal component of the employed light beam upon tight focusing, which is a direct consequence of spin-to-orbit coupling. We study this angular-momentum-transfer-assisted generation of the twisted ribbon structures theoretically and experimentally for tightly focused circularly polarized beams of different vorticity, paving the way to tailored topologically robust excitations of novel coherent light–matter states.

Chalcogenide fibers for Kerr squeezing

Elena A. Anashkina, Alexey Andrianov V, Joel F. Corney, Gerd Leuchs

We propose and investigate theoretically the Kerr squeezing of light at a wavelength of 2 mu m in chalcogenide fibers with large nonlinearity and-this is the advance-with much reduced attenuation. We present suitably realistic but straightforward designs of low-loss step-index single-mode fibers with the nonlinear Kerr coefficient 3 to 4 orders of magnitude higher than for standard telecommunication fibers, and we give estimations of optimal squeezing for continuous wave laser signal in the considered fibers based. on As2S3 or As2Se3 glasses. (C) 2020 Optical Society of America

Microsphere-Based Optical Frequency Comb Generator for 200 GHz Spaced WDM Data Transmission System

Elena A. Anashkina, Maria P. Marisova, Alexey Andrianov V, Rinat A. Akhmedzhanov, Rihards Murnieks, Mikhail D. Tokman, Laura Skladova, Ivan Oladyshkin V, Toms Salgals, et al.

Optical frequency comb (OFC) generators based on whispering gallery mode (WGM) microresonators have a massive potential to ensure spectral and energy efficiency in wavelength-division multiplexing (WDM) telecommunication systems. The use of silica microspheres for telecommunication applications has hardly been studied but could be promising. We propose, investigate, and optimize numerically a simple design of a silica microsphere-based OFC generator in the C-band with a free spectral range of 200 GHz and simulate its implementation to provide 4-channel 200 GHz spaced WDM data transmission system. We calculate microsphere characteristics such as WGM eigenfrequencies, dispersion, nonlinear Kerr coefficient with allowance for thermo-optical effects, and simulate OFC generation in the regime of a stable dissipative Kerr soliton. We show that by employing generated OFC lines as optical carriers for WDM data transmission, it is possible to ensure error-free data transmission with a bit error rate (BER) of 4.5 x 10(-30), providing a total of 40 Gbit/s of transmission speed on four channels.

Wigner function for SU(1,1)

Ulrich Seyfarth, Andrei B. Klimov, Hubert de Guise, Gerd Leuchs, Luis Sanchez-Soto

In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.

Highly efficient coherent beam combining of tiled aperture arrays using out-of-phase pattern

Alexey Andrianov, Nikolay Kalinin, Elena Anashkina, Gerd Leuchs

We propose a simple, highly scalable, and very efficient scheme for coherent combining of tiled aperture arrays. The scheme relies on changing the beam phasing paradigm from the commonly used in-phase pattern to the out-of-phase pattern (interleaved 0/pi phases in the neighboring channels) and using an additional simple combining stage (a beamsplitter). In a proof-of-concept experiment with a one-dimensional fiber array, we achieved 89% of the power in the main combined beam. In numerical modeling, we found optimal conditions leading to 98% efficiency for an unlimited number of channels and arbitrary small initial aperture fill factors. The scheme is highly resistant to the effect of sub-aperture clipping and suitable for combining ultrashort pulses. (C) 2020 Optical Society of America

Fundamental quantum limits in ellipsometry

L. Rudnicki, Luis Sanchez-Soto, Gerd Leuchs, R. W. Boyd

We establish the ultimate limits that quantum theory imposes on the accuracy attainable in optical ellipsometry. We show that the standard quantum limit, as usual reached when the incident light is in a coherent state, can be surpassed with the use of appropriate squeezed states and, for tailored beams, even pushed to the ultimate Heisenberg limit.

Toward High‐Speed Nanoscopic Particle Tracking via Time‐Resolved Detection of Directional Scattering

Paul Beck, Martin Neugebauer, Peter Banzer

Owing to their immediate relevance for high precision position sensors, a variety of different sub‐wavelength localization techniques has been developed in the past decades. However, many of these techniques suffer from low temporal resolution or require expensive detectors. Here, a method is presented that is based on the ultrafast detection of directionally scattered light with a quadrant photodetector operating at a large bandwidth, which exceeds the speed of most cameras. The directionality emerges due to the position dependent tailored excitation of a high‐refractive index nanoparticle with a tightly focused vector beam. A spatial resolution of 1.1nm and a temporal resolution of 8kHz is reached experimentally, which is not a fundamental but rather a technical limit. The detection scheme enables real‐time particle tracking and sample stabilization in many optical setups sensitive to drifts and vibrations.

Nonlinear power dependence of the spectral properties of an optical parametric oscillator below threshold in the quantum regime

Golnoush Shafiee, Dmitry V. Strekalov, Alexander Otterpohl, Florian Sedlmeir, Gerhard Schunk, Ulrich Vogl, Harald Schwefel, Gerd Leuchs, Christoph Marquardt

Photon pairs and heralded single photons, obtained from cavity- assisted parametric down conversion (PDC), play an important role in quantum communications and technology. This motivated a thorough study of the spectral and temporal properties of parametric light, both above the Optical Parametric Oscillator (OPO) threshold, where the semiclassical approach is justified, and deeply below it, where the linear cavity approximation is applicable. The pursuit of a higher two- photon emission rate leads into an interesting intermediate regime where the OPO still operates considerably below the threshold but the nonlinear cavity phenomena cannot be neglected anymore. Here, we investigate this intermediate regime and show that the spectral and temporal properties of the photon pairs, as well as their emission rate, may significantly differ from the widely accepted linear model. The observed phenomena include frequency pulling and broadening in the temporal correlation for the down converted optical fields. These factors need to be taken into account when devising practical applications of the high-rate cavity-assisted SPDC sources.

Hybrid Orthorhombic Carbon Flakes Intercalated with Bimetallic Au-Ag Nanoclusters: Influence of Synthesis Parameters on Optical Properties

Muhammad Abdullah Butt, Daria Mamonova, Yuri Petrov, Alexandra Proklova, Ilya Kritchenkov, Alina Manshina, Peter Banzer, Gerd Leuchs

Until recently, planar carbonaceous structures such as graphene did not show any birefringence under normal incidence. In contrast, a recently reported novel orthorhombic carbonaceous structure with metal nanoparticle inclusions does show intrinsic birefringence, outperforming other natural orthorhombic crystalline materials. These flake-like structures self-assemble during a laser-induced growth process. In this article, we explore the potential of this novel material and the design freedom during production. We study in particular the dependence of the optical and geometrical properties of these hybrid carbon-metal flakes on the fabrication parameters. The influence of the laser irradiation time, concentration of the supramolecular complex in the solution, and an external electric field applied during the growth process are investigated. In all cases, the self-assembled metamaterial exhibits a strong linear birefringence in the visible spectral range, while the wavelength-dependent attenuation was found to hinge on the concentration of the supramolecular complex in the solution. By varying the fabrication parameters one can steer the shape and size of the flakes. This study provides a route towards fabrication of novel hybrid carbon-metal flakes with tailored optical and geometrical properties.

Quantum-limited measurements of intensity noise levels in Yb-doped fiber amplifiers

Alexandra Popp, Victor Distler, Kevin Jaksch, Florian Sedlmeir, Christian Müller, Nicoletta Haarlammert, Thomas Schreiber, Christoph Marquardt, Andreas Tünnermann, et al.

We investigate the frequency-resolved intensity noise spectrum of an Yb-doped fiber amplifier down to the fundamental limit of quantum noise. We focus on the kHz and low MHz frequency regime with special interest in the region between 1 and 10 kHz. Intensity noise levels up to ≥60 dB above the shot noise limit are found, revealing great optimization potential. Additionally, two seed lasers with different noise characteristics were amplified, showing that the seed source has a significant impact and should be considered in the design of high power fiber amplifiers.

Towards fully integrated photonic displacement sensors

Ankan Bag, Martin Neugebauer, Uwe Mick, Sillke Christiansen, Sebastian A Schulz, Peter Banzer

The field of optical metrology with its high precision position, rotation and wavefront sensors represents the basis for lithography and high resolution microscopy. However, the on-chip integration - a task highly relevant for future nanotechnological devices - necessitates the reduction of the spatial footprint of sensing schemes by the deployment of novel concepts. A promising route towards this goal is predicated on the controllable directional emission of the fundamentally smallest emitters of light, i.e. dipoles, as an indicator. Here we realize an integrated displacement sensor based on the directional emission of Huygens dipoles excited in an individual dipolar antenna. The position of the antenna relative to the excitation field determines its directional coupling into a six-way crossing of photonic crystal waveguides. In our experimental study supported by theoretical calculations, we demonstrate the first prototype of an integrated displacement sensor with a standard deviation of the position accuracy below λ/300 at room temperature and ambient conditions.

Universal compressive characterization of quantum dynamics

Yosep Kim, Yong Siah Teo, Daekun Ahn, Dong-Gil Im, Young-Wook Cho, Gerd Leuchs, Luis Sanchez-Soto, Hyunseok Jeong, Yoon-Ho Kim

Recent quantum technologies utilize complex multidimensional processes that<br>govern the dynamics of quantum systems. We develop an adaptive<br>diagonal-element-probing compression technique that feasibly characterizes any<br>unknown quantum processes using much fewer measurements compared to<br>conventional methods. This technique utilizes compressive projective<br>measurements that are generalizable to arbitrary number of subsystems. Both<br>numerical analysis and experimental results with unitary gates demonstrate low<br>measurement costs, of order O(d^2) for d-dimensional systems, and<br>robustness against statistical noise. Our work potentially paves the way for a<br>reliable and highly compressive characterization of general quantum devices.<br>

Prospects of Trapping Atoms with an Optical Dipole Trap in a Deep Parabolic Mirror for Light-Matter-Interaction Experiments

Markus Sondermann, Martin Fischer, Gerd Leuchs

The prospects of employing a deep parabolic mirror as a focusing device for trapping neutral atoms in an optical dipole trap are evaluated. It is predicted that such a dipole trap will result in a deep trapping potential as well as in a small spatial spread of the atom's center of mass wave function already for a Doppler cooled atom. This strong confinement is beneficial for many applications, one of which is the increase of the interaction strength between an atom and a light field focused from full solid angle.

Chiral Surface Lattice Resonances

Eric S. A. Goerlitzer, Reza Mohammadi, Sergey Nechayev, Kirsten Volk, Marcel Rey, Peter Banzer, Matthias Karg, Nicolas Vogel

Collective excitation of periodic arrays of metallic nanoparticles by coupling localized surface plasmon resonances to grazing diffraction orders leads to surface lattice resonances with narrow line width. These resonances may find numerous applications in optical sensing and information processing. Here, a new degree of freedom of surface lattice resonances is experimentally investigated by demonstrating handedness-dependent excitation of surface lattice resonances in arrays of chiral plasmonic crescents. The self-assembly of particles used as mask and modified colloidal lithography is applied to produce arrays of planar and 3D gold crescents over large areas. The excitation of surface lattice resonances as a function of the interparticle distance and the degree of order within the arrays is investigated. The chirality of the individual 3D crescents leads to the formation of chiral lattice modes, that is, surface lattice resonances that exhibit optical activity.

Properties of bright squeezed vacuum at increasing brightness

P. R. Sharapova, Gaetano Frascella, A. M. Perez, O. V. Tikhonova, S. Lemieux, R. W. Boyd, Gerd Leuchs, M. V. Chekhova

A bright squeezed vacuum (BSV) is a nonclassical macroscopic state of light, which is generated through high-gain parametric down-conversion or four-wave mixing. Although the BSV is an important tool in quantum optics and has a lot of applications, its theoretical description is still not complete. In particular, the existing description in terms of Schmidt modes with gain-independent shapes fails to explain the spectral broadening observed in the experiment as the mean number of photons increases. Meanwhile, the semiclassical description accounting for the broadening does not allow us to decouple the intermodal photon-number correlations. In this work, we present a new generalized theoretical approach to describe the spatial properties of a multimode BSV. In the multimode case, one has to take into account the complicated interplay between all involved modes: each plane-wave mode interacts with all other modes, which complicates the problem significantly. The developed approach is based on exchanging the (k, t ) and (ω, z) representations and solving a system of integrodifferential equations. Our approach predicts correctly the dynamics of the Schmidt modes and the broadening of the angular distribution with the increase in the BSV mean photon number due to a stronger pumping. Moreover, the model correctly describes various properties of a widely used experimental configuration with two crystals and an air gap between them, namely, an SU(1,1) interferometer. In particular, it predicts the narrowing of the intensity distribution, the reduction and shift of the side lobes, and the decline in the interference visibility as the mean photon number increases due to stronger pumping. The presented experimental results confirm the validity of the new approach. The model can be easily extended to the case of the frequency spectrum, frequency Schmidt modes, and other experimental configurations.

Towards Polarization-based Excitation Tailoring for Extended Raman Spectroscopy

Simon Grosche, Richard Hünermann, George Sarau, Silke Christiansen, Robert W. Boyd, Gerd Leuchs, Peter Banzer

Undoubtedly, Raman spectroscopy is one of the most elaborated spectroscopy tools in materials science, chemistry, medicine and optics. However, when it comes to the analysis of nanostructured specimens, <br> accessing the Raman spectra resulting from an exciting electric field component oriented perpendicularly to the substrate plane is a difficult task and conventionally can only be achieved by mechanically tilting the sample, or by sophisticated sample preparation.<br>Here, we propose a novel experimental method based on the utilization of polarization tailored light for Raman spectroscopy of individual nanostructures. As a proof of principle, we create three-dimensional electromagnetic field distributions at the nanoscale using tightly focused cylindrical vector beams impinging normally onto the specimen, hence keeping<br>the conventional beam-path of commercial Raman systems. Using this excitation<br>scheme, we experimentally show that the recorded Raman spectra of individual<br>gallium-nitride nanostructures of sub-wavelength diameter used as a test<br>platform depend sensitively on their location relative to the focal vector field. The observed Raman spectra can be attributed to the interaction with transverse or longitudinal electric field components. This novel technique may pave the way towards a characterization of Raman active nanosystems using full information of all Raman modes.

Roadmap on quantum light spectroscopy

Shaul Mukamel, Matthias Freyberger, Wolfgang Schleich, Marco Bellini, Alessandro Zavatta, Gerd Leuchs, Christine Silberhorn, Robert W. Boyd, Luis Lorenzo Sánchez-Soto, et al.

Conventional spectroscopy uses classical light to detect matter properties through the variation<br>of its response with frequencies or time delays. Quantum light opens up new avenues for<br>spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and<br>through the variation of photon statistics by coupling to matter. This Roadmap article focuses on<br>using quantum light as a powerful sensing and spectroscopic tool to reveal novel information<br>about complex molecules that is not accessible by classical light. It aims at bridging the quantum<br>optics and spectroscopy communities which normally have opposite goals: manipulating<br>complex light states with simple matter e.g. qubits versus studying complex molecules with<br>simple classical light, respectively. Articles cover advances in the generation and manipulation<br>of state-of-the-art quantum light sources along with applications to sensing, spectroscopy,<br>imaging and interferometry.

Helstrom measurement: A nondestructive implementation

Rui Han, Gerd Leuchs, Janos A. Bergou

We discuss an implementation of the minimum error state discrimination measurement, originally introduced by Helstrom [Quantum Detection and Estimation Theory (Academic Press, New York, 1976)]. In this implementation, instead of performing the optimal projective measurement directly on the system, it is first entangled to an ancillary system and the measurement is performed on the ancilla. We show that, by an appropriate choice of the entanglement transformation, the Helstrom bound can be attained. The advantage of this approach is twofold. First, it provides an implementation when the optimal projective measurement cannot be directly performed. For example, in the case of continuous variable states (binary and N phase-shifted coherent signals), the available detection methods, photon counting and homodyning, are insufficient to perform the required cat-state projection. In the case of symmetric states, the square-root measurement is optimal, but it is not easy to perform directly for more than two states. Our approach provides a feasible alternative in both cases. Second, the measurement is nondestructive from the point of view of the original system and one has a certain amount of freedom in designing the post-measurement state, which can then be processed further.

Objective Compressive Quantum Process Tomography

Y. S. Teo, G. I. Struchalin, E. V. Kovlakov, D. Ahn, H. Jeong, S. S. Straupe, S. P. Kulik, Gerd Leuchs, Luis Sanchez-Soto

We present a compressive quantum process tomography scheme that fully<br>characterizes any rank-deficient completely-positive process with no a priori<br>information about the process apart from the dimension of the system on which<br>the process acts. It uses randomly-chosen input states and adaptive output von<br>Neumann measurements. Both entangled and tensor-product configurations are<br>flexibly employable in our scheme, the latter which naturally makes it<br>especially compatible with many-body quantum computing. Two main features of<br>this scheme are the certification protocol that verifies whether the<br>accumulated data uniquely characterize the quantum process, and a compressive<br>reconstruction method for the output states. We emulate multipartite scenarios<br>with high-order electromagnetic transverse modes and optical fibers to<br>positively demonstrate that, in terms of measurement resources, our<br>assumption-free compressive strategy can reconstruct quantum processes almost<br>equally efficiently using all types of input states and basis measurement<br>operations, operations, independent of whether or not they are factorizable<br>into tensor-product states.<br>

Shaping Field Gradients for Nanolocalization

Sergey Nechayev, Jörg Eismann, Martin Neugebauer, Peter Banzer

Deep sub-wavelength localization and displacement sensing of optical nanoantennas have emerged as extensively pursued objectives in nanometrology, where focused beams serve as high-precision optical rulers while the scattered light provides an optical readout. Here, we show that in these schemes using an optical excitation as a position gauge implies that the sensitivity to displacements of a nanoantenna depends on the spatial gradients of the excitation field. Specifically, we explore one of such novel localization schemes based on appearance of transversely spinning fields in strongly confined optical beams, resulting in far-field segmentation of left- and right-hand circular polarizations of the scattered light, an effect known as the giant spin-Hall effect of light. We construct vector beams with augmented transverse spin density gradient in the focal plane and experimentally confirm enhanced sensitivity of the far-field spin-segmentation to lateral displacements of an electric-dipole nanoantenna. We conclude that sculpturing of electromagnetic field gradients and intelligent design of scatterers pave the way towards future improvements in displacement sensitivity.

Lower bounds for the time-bandwidth product of a single-photon pulse

V Averchenko, D. A. Reiss, D. Sych, Gerd Leuchs

Two complementary properties, such as frequency and duration of a pulse, cannot be precisely measured simultaneously. The lower bound on the time-bandwidth product, known also as uncertainty relation, plays a very important role in quantum theory. In this work, we consider single-photon pulses with arbitrary temporal and spectral profiles, and derive a lower bound for the single-photon time-bandwidth product. We investigate how this bound depends on the modal purity, the single-mode fidelity, and the effective number of modes. Our results can be used to solve the inverse problem, namely, to estimate characteristics of the single-photon pulse based on the time-bandwidth product obtained from temporal and spectral measurements of the pulse.

Numerical simulation of dispersion and nonlinear characteristics of microstructured silica fibres with a thin suspended core in a wide range of their parameters

E. A. Anashkina, A. V. Andrianov, Gerd Leuchs

Dispersion and nonlinear characteristics of microstructured silica fibres with a thin suspended core surrounded by three, four or six air holes have been studied theoretically in the wavelength range 1 - 2 mu m. It has been shown that, owing to strong fundamental mode confinement near the core, the Kerr nonlinearity coefficient can exceed the nonlinearity coefficient of standard telecom fibre SMF28e by two orders of magnitude. The large waveguide contribution allows for effective group velocity dispersion management. Estimates are presented that demonstrate the feasibility of using suspended core fibre exhibiting Kerr nonlinearity for generating non-classical light: a state with squeezed quantum fluctuations in one of the quadrature components of a cw laser signal at a wavelength near 1.55 mu m.

Vector-light quantum complementarity and the degree of polarization

Andreas Norrman, Ari T. Friberg, Gerd Leuchs

The dual wave-particle nature of light and the degree of polarization are fundamental concepts in quantum physics and optical science, but their exact relation has not been explored within a full vector-light quantum framework that accounts for interferometric polarization modulation. Here, we consider vector-light quantum complementarity in double-pinhole photon interference and derive a general link between the degree of polarization and wave-particle duality of light. The relation leads to an interpretation for the degree of polarization as a measure describing the complementarity strength between photon path predictability and so-called Stokes visibility, the latter taking into account both intensity and polarization variations in the observation plane. It also unifies results advanced in classical studies by showing that the degree of polarization can be viewed as the ability of a light beam to exhibit intensity and polarizationstate fringes. The framework we establish thus provides novel aspects and deeper insights into the role of the degree of polarization in quantum-light complementarity and photon interference. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

QED Response of the Vacuum

Gerd Leuchs, Margaret Hawton, Luis Sanchez-Soto

We present a new perspective on the link between quantum electrodynamics (QED) and Maxwell's equations. We demonstrate that the interpretation of the electric displacement vector <mml:semantics>D=epsilon 0E</mml:semantics>, where <mml:semantics>E</mml:semantics> is the electric field vector and <mml:semantics>epsilon 0</mml:semantics> is the permittivity of the vacuum, as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter runs, as it should.

Efficient generation of temporally shaped photons using nonlocal spectral filtering

V. Averchenko, D. Sych, C. Marquardt, G. Leuchs

We study the generation of single-photon pulses with the tailored temporal shape via nonlocal spectral filtering. A shaped photon is heralded from a time-energy entangled photon pair upon spectral filtering and time-resolved detection of its entangled counterpart. We show that the temporal shape of the heralded photon is defined by the time-inverted impulse response of the spectral filter and does not depend on the heralding instant. Thus one can avoid postselection of particular heralding instants and achieve a substantially higher heralding rate of shaped photons as compared to the generation of photons via nonlocal temporal modulation. Furthermore, the method can be used to generate shaped photons with a coherence time in the ns-μs range and is particularly suitable to produce photons with the exponentially rising temporal shape required for efficient interfacing to a single quantum emitter in free space.

Single Photons Emitted by Nanocrystals Optically Trapped in a Deep Parabolic Mirror

Vsevolod Salakhutdinov, Markus Sondermann, Luigi Carbone, Elisabeth Giacobino, Alberto Bramati, Gerd Leuchs

We investigate the emission of single photons from CdSe/CdS dots-in-rod which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4π emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap, we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble of linear dipoles with the electromagnetic field in free space.

Full-field mode sorter using two optimized phase transformations for high-dimensional quantum cryptography

Robert Fickler, Frederic Bouchard, Enno Giese, Vincenzo Grillo, Gerd Leuchs, Ebrahim Karimi

High-dimensional encoding schemes have emerged as a novel way to perform quantum information tasks. For high dimensionality, temporal and transverse spatial modes of photons are the two paradigmatic degrees of freedom commonly used in such experiments. Nevertheless, general devices for multi-outcome measurements are still needed to take full advantage of the high-dimensional nature of encoding schemes. We propose a general full-field mode sorting scheme consisting of only up to two optimized phase elements based on evolutionary algorithms that allows for joint sorting of azimuthal and radial modes. We further study the performance of our scheme through simulations in the context of high-dimensional quantum cryptography, where sorting in different mutually unbiased bases and high-fidelity measurement schemes are crucial.

Microscale Generation of Entangled Photons without Momentum Conservation

Cameron Okoth, Andrea Cavanna, Tomas Santiago-Cruz, Maria Chekhova

We report, for the first time, the observation of spontaneous parametric down-conversion (SPDC) free of phase matching (momentum conservation).We alleviate the need to conserve momentum by exploiting the<br>position-momentum uncertainty relation and using a planar geometry source, a 6 μm thick layer of lithium niobate. Nonphase-matched SPDC opens up a new platform on which to investigate fundamental quantum<br>effects but it also has practical applications. The ultrasmall thickness leads to a frequency spectrum an order of magnitude broader than that of phase-matched SPDC. The strong two-photon correlations are still<br>preserved due to energy conservation. This results in ultrashort temporal correlation widths and huge frequency entanglement. The studies we make here can be considered as the initial steps into the emerging field of nonlinear quantum optics on the microscale and nanoscale.

Fading channel estimation for free-space continuous-variable secure quantum communication

László Ruppert, Christian Peuntinger, Bettina Heim, Kevin Günthner, Vladyslav C. Usenko, Dominique Elser, Gerd Leuchs, Radim Filip, Christoph Marquardt

We investigate estimation of fluctuating channels and its effect on security of continuous-variable quantum key distribution. We propose a novel estimation scheme which is based on the clusterization of the estimated transmittance data. We show that uncertainty about whether the transmittance is fixed or not results in a lower key rate. However, if the total number of measurements is large, one can obtain using our method a key rate similar to the non-fluctuating channel even for highly fluctuating channels. We also verify our theoretical assumptions using experimental data from an atmospheric quantum channel. Our method is therefore promising for secure quantum communication over strongly fluctuating turbulent atmospheric channels.

Quasiprobability currents on the sphere

I. Valtierra, A. B. Klimov, Gerd Leuchs, Luis Sanchez-Soto

We present analytic expressions for the s-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exploring the appearance of the semiclassical limit in stable, unstable and tunnelling regimes.

Spin-orbit coupling affecting the evolution of transverse spin

Jörg Eismann, Peter Banzer, Martin Neugebauer

We investigate the evolution of transverse spin in tightly focused circularly polarized beams of light, where spin-orbit coupling causes a local rotation of the polarization ellipses upon propagation through the focal volume. The effect can be explained as a relative Gouy-phase shift between the circularly polarized transverse field and the longitudinal field carrying orbital angular momentum. The corresponding rotation of the electric transverse spin density is observed experimentally by utilizing a recently developed reconstruction scheme, which relies on transverse-spin-dependent directional scattering of a nano-probe.

Single-shot reconstruction of a subpicosecond pulse from a fiber laser system via processing strongly self-phase modulated spectra

E. A. Anashkina, A. Andrianov V, Gerd Leuchs

The single-shot reconstruction of an ultrashort pulse from a fiber laser system by the method based on recording and numerical processing of two self-phase modulated spectra after a nonlinear fiber is demonstrated experimentally. The 0.7-ps asymmetrical signal with an energy of similar to 1 mu J retrieved by this method without time direction ambiguity is in good agreement with independent measurements by second harmonic generation frequency-resolved optical gating (SHG FROG) technique.

Numerical simulation of multi-color laser generation in TM-doped tellurite microsphere at 1.9, 1.5 and 2.3 microns

E. A. Anashkina, Gerd Leuchs, A. V. Andrianov

We present the first detailed theoretical analysis of multi-color continuous wave lasing in Tm-doped tellurite spherical microresonators with whispering gallery modes pumped at a wavelength of 792 nm. The numerical model is based on solving a system of equations for intracavity field amplitudes and rate equations using the parameters of Tm-doped tellurite glass measured in the previous experiments. All fundamental whispering gallery modes in the gain bands are taken into account. We demonstrate diagrams of generation regimes depending on Q-factors and pump power, which show a possibility of single-color lasing at a wavelength of similar to 1.9 mu m, two-color lasing at wavelengths of similar to 1.9&1.5 mu m and at similar to 1.9&2.3 mu m, and three-color lasing at wavelengths of similar to 1.9&1.5&2.3 mu m. Such microlasers can play a significant role in sensing applications.

Measuring the temperature and heating rate of a single ion by imaging

Bharath Srivathsan, Martin Fischer, Lucas Alber, Markus Weber, Markus Sondermann, Gerd Leuchs

We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the heating rate induced by any kind of effect other than photon scattering. In contrast to other established schemes for measuring the heating rate, the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.

R&D advances for quantum communication systems

Gerd Leuchs, Christoph Marquardt, Luis Sanchez-Soto, Dmitry V. Strekalov, Alan E. Willner

Understanding the nature of light leads to the question of how the principles of quantum physics can be harnessed in practical optical communication. A deeper understanding of fundamental physics has always advanced technology. However, the quantum principles certainly have a distinctly limiting character when looked upon from the engineering point of view. A particle cannot have well-defined momentum and position at the same time. An informative measurement will unpredictably alter the state of a quantum object. One cannot reliably clone an arbitrary quantum state. These and a number of other similar principles give rise to what is commonly known as the quantum “no-go theorems”—a disconcerting term when it comes to building something practical. And yet a search for novel principles of communication enabled by quantum physics began already in its early days and has only intensified since. On this path physicists are faced with a remarkable challenge: to turn a series of negative statements into new technological recipes.

Squeezed vacuum states from a whispering gallery mode resonator

Alexander Otterpohl, Florian Sedlmeir, Ulrich Vogl, Thomas Dirmeier, Golnoush Shafiee, Gerhard Schunk, Dmitry Strekalov, Harald G. L. Schwefel, Tobias Gehring, et al.

Squeezed vacuum states enable optical measurements below the quantum limit and hence are a valuable resource for applications in quantum metrology and also quantum communication. However, most available sources require high pump powers in the milliwatt range and large setups that hinder real-world applications. Furthermore, degenerate operation of such systems presents a challenge. Here, we use a compact crystalline whispering gallery mode resonator made of lithium niobate as a degenerate parametric oscillator. We demonstrate about 1.4 dB noise reduction below the shot-noise level for only 300 μW of pump power in degenerate single-mode operation. Furthermore, we report a record pump threshold as low as 1.35 μW. Our results show that the whispering gallery-based approach presents a promising platform for a compact and efficient source for nonclassical light.

Development of infrared fiber lasers at 1555 nm and at Er-doped zinc-tellurite glass fiber

E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, A. V. Kim, V. V. Koltashev, Gerd Leuchs, S. E. Motorin, S. V. Muravyev, A. D. Plekhovich

We manufactured and characterized a low-loss gain fiber based on high-purity TeO2 -ZnO-La2O3-Na2O undoped glass for 100-mu m cladding and TeO2 -ZnO-La2O3-Na2O glass for 10-mu m core doped with 0.24 mol% Er2O3. To confirm that the produced fiber is a promising active element for the infrared range, we demonstrated experimentally broadband laser amplification and CW generation at the I-4(13/2) -> I-4(15/2) transition at 1555 nm with a single-mode diode pump at 975 nm at the I-4(15/2) -> I-4(11/2) transition. We developed a numerical model calibrated to the experimental data for prediction and optimization of laser characteristics in schemes with different parameters. The model describes single- wavelength lasing as well as dual-wavelength cascade lasing at 1555 nm and 2800 nm. It was shown numerically that for the optimized parameters, the maximum slope efficiency at 2800 nm at the I-4(11/2) -> I-4(13/2) transition can reach similar to 20%. The maximum calculated efficiency at 1555 nm exceeds 30%.

The standard quantum limit of coherent beam combining

Christian Müller, Florian Sedlmeir, Vitaliy O. Martynov, Christoph Marquardt, Alexey V. Andrianov , Gerd Leuchs

Coherent beam combining refers to the process of generating a bright output beam by merging independent input beams of individually diffusing relative phases by locking them to each other. We report the first quantum mechanical noise limit calculations for coherent beam combining and compare our results to quantum-limited amplification. Our coherent beam combining scheme is based on an optical Fourier transformation which renders the scheme compatible with integrated optics combined with feed-back stabilization of the relative phases. The scheme can be layed out for an arbitrary number of input beams and approaches the shot noise limit for a large number of inputs.

Indefinite-Mean Pareto Photon Distribution from Amplified Quantum Noise

Mathieu Manceau, Kirill Spasibko, Gerd Leuchs, Radim Filip, Maria Chekhova

Extreme events appear in many physics phenomena, whenever the probability distribution has a "heavy tail" differing very much from the equilibrium one. Most unusual are the cases of power-law (Pareto) probability distributions. Among their many manifestations in physics, from "rogue waves" in the ocean to Levy flights in random walks, Pareto dependences can follow very different power laws. For some outstanding cases, the power exponents are less than 2, leading to indefinite values not only for higher moments but also for the mean. Here we present the first evidence of indefinite-mean Pareto distribution of photon numbers at the output of nonlinear effects pumped by parametrically amplified vacuum noise, known as bright squeezed vacuum (BSV). We observe a Pareto distribution with power exponent 1.31 when BSV is used as a pump for supercontinuum generation, and other heavy-tailed distributions (however, with definite moments) when it pumps optical harmonics generation. Unlike in other fields, we can flexibly control the Pareto exponent by changing the experimental parameters. This extremely fluctuating light is interesting for ghost imaging and for quantum thermodynamics as a resource to produce more efficiently nonequilibrium states by single-photon subtraction, the latter of which we demonstrate experimentally.

Characterization of an underwater channel for quantum communications in the Ottawa River

Felix Hufnagel, Alicia Sit, Florence Grenapin, Frederic Bouchard, Khabat Heshami, Duncan England, Yingwen Zhang, Benjamin J. Sussman, Robert W. Boyd, et al.

We examine the propagation of optical beams possessing different polarization states and spatial modes through the Ottawa River in Canada. A Shack-Hartmann wavefront sensor is used to record the distorted beam's wavefront. The turbulence in the underwater channel is analysed, and associated Zernike coefficients are obtained in real-time. Finally, we explore the feasibility of transmitting polarization states as well as spatial modes through the underwater channel for applications in quantum cryptography. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Interaction of light carrying orbital angular momentum with a chiral dipolar scatterer

Pawel Wozniak, Israel De León, Katja Höflich, Gerd Leuchs, Peter Banzer

The capability to distinguish the handedness of circularly polarized light is a well-known intrinsic property of a chiral nanostructure. It is a long-standing controversial debate, however, whether a chiral object can also sense the vorticity, or the orbital angular momentum (OAM), of a light field. Since OAM is a non-local property, it seems rather counter-intuitive that a point-like chiral object could be able to distinguish the sense of the wave-front of light carrying OAM. Here, we show that a dipolar chiral nanostructure is indeed capable of distinguishing the sign of the phase vortex of the incoming light beam. To this end, we take advantage of the conversion of the sign of OAM, carried by a linearly polarized Laguerre-Gaussian beam, into the sign of optical chirality upon tight focusing. Our study provides for a deeper insight into the discussion of chiral light-matter interactions and the respective role of OAM.

Adaptive compressive tomography: A numerical study

D. Ahn, Y. S. Teo, H. Jeong, D. Koutny, J. Rehacek, Z. Hradil, Gerd Leuchs, Luis Sanchez-Soto

We perform several numerical studies for our recently published adaptive compressive tomography scheme [D. Ahn et al., Phys. Rev. Lett. 122, 100404 (2019)], which significantly reduces the number of measurement settings to unambiguously reconstruct any rank-deficient state without any a priori knowledge besides its dimension. We show that both entangled and product bases chosen by our adaptive scheme perform comparably well with recently known compressed-sensing element-probing measurements, and also beat random measurement bases for low-rank quantum states. We also numerically conjecture asymptotic scaling behaviors for this number as a function of the state rank for our adaptive schemes. These scaling formulas appear to be independent of the Hilbert-space dimension. As a natural development, we establish a faster hybrid compressive scheme that first chooses random bases, and later adaptive bases as the scheme progresses. As an epilogue, we reiterate important elements of informational completeness for our adaptive scheme.

Nonlinear optics with full three-dimensional illumination

Rojiar Penjweini, Markus Weber, Markus Sondermann, Robert W. Boyd, Gerd Leuchs

Nonlinear optical interactions play a crucial role in modern technology and lead to important applications such as optical switching, optical harmonic generation, and the characterization of ultrafast material processes. Nonlinear interactions are enhanced by using a tightly focused laser beam, but nonetheless they are typically excited by a loosely focused (that is, paraxial) laser beam. Here we investigate a specific process, third-harmonic generation, excited by a highly nonparaxial beam that illuminates an interaction region from a nearly full solid angle. We elucidate the influence of the focal volume and the pump intensity on the number of frequency-tripled photons by varying the solid angle from which the pump light is focused, and we find good agreement between the experiments and numerical calculations. As the pump light is focused to a spot size much smaller than the laser wavelength, the Gouy phase does not limit the yield of frequency-converted photons, in stark contrast to the paraxial regime. We believe that our findings are generic and apply to many other nonlinear optical processes when the pump light is focused from a full solid angle.

Emission of circularly polarized light by a linear dipole

Martin Neugebauer, Peter Banzer, Sergey Nechayev

Controlling the polarization state and the propagation direction of photons is a fundamental prerequisite for many nanophotonic devices and a precursor for future on-chip communication, where the emission properties of individual emitters are particularly relevant. Here, we report on the emission of partially circularly polarized photons by a linear dipole. The underlying effect is linked to the near-field part of the angular spectrum of the dipole, and it occurs in any type of linear dipole emitter, ranging from atoms and quantum dots to molecules and dipole-like antennas. We experimentally observe it by near-field to far-field transformation at a planar dielectric interface and numerically demonstrate the utility of this phenomenon by coupling the circularly polarized light to the individual paths of crossing waveguides.

Reconstruction of Optical Pulse Intensity and Phase Based on SPM Spectra Measurements in Microstructured Tellurite Fiber in Telecommunication Range

Elena Anashkina, Maxim Koptev, Alexey Andrianov, Vitaly Dorofeev, Surinder Singh, Gerd Leuchs, Arkady Kim

We report novel functionalities of a very simple, robust, and low-cost optical metrology method for the reconstruction of an intensity profile and phase of pulses in the telecommunication range based on measuring the fundamental spectrum and two self-phase modulated spectra after a nonlinear element with Kerr nonlinearity. We demonstrate, for the first time, to the best of our knowledge, the possibility of implementing this method using a microstructured tellurite fiber (with a zero dispersion wavelength of 1.55 mu m and nonlinear coefficient >500 (W km)(-1)) as a nonlinear element for characterizing optical pulses with a wide range of parameters: wavelengths from O-band to L-band, durations from <100 fs to similar to 100 ps, low energies (similar to 100 pJ), and/or low peak powers (similar to 1 W). The intensity and phase of 80-fs ultrashort pulses with an energy of similar to 100 pJ are retrieved experimentally. We give a detailed theoretical analysis of the possibilities of reconstructing telecommunication pulses, including the important problem of measuring two coherent neighboring pulses whose wings may overlap.

Vectorial vortex generation and phase singularities upon Brewster reflection

Rene Barczyk, Sergey Nechayev, Muhammad Abdullah Butt, Gerd Leuchs, Peter Banzer

We experimentally demonstrate the emergence of a purely azimuthally polarized vectorial vortex beam with a phase singularity upon Brewster reflection of focused circularly polarized light from a dielectric substrate. The effect originates from the polarizing properties of the Fresnel reflection coefficients described in Brewster’s law. An astonishing consequence of this effect is that the reflected<br>field’s Cartesian components acquire local phase singularities at Brewster’s angle. Our observations are crucial for polarization microscopy and open new avenues for the generation of exotic states of light based on spin-to-orbit coupling, without the need for sophisticated optical elements.

Reading out Fisher information from the zeros of the point spread function

M. Paúr, B. Stoklasa, D. Koutný, J. Řeháček, Z. Hradil, J. Grover, A. Krzic, Luis Sanchez-Soto

We show that, for optical systems whose point spread functions exhibit isolated zeros, the information one can gain about the separation between two incoherent point light sources does not scale quadratically with the separation (which is the distinctive dependence causing Rayleigh’s curse) but only linearly. Moreover, the dominant contribution to the separation information comes from regions in the vicinity of these zeros. We experimentally confirm this idea, demonstrating significant superresolution using natural or artificially created spectral doublets.

Compressed sensing of twisted photons

F. Bouchard, D. Koutny, F. Hufnagel, Z. Hradil, J. Rehacek, Y. S. Teo, D. Ahn, H. Jeong, Luis Sanchez-Soto, et al.

The ability to completely characterize the state of a quantum system is an essential element for the emerging quantum technologies. Here, we present a<br>compressed-sensing inspired method to ascertain any rank-deficient qudit state, which we experimentally encode in photonic orbital angular momentum. We efficiently reconstruct these qudit states from a few scans with an intensified CCD camera. Since it requires only a few intensity measurements, our technique<br>would provide an easy and accurate way to identify quantum sources, channels, and systems.

Experimental demonstration of linear and spinning Janus dipoles for polarisation and wavelength selective near-field coupling

M. F. Picardi, Martin Neugebauer, Jörg Eismann, Gerd Leuchs, Peter Banzer, F. J. Rodriguez-Fortuno, A. V. Zayats

The electromagnetic field scattered by nano-objects contains a broad range of wave vectors and can be efficiently coupled to waveguided modes. The dominant ontribution to scattering from subwavelength dielectric and plasmonic nanoparticles is determined by electric and magnetic dipolar<br>responses. Here, we experimentally demonstrate spectral and phase selective excitation of Janus dipoles, sources with electric and magnetic dipoles oscillating out of phase, in order to control near-field interference and directional coupling to waveguides. We show that by controlling the<br>polarisation state of the dipolar excitations and the excitation wavelength to adjust their relative contributions, directionality and coupling strength can be fully tuned. Furthermore, we introduce a novel spinning Janus dipole featuring cylindrical symmetry in the near and far field, which results in either omnidirectional coupling or noncoupling. Controlling the propagation of guided light waves via fast and robust near-field <br> interference between polarisation components of a source is required in many applications in nanophotonics and quantum optics.

Mimicking Chiral Light-Matter Interaction

Sergey Nechayev, Peter Banzer

We demonstrate that electric-dipole scatterers can mimic chiral light-matter interaction by generating far-field circular polarization upon scattering, even though the optical chirality of the incident field as well as that of the scattered light is zero. The presented effect originates from the fact that electric-dipole scatterers respond selectively only to the incident electric field, which eventually results in depolarization of the transmitted beam and in generation of far-field circular polarization. To experimentally demonstrate this effect we utilize a cylindrical vector beam with spiral polarization and a spherical gold nanoparticle positioned on the optical axis -- the axis of rotational symmetry of the system. Our experiment and a simple theoretical model address the fundamentals of duality symmetry in optics and chiral light-matter interactions, accentuating their richness and ubiquity yet in highly symmetric configurations.

Large-Area 3D Plasmonic Crescents with Tunable Chirality

Eric S. A. Goerlitzer, Reza Mohammadi, Sergey Nechayev, Peter Banzer, Nicolas Vogel

Abstract Chiral plasmonic nanostructures hold promise for enhanced chiral sensing and circular dichroism spectroscopy of chiral molecules. It is therefore of interest to fabricate chiral plasmonic nanostructures with tailored chiroptical properties over large areas with reasonable effort. Here, a colloidal lithography approach is used to produce macroscopic arrays of sub-micrometer 3D chiral plasmonic crescent structures over areas >1 cm2. The chirality originates from symmetry breaking by the introduction of a step within the crescent structure. This step is produced by an intermediate layer of silicon dioxide onto which the metal crescent structure is deposited. It is experimentally demonstrated that the chiroptical properties in such structures can be tailored by changing the position of the step within the crescent. These experiments are complemented by finite element simulations and the application of a multipole expansion to elucidate the physical origin of the circular dichroism of the crescent structures.

Multi-twist polarization ribbon topologies in highly-confined optical fields

Thomas Bauer, Peter Banzer, Frédéric Bouchard, Sergej Orlov, Lorenzo Marrucci, Enrico Santamato, Robert W Boyd, Ebrahim Karimi, Gerd Leuchs

Electromagnetic plane waves, solutions to Maxwell's equations, are said to be 'transverse' in vacuum. Namely, the waves' oscillatory electric and magnetic fields are confined within a plane transverse to the waves' propagation direction. Under tight-focusing conditions however, the field can exhibit longitudinal electric or magnetic components, transverse spin angular momentum, or non-trivial topologies such as Möbius strips. Here, we show that when a suitably spatially structured beam is tightly focused, a 3-dimensional polarization topology in the form of a ribbon with two full twists appears in the focal volume. We study experimentally the stability and dynamics of the observed polarization ribbon by exploring its topological structure for various radii upon focusing and for different propagation planes.

Substrate-Induced Chirality in an Individual Nanostructure

Sergey Nechayev, Rene Barczyk, Uwe Mick, Peter Banzer

We experimentally investigate the chiral optical response of an individual nanostructure consisting of three equally sized spherical nanoparticles made of different materials and arranged in \ang{90} bent geometry. Placing the nanostructure on a substrate converts its morphology from achiral to chiral. Chirality leads to pronounced differential extinction, i.e., circular dichroism and optical rotation, or equivalently, circular birefringence, which would be strictly forbidden in the absence of a substrate or heterogeneity. This first experimental observation of the substrate-induced break of symmetry in an individual heterogeneous nanostructure sheds new light on chiral light-matter interactions at substrate-nanostructure interfaces.

Investigating the Optical Properties of a Laser Induced 3D Self‐Assembled Carbon–Metal Hybrid Structure

Muhammad Abdullah Butt, Antonino Calà Lesina, Martin Neugebauer, Thomas Bauer, Lora Ramunno, Alessandro Vaccari, Pierre Berini, Yuriy Petrov, Denis Danilov, et al.

Carbon‐based and carbon–metal hybrid materials hold great potential for applications in optics and electronics. Here, a novel material made of carbon and gold–silver nanoparticles is discussed, fabricated using a laser‐induced self‐assembly process. This self‐assembled metamaterial manifests itself in the form of cuboids with lateral dimensions on the order of several micrometers and a height of tens to hundreds of nanometers. The carbon atoms are arranged following an orthorhombic unit cell, with alloy nanoparticles intercalated in the crystalline carbon matrix. The optical properties of this metamaterial are analyzed experimentally using a microscopic Müller matrix measurement approach and reveal a high linear birefringence across the visible spectral range. Theoretical modeling based on local‐field theory applied to the carbon matrix links the birefringence to the orthorhombic unit cell, while finite‐difference time‐domain simulations of the metamaterial relates the observed optical response to the distribution of the alloy nanoparticles and the optical density of the carbon matrix.

Resonant electro-optic frequency comb

Alfredo Rueda, Florian Sedlmeir, Madhuri Kumari, Gerd Leuchs, Harald G. L. Schwefel

High-speed optical telecommunication is enabled by wavelength-division multiplexing, whereby hundreds of individually stabilized lasers encode information within a single-mode optical fibre. Higher bandwidths require higher total optical power, but the power sent into the fibre is limited by optical nonlinearities within the fibre, and energy consumption by the light sources starts to become a substantial cost factor1. Optical frequency combs have been suggested to remedy this problem by generating numerous discrete, equidistant laser lines within a monolithic device; however, at present their stability and coherence allow them to operate only within small parameter ranges2,3,4. Here we show that a broadband frequency comb realized through the electro-optic effect within a high-quality whispering-gallery-mode resonator can operate at low microwave and optical powers. Unlike the usual third-order Kerr nonlinear optical frequency combs, our combs rely on the second-order nonlinear effect, which is much more efficient. Our result uses a fixed microwave signal that is mixed with an optical-pump signal to generate a coherent frequency comb with a precisely determined carrier separation. The resonant enhancement enables us to work with microwave powers that are three orders of magnitude lower than those in commercially available devices. We emphasize the practical relevance of our results to high rates of data communication. To circumvent the limitations imposed by nonlinear effects in optical communication fibres, one has to solve two problems: to provide a compact and fully integrated, yet high-quality and coherent, frequency comb generator; and to calculate nonlinear signal propagation in real time5. We report a solution to the first problem.

Huygens' Dipole for Polarization-Controlled Nanoscale Light Routing

Sergey Nechayev, Jörg Eismann, Martin Neugebauer, Pawel Wozniak, Ankan Bag, Gerd Leuchs, Peter Banzer

Structured illumination allows for satisfying the first Kerker condition of in-phase perpendicular electric and magnetic dipole moments in any isotropic scatterer that supports electric and magnetic dipolar resonances. The induced Huygens' dipole may be utilized for unidirectional coupling to waveguide modes that propagate transverse to the excitation beam. We study two <br> configurations of a Huygens' dipole -- longitudinal electric and transverse magnetic dipole moments or vice versa. We experimentally show that only the radially polarized emission of the first and azimuthally polarized emission of the second configuration are directional in the far-field. This polarization selectivity implies that directional excitation of either TM or TE waveguide modes is possible. Applying this concept to a single nanoantenna excited with structured light, we are able to experimentally achieve scattering directivities of around 23 dB and 18 dB in TM and TE modes, respectively. This strong directivity paves the way for tunable polarization-controlled nanoscale light routing and applications in optical metrology, <br> ocalization microscopy and on-chip optical devices.

Seeded and unseeded high-order parametric down-conversion

Cameron Okoth, Andrea Cavanna, Nicolas Joly, Maria Chekhova

Spontaneous parametric down-conversion (SPDC) has been one of the foremost tools in quantum optics for over five decades. Over that time, it has been used to demonstrate some of the curious features that arise from quantum mechanics. Despite the success of SPDC, its higher-order analogs have never been observed, even though it has been suggested that they generate far more unique and exotic states than SPDC. An example of this is the emergence of non-Gaussian states without the need for postselection. Here we calculate the expected rate of emission for nth-order SPDC with and without external stimulation (seeding). Focusing primarily on third-order parametric down-conversion, we estimate the photon detection rates in a rutile crystal for both the unseeded and seeded regimes.

Quantum correlations in separable multi-mode states and in classically entangled light

N. Korolkova, Gerd Leuchs

In this review we discuss intriguing properties of apparently classical optical fields, that go beyond purely classical context and allow us to speak about quantum characteristics of such fields and about their applications in quantum technologies. We briefly define the genuinely quantum concepts of entanglement and steering. We then move to the boarder line between classical and quantum world introducing quantum discord, a more general concept of quantum coherence, and finally a controversial notion of classical entanglement. To unveil the quantum aspects of often classically perceived systems, we focus more in detail on quantum discordant correlations between the light modes and on nonseparability properties of optical vector fields leading to entanglement between different degrees of freedom of a single beam. To illustrate the aptitude of different types of correlated systems to act as quantum or quantum-like resource, entanglement activation from discord, high-precision measurements with classical entanglement and quantum information tasks using intra-system correlations are discussed. The common themes behind the versatile quantum properties of seemingly classical light are coherence, polarization and inter and intra-mode quantum correlations.

Adaptive Compressive Tomography with No a priori Information

Daekun Ahn, Yong Siah Teo, Hyunseok Jeong, Frédéric Bouchard, Felix Hufnagel, Ebrahim Karimi, D Koutny, Jarda Rehacek, Zdenek Hradil, et al.

Quantum state tomography is both a crucial component in the field of quantum information and computation and a formidable task that requires an incogitable number of measurement configurations as the system dimension grows. We propose and experimentally carry out an intuitive adaptive compressive tomography scheme, inspired by the traditional compressed-sensing protocol in signal recovery, that tremendously reduces the number of configurations needed to uniquely reconstruct any given quantum state without any additional a priori assumption whatsoever (such as rank information, purity, etc.) about the state, apart from its dimension.

Plasmonic carbon nanohybrids from laser-induced deposition: controlled synthesis and SERS properties

Anastasia Povolotckaia, Dmitrii Pankin, Yuriy Petrov, Anna Vasileva, Ilya Kolesnikov, George Sarau, Silke Christiansen, Gerd Leuchs, Alina Manshina

A novel single-step, laser-induced and solution-based process is presented for synthesizing complex hybrid metal/carbon nanostructures. The process relies on simply illuminating the interface between a substrate and a liquid solution of the supramolecular complex [Au13Ag12(C2Ph)(20)(PPh2(C6H4)(3)PPh2)(3)][PF6](5) (hereinafter abbreviated as SMC) with an unfocussed He-Cd laser having a wavelength of 325nm and an intensity of I=0.5W/cm(2). The process results in hybrid nanostructures of well-controlled morphology: nanoparticles (NP) and 2D flakes, which may also grow jointly to form 3D morphologically complex multipetal flower-like' structures. At the atomic scale, the obtained metamaterials are complex in composition and structure, i.e., they contain bimetallic Au-Ag nanoclusters of diameter 3-5nm incorporated inside a carbonaceous matrix. This matrix can be amorphous or crystalline, and the details of the compositional outcome can be controlled and steered by the laser deposition parameters. Au-Ag nanoclusters show plasmonic behavior including the enhancement of electromagnetic fields of visible light. This leads to the enhancement of Raman scattering by the Au-Ag nanoparticle ensemble within the carbonaceous matrix. This enables a 3D architecture for stimulating surface-enhanced Raman scattering (SERS).

Structured quantum projectiles

Hugo Larocque, Robert Fickler, Eliahu Cohen, Vincenzo Grillo, Rafal E. Dunin-Borkowski, Gerd Leuchs, Ebrahim Karimi

Matter wave interferometry is becoming an increasingly important technique in quantum metrology. However, unlike its photonic counterpart, this technique relies on the interference of particles possessing a nonzero rest mass and an electric charge. Matter waves can therefore experience alterations in their wavelike features while propagating through uniform fields to which a linear potential can be attributed, e.g., the Newtonian gravitational potential. Here, we derive the propagation kernel attributed to matter waves within such a potential. This kernel thereafter allows us to provide analytical formulations for structured matter waves subjected to a linear potential. Our formulations are in agreement with both the classical dynamics attributed to such waves and with previous interferometry experiments. Eigenbasis representations of structured matter waves are also introduced along with their application to enhanced interferometric measurements. Our results are not only relevant to matter wave interferometry, but also emphasize its fundamental differences with respect to photonic interferometry.

Orbital-to-Spin Angular Momentum Conversion Employing Local Helicity

Sergey Nechayev, Jörg Eismann, Gerd Leuchs, Peter Banzer

Spin-orbit interactions in optics traditionally describe an influence of the polarization degree of freedom of light on its spatial properties. The most prominent example is the generation of a spin-dependent optical vortex upon focusing or scattering of a circularly polarized plane-wave by a nanoparticle, converting spin to orbital angular momentum of light. Here, we present a mechanism of conversion of orbital-to-spin angular momentum of light upon scattering of a linearly polarized vortex beam by a spherical silicon nanoparticle. We show that focused linearly polarized Laguerre-Gaussian beams of first order (ℓ=±1) exhibit an ℓ-dependent spatial distribution of helicity density in the focal volume. By using a dipolar scatterer the helicity density can be manipulated locally, while influencing globally the spin and orbital angular momentum of the beam. Specifically, the scattered light can be purely circularly polarized with the handedness depending on the orbital angular momentum of the incident beam. We corroborate our findings with theoretical calculations and an experimental demonstration. Our work sheds new light on the global and local properties of helicity conservation laws in electromagnetism.

The Wigner flow on the sphere

P. Yang, I. F. Valtierra, A. B. Klimov, S. -T. Wu, R. -K. Lee, Luis Sanchez-Soto, Gerd Leuchs

We derive a continuity equation for the evolution of the SU(2) Wigner function under nonlinear Kerr evolution. We give explicit expressions for the resulting quantum Wigner current, and discuss the appearance of the classical limit. We show that the global structure of the quantum current significantly differs from the classical one, which is clearly reflected in the form of the corresponding stagnation lines.

Weak measurement enhanced spin Hall effect of light for particle displacement sensing

Martin Neugebauer, Sergey Nechayev, Martin Vorndran, Gerd Leuchs, Peter Banzer

A spherical nanoparticle can scatter tightly focused optical beams in a spin-segmented manner, meaning that the far field of the scattered light exhibits laterally separated left- and right-handed circularly polarized components. This effect, commonly referred to as giant spin Hall effect of light, strongly depends on the position of the scatterer in the focal volume. Here, a scheme that utilizes an optical weak measurement in a cylindrical polarization basis is put forward to drastically enhance the spin-segmentation and, therefore, the sensitivity to small displacements of a scatterer. In particular, we experimentally achieve a change of the spin-splitting signal of 5% per nanometer displacement.

Uncertainty-reality complementarity and entropic uncertainty relations

Łukasz Rudnicki

Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures (Dieguez and Angelo 2018 Phys. Rev. A 97 022107). However, there is no state-independent 'reality trade-off' between non-commuting observables, as in certain systems all observables are real (Bilobran and Angelo 2015 Europhys. Lett. 112 40005). We show that the entropic uncertainty relation in the presence of quantum memory (Berta et al 2010 Nat. Phys. 6 659) perfectly supplements the discussed notion of reality, rendering trade-offs between reality and quantum uncertainty. State-independent complementarity inequalities involving entropic measures of both, uncertainty and reality, for two observables are presented.

Inherent security of phase coding quantum key distribution systems against detector blinding attacks

Aleksey Fedorov, Ilja Gerhardt, Anqi Huang, Jonathan Jogenfors, Yury Kurochkin, Antia Lamas-Linares, Jan-Ake Larsson, Gerd Leuchs, Lars Lydersen, et al.

An attack exploiting single-photon avalanche diode (SPAD) blinding is one of the effective methods of 'quantum hacking' (Lydersen et al 2010 Nat. Photon. 4 686) or cracking quantum key distribution (QKD) systems. This attack was experimentally demonstrated for various QKD systems based on both phase and polarization coding. After such an attack, the eavesdropper knows the whole key, has not produced errors, and is not detected. So far this attack is the only one that was demonstrated in the explicit form on many real QKD systems. It is important that these demonstrations were actually performed in reality, i.e. not in speculations as some other attacks. Therefore, the presence of vulnerability in QKD systems based on polarization coding is an existing fact, rather than just a potential threat. It is often assumed that all systems regardless of the encoding method are vulnerable to such an attack. However, in the case of phase coding, some essential features of photocount statistics on the receiving side make a difference. In this Letter we prove that detector blinding attack, when acts on QKD systems with phase coding, leads to a distortion of the photocounts statistics so the eavesdropper may always be detected. Moreover, one does not need to change the design of the QKD system and/or its control electronics, as it is sufficient to amend only the processing of the quantum states registration results to make the system secure. At the same time, polarization coding-based systems remain vulnerable to such an attack and do not guarantee key security.

Weak measurement of elliptical dipole moments by C point splitting

Sergey Nechayev, Martin Neugebauer, Martin Vorndran, Gerd Leuchs, Peter Banzer

We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these C points and the dipole moment. In the case of highly eccentric dipoles, the C points of opposite handedness exhibit only a small angular separation and occur in the low intensity region of the emission pattern. In this regard, we introduce an optical weak measurement approach that utilizes the transverse electric (azimuthal) and transverse magnetic (radial) far-eld polarization basis. Projecting the far field<br>onto a spatially varying post-selected polarization state reveals the angular separation and the helicity of the C points. We demonstrate the applicability of this approach and determine the elliptical dipole moment of a particle sitting on an interface by measuring the C points in its far field.

Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons

Frédéric Bouchard, Khabat Heshami, Duncan England, Robert Fickler, Robert W. Boyd, Berthold-Georg Englert, Luis Sanchez-Soto, Ebrahim Karimi

Quantum key distribution is on the verge of real world applications, where perfectly secure information can be distributed among multiple parties. Several quantum cryptographic protocols have been theoretically proposed and independently realized in different experimental conditions. Here, we develop an experimental platform based on high-dimensional orbital angular momentum states of single photons that enables implementation of multiple quantum key distribution protocols with a single experimental apparatus. Our versatile approach allows us to experimentally survey different classes of quantum key distribution techniques, such as the 1984 Bennett & Brassard (BB84), tomographic protocols including the six-state and the Singapore protocol, and to investigate, for the first time, a recently introduced differential phase shift (Chau15) protocol using twisted photons. This enables us to experimentally compare the performance of these techniques and discuss their benefits and deficiencies in terms of noise tolerance in different dimensions.

Stabilization of transmittance fluctuations caused by beam wandering in continuous-variable quantum communication over free-space atmospheric channels

Vladyslav C. Usenko, Christian Peuntinger, Bettina Heim, Kevin Günthner, Ivan Derkach, Dominique Elser, Christoph Marquardt, Radim Filip, Gerd Leuchs

Transmittance fluctuations in turbulent atmospheric channels result in quadrature excess noise which limits applicability of continuous-variable quantum communication. Such fluctuations are commonly caused by beam wandering around the receiving aperture. We study the possibility to stabilize the fluctuations by expanding the beam, and test this channel stabilization in regard of continuous-variable entanglement sharing and quantum key distribution. We perform transmittance measurements of a real free-space atmospheric channel for different beam widths and show that the beam expansion reduces the fluctuations of the channel transmittance by the cost of an increased overall loss. We also theoretically study the possibility to share an entangled state or to establish secure quantum key distribution over the turbulent atmospheric channels with varying beam widths. We show the positive effect of channel stabilization by beam expansion on continuous-variable quantum communication as well as the necessity to optimize the method in order to maximize the secret key rate or the amount of shared entanglement. Being autonomous and not requiring adaptive control of the source and detectors based on characterization of beam wandering, the method of beam expansion can be also combined with other methods aiming at stabilizing the fluctuating free-space atmospheric channels.

Transverse Kerker Scattering for Ångström Localization of Nanoparticles

Ankan Bag, Martin Neugebauer, Pawel Wozniak, Gerd Leuchs, Peter Banzer

Angstrom precision localization of a single nanoantenna is a crucial step towards advanced nanometrology, medicine and biophysics. Here, we show that single nanoantenna displacements<br>down to few Angstroms can be resolved with sub-Angstrom precision using an all-optical method.<br>We utilize the tranverse Kerker scattering scheme where a carefully structured light beam excites a combination of multipolar modes inside a dielectric nanoantenna, which then upon interference, scatters directionally into the far-field. We spectrally tune our scheme such that it is most sensitive<br>to the change in directional scattering per nanoantenna displacement. Finally, we experimentally show that antenna displacement down to 3 A˚ is resolvable with a localization precision of 0.6 A˚.

Sensitivity limits of millimeter-wave photonic radiometers based on efficient electro-optic upconverters

Gabriel Santamaria Botello, Florian Sedlmeir, Alfredo Rueda, Kerlos Atia Abdalmalak, Elliott R. Brown, Gerd Leuchs, Sascha Preu, Daniel Segovia-Vargas, Dmitry V. Strekalov, et al.

Conventional ultra-high sensitivity detectors in the millimeter-wave range are usually cooled as their own thermal noise at room temperature would mask the weak received radiation. The need for cryogenic systems increases the cost and complexity of the instruments, hindering the development of, among others, airborne and space applications. In this work, the nonlinear parametric upconversion of millimeter-wave radiation to the optical domain inside high-quality (Q) lithium niobate whispering-gallery mode (WGM) resonators is proposed for ultra-low noise detection. We experimentally demonstrate coherent upconversion of millimeter-wave signals to a 1550 nm telecom carrier, with a photon conversion efficiency surpassing the state-of-the-art by 2 orders of magnitude. Moreover, a theoretical model shows that the thermal equilibrium of counterpropagating WGMs is broken by overcoupling the millimeter-wave WGM, effectively cooling the upconverted mode and allowing ultra-low noise detection. By theoretically estimating the sensitivity of a correlation radiometer based on the presented scheme, it is found that room-temperature radiometers with better sensitivity than state-of-the-art high-electron-mobility transistor (HEMT)-based radiometers can be designed. This detection paradigm can be used to develop room-temperature instrumentation for radio astronomy, earth observation, planetary missions, and imaging systems. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

The Geometrical Basis of PT Symmetry

Luis Sanchez-Soto, Juan J. Monzon

We reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Mobius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.

Nonregularity of three-dimensional polarization states

José J. Gil, Andreas Norrman, Ari T. Friberg, Tero Setälä

Regular states of polarization are defined as those that can be decomposed into a pure state (fully polarized), a two-dimensional (2D) unpolarized state (a state whose polarization ellipse evolves fully randomly in a fixed plane), and a three-dimensional (3D) unpolarized state (a state whose polarization ellipse evolves fully randomly in the 3D space) \[Phys. Rev. A95, 053856 (2017)PLRAAN1050-294710.1103/PhysRevA.95.053856\]. For nonregular states, the middle component can be considered as an equiprobable mixture of two pure states, whose polarization ellipses lie in different planes. In this work, we identify a perfect nonregular state and introduce the degree of nonregularity as a measure of the proximity of a nonregular state to regularity. We also analyze and interpret the notion of polarization-state regularity in terms of polarimetric parameters. Our results bring new insights into the polarimetric structure of 3D light fields.

Tempering Rayleigh’s curse with PSF shaping

Martin Paúr, Bohumil Stoklasa, Jai Grover, Andrej Krzic, Luis Sanchez-Soto, Zdeněk Hradil, Jaroslav Řeháček

It has been argued that, for a spatially invariant imaging system, the information one can gain about the separation of two incoherent point sources decays quadratically to zero with decreasing separation. The effect is termed Rayleighx2019;s curse. Contrary to this belief, we identify a class of point-spread functions (PSFs) with a linear information decrease. Moreover, we show that any well-behaved symmetric PSF can be converted into such a form with a simple nonabsorbing signum filter. We experimentally demonstrate significant superresolution capabilities based on this idea.

Tomography from collective measurements

A. Muñoz, A. B. Klimov, Markus Grassl, Luis Sanchez-Soto

We discuss the tomography of N-qubit states using collective measurements.The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2) blocks. For the fully symmetric sector, the reconstruction protocol can be reduced to projections onto a canonically chosen set of pure states.<br>

Quantum-limited time-frequency estimation through mode-selective photon measurement

John M. Donohue, Vahid Ansari, Jaroslav Řeháček, Zdeněk Hradil, Bohumil Stoklasa, Martin Paúr, Luis Sanchez-Soto, Christine Silberhorn

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision,<br>free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of<br>single-photon level signals ten times smaller than their optical bandwidths with a ten-fold improvement in precision over the intensity-only Cramér-Rao<br>bound.

Exciting a chiral dipole moment in an achiral nanostructure

Jörg S. Eismann, Martin Neugebauer, Peter Banzer

Controlling the electric and magnetic dipole moments of optical nanostructures is a fundamental prerequisite for light routing and polarization multiplexing at the nanoscale. A versatile approach for inducing tailored dipole moments is structured illumination. Here, we discuss the excitation of a chiral dipole moment in an achiral silicon nanoparticle. In particular, we make use of the electric and magnetic polarizabilities of the silicon nanoparticle to coherently excite a superposition of parallel electric and magnetic dipole moments phase-shifted by +/-pi/2, which resembles the fundamental mode of a three-dimensional chiral nanostructure. We demonstrate the wavelength dependence of the excitation scheme and measure the spin and orbital angular momenta in the emission of the induced chiral dipole moments. Our results highlight the capabilities of such tunable chiral dipole emitters-not limited by structural properties-as flexible sources of spin-polarized light for nanoscopic devices. (c) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Quantum cryptography with twisted photons through an outdoor underwater channel

Frédéric Bouchard, Alicia Sit, Felix Hufnagel, Aazad Abbas, Yingwen Zhang, Khabat Heshami, Robert Fickler, Christoph Marquardt, Gerd Leuchs, et al.

Quantum communication has been successfully implemented in optical fibres and through free-space. Fibre systems, though capable of fast key and low error rates, are impractical in communicating with destinations without an established fibre link. Free-space quantum channels can overcome such limitations and reach long distances with the advent of satellite-to-ground links. However, turbulence, resulting from local fluctuations in refractive index, becomes a major challenge by adding errors and losses. Recently, an interest in investigating the possibility of underwater quantum channels has arisen. Here, we investigate the effect of turbulence on an underwater quantum channel using twisted photons in outdoor conditions. We study the effect of turbulence on transmitted error rates, and compare different quantum cryptographic protocols in an underwater quantum channel, showing the feasibility of high-dimensional encoding schemes. Our work may open the way for secure high-dimensional quantum communication between submersibles, and provides important input for potential submersibles-to-satellite quantum communication.

Chirality of Symmetric Resonant Heterostructures

Sergey Nechayev, Pawel Wozniak, Martin Neugebauer, Rene Barczyk, Peter Banzer

Chiroptical effects arising in mirror‐symmetric geometrically achiral resonant heterostructures are investigated. It is shown that coalescence of extrinsic chirality, heterogeneous morphology, and substrate‐induced break of symmetry leads to pronounced circular dichroism and circular birefringence. The physics of the involved phenomena is elucidated by studying spin‐splitting in scattering and hybridized dipolar modes of a heterodimer made of gold and silicon nanoparticles of the same shape and size. The work sheds new light on the optical properties of heterogeneous nanostructures and paves the way for designing polarization‐controlled tunable heterogeneous optical elements.

Chiroptical response of a single plasmonic nanohelix

Pawel Wozniak, Israel De Leon, Katja Hoeflich, Caspar Haverkamp, Silke Christiansen, Gerd Leuchs, Peter Banzer

We investigate the chiroptical response of a single plasmonic nanohelix interacting with a weakly focused circularly polarized Gaussian beam. The optical scattering at the fundamental resonance is characterized experimentally and numerically. The angularly resolved scattering of the excited nanohelix is verified experimentally and it validates the numerical results. We employ a multipole decomposition analysis to study the fundamental and first higher-order resonance of the nanohelix, explaining their chiral properties in terms of the formation of chiral dipoles. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Coherence lattices in surface plasmon polariton fields

Yahong Chen, Andreas Norrman, Sergey A. Ponomarenko, Ari T. Friberg

We explore electromagnetic coherence lattices in planar polychromatic surface plasmon polariton (SPP) fields. When the SPP constituents are uncorrelated-and thus do not interfere-coherence lattices arise from statistical similarity of the random SPP electromagnetic field. As the SPP correlations become stronger, the coherence lattices fade away, but the lattice structure reemerges in the spectral density of the field. The polarization states of the structured SPP lattice fields are also investigated. Controllable plasmonic coherence and spectral density lattices can find applications in nanophotonics, such as nanoparticle manipulation. (C) 2018 Optical Society of America

Optimal measurements for quantum spatial superresolution

J. Rehacek, Z. Hradil, D. Koutny, J. Grover, A. Krzic, Luis Sanchez-Soto

We construct optimal measurements, achieving the ultimate precision predicted by quantum theory, for the simultaneous estimation of centroid, separation, and relative intensities of two incoherent point sources using a linear optical system. We discuss the physical feasibility of the scheme, which could pave the way for future practical implementations of quantum-inspired imaging.

Renyi relative entropies of quantum Gaussian states

Kaushik P Seshadreesan, Ludovico Lami, Mark M Wilde

The quantum Renyi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory. On a different thread, quantum Gaussian states have been intensely investigated theoretically, motivated by the fact that they are more readily accessible in the laboratory than are other, more exotic quantum states. In this paper, we derive formulas for the quantum Renyi relative entropies of quantum Gaussian states. We consider both the traditional (Petz) Renyi relative entropy as well as the more recent sandwiched Renyi relative entropy, finding formulas that are expressed solely in terms of the mean vectors and covariance matrices of the underlying quantum Gaussian states. Our development handles the hitherto elusive case for the Petz-Renyi relative entropy when the Renyi parameter is larger than one. Finally, we also derive a formula for the max-relative entropy of two quantum Gaussian states, and we discuss some applications of the formulas derived here.

Space QUEST mission proposal: experimentally testing decoherence due to gravity

Siddarth Koduru Joshi, Jacques Pienaar, Timothy C. Ralph, Luigi Cacciapuoti, Will McCutcheon, John Rarity, Dirk Giggenbach, Jin Gyu Lim, Vadim Makarov, et al.

Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum correlations, such as entanglement, may exhibit different behavior to purely classical correlations in curved space. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph et al [5] and Ralph and Pienaar [1], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's Space QUEST (Space-Quantum Entanglement Space Test) mission, and study the feasibility of the mission scheme.

Uncertainty Relations for Coarse-Grained Measurements: An Overview

Fabricio Toscano, Daniel S. Tasca, Łukasz Rudnicki, Stephen P. Walborn

Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.

Off-resonant emission of photon pairs in nonlinear optical cavities

Valentin Averchenko, Gerhard Schunk, Michael Förtsch, Martin Fischer, Dmitry Strekalov, Gerd Leuchs, Christoph Marquardt

Cavity-assisted spontaneous parametric down-conversion (SPDC) and spontaneous four-wave mixing (SFWM) in nonlinear optical materials are practical and versatile methods to generate narrowband time-energy entangled photon pairs. Time- energy entangled photons with tailored spectro-temporal properties are particularly useful for efficient quantum optical interfaces. In this work we study the generation of photon pairs in cavity-assisted SPDC and SFWM for the general case of off-resonant conversion, namely, when the frequencies of the generated photons do not match the cavity resonances. Such a frequency mismatch in particular depends on temperature and requires an additional control in the experiment. First, we propose a generic model, for description of cavity-assisted SPDC and SFWM. We show that in both processes the mismatch reduces the generation rate of photons, distorts the spectrum and the auto-correlation function of the generated fields, as well as affects the photon generation dynamics. Second, we verify the results experimentally using parametric generation of photon pairs in a nonlinear whispering gallery mode resonator (WGMR) as an experimental platform with controlled frequency mismatch. Our work reveals the role of the frequency mismatch in the photon generation process and shows a way to control it. Obtained results constitute one more step in the direction of full control over the spectro-temporal properties of entangled photon pairs and the heralded generation of single-photon pulses with a tailored temporal mode.

Tailoring multipolar Mie scattering with helicity and angular momentum

Xavier Zambrana-Puyalto, Xavier Vidal, Pawel Wozniak, Peter Banzer, Gabriel Molina-Terriza

Linear scattering processes are usually described as a function of the parameters of the incident beam. The wavelength, the intensity distribution, the polarization or the phase are among them. Here, we discuss and experimentally demonstrate how the angular momentum and the helicity of light influence the light scattering of spherical particles. We measure the backscattering of a 4 μm diameter TiO2 single particle deposited on a glass substrate. The particle is probed at different wavelengths by different beams with total angular momenta ranging from −8 to +8 units. It is observed that the spectral behavior of the particle is highly dependent on the angular momentum and helicity of the incoming beam. While some of the properties of the scattered field can be described with a simple resonator model, the scattering of high angular momentum beams requires a deeper understanding of the multipolar modes induced in the sphere. We observe that tailoring these induced multipolar modes can cause a shift and a spectral narrowing of the peaks of the scattering spectrum. Furthermore, specific combinations of helicity and angular momentum for the excitation lead to differences in the conservation of helicity by the system, which has clear consequences on the scattering pattern.

Magnetic and Electric Transverse Spin Density of Spatially Confined Light

Martin Neugebauer, Jörg Eismann, Thomas Bauer, Peter Banzer

When a beam of light is laterally confined, its field distribution can exhibit points where the local magnetic and electric field vectors spin in a plane containing the propagation direction of the electromagnetic wave. The phenomenon indicates the presence of a nonzero transverse spin density. Here, we experimentally investigate this transverse spin density of both magnetic and electric fields, occurring in highly confined structured fields of light. Our scheme relies on the utilization of a high-re fractiv-indcx e-noperticlc as a lecal field probe, exhibiting magnetic and electric dipole resonances in the visible spectral range. Because of the directional emission of dipole moments that spin around an axis parallel to a nearby dielectric interface, such a probe particle is capable of locally sensing the magnetic and electric transverse spin density of a tightly focused beam impinging under normal incidence with respect to said interface. We exploit the achieved experimental results to emphasize the difference between magnetic and electric transverse spin densities.

Mutually unbiased coarse-grained measurements of two or more phase-space variables

E.C. Paul, S.P. Walborn, D.S. Tasca, Łukasz Rudnicki

Mutual unbiasedness of the eigenstates of phase-space operators-such as position and momentum, or their standard coarse-grained versions-exists only in the limiting case of infinite squeezing. In Phys. Rev. Lett. 120, 040403 (2018), it was shown that mutual unbiasedness can be recovered for periodic coarse graining of these two operators. Here we investigate mutual unbiasedness of coarse-grained measurements for more than two phase-space variables. We show that mutual unbiasedness can be recovered between periodic coarse graining of any two nonparallel phase-space operators. We illustrate these results through optics experiments, using the fractional Fourier transform to prepare and measure mutually unbiased phase-space variables. The differences between two and three mutually unbiased measurements is discussed. Our results contribute to bridging the gap between continuous and discrete quantum mechanics, and they could be useful in quantum-information protocols.

Towards an integrated AlGaAs waveguide platform for phase and polarisation shaping

G Maltese, Y Halioua, A Lemaitre, C Gomez-Carbonell, E Karimi, Peter Banzer, S Ducci

We propose, design and fabricate an on-chip AlGaAs waveguide capable of generating a controlled phase delay of pi/2 between the guided transverse electric and magnetic modes. These modes possess significantly strong longitudinal field components as a direct consequence of their strong lateral confinement in the waveguide. We demonstrate that the effect of the device on a linearly polarised input beam is the generation of a field, which is circularly polarised in its transverse components and carries a phase vortex in its longitudinal component. We believe that the discussed integrated platform enables the generation of light beams with tailored phase and polarisation distributions.

Near optimal discrimination of binary coherent signals via atom–light interaction

Rui Han, János A Bergou, Gerd Leuchs

We study the discrimination of weak coherent states of light with significant overlaps by nondestructive measurements on the light states through measuring atomic states that are entangled to the coherent states via dipole coupling. In this way, the problem of measuring and discriminating coherent light states is shifted to finding the appropriate atom–light interaction and atomic measurements. We show that this scheme allows us to attain a probability of error extremely close to the Helstrom bound, the ultimate quantum limit for discriminating binary quantum states, through the simple Jaynes–Cummings interaction between the field and ancilla with optimized light–atom coupling and projective measurements on the atomic states. Moreover, since the measurement is nondestructive on the light state, information that is not detected by one measurement can be extracted from the post-measurement light states through subsequent measurements.

Testing for entanglement with periodic coarse-graining

Daniel S. Tasca, Łukasz Rudnicki, Reuben S. Aspden, Miles J. Padgett, Paulo H. Souto Ribeiro, Stephen P. Walborn

Continuous variables systems find valuable applications in quantum<br>information processing. To deal with an infinite-dimensional Hilbert space, one<br>in general has to handle large numbers of discretized measurements in tasks<br>such as entanglement detection. Here we employ the continuous transverse<br>spatial variables of photon pairs to experimentally demonstrate novel<br>entanglement criteria based on a periodic structure of coarse-grained<br>measurements. The periodization of the measurements allows for an efficient<br>evaluation of entanglement using spatial masks acting as mode analyzers over<br>the entire transverse field distribution of the photons and without the need to<br>reconstruct the probability densities of the conjugate continuous variables.<br>Our experimental results demonstrate the utility of the derived criteria with a<br>success rate in entanglement detection of $\sim60\%$ relative to $7344$ studied<br>cases.<br>

Majorization uncertainty relations for mixed quantum states

Zbigniew Puchała, Łukasz Rudnicki, Aleksandra Krawiec, Karol Życzkowski

Majorization uncertainty relations are generalized for an arbitrary mixed quantum state ρ of a finite size N . In particular, a lower bound for the sum of two entropies characterizing the probability distributions corresponding to measurements with respect to two arbitrary orthogonal bases is derived in terms of the spectrum of ρ and the entries of a unitary matrix U relating both bases. The results obtained can also be formulated for two measurements performed on a single subsystem of a bipartite system described by a pure state, and consequently expressed as an uncertainty relation for the sum of conditional entropies.

Residual and Destroyed Accessible Information after Measurements

Rui Han, Gerd Leuchs, Markus Grassl

When quantum states are used to send classical information, the receiver performs a measurement on the signal states. The amount of information extracted is often not optimal due to the receiver’s measurement scheme and experimental apparatus. For quantum nondemolition measurements, there is potentially some residual information in the postmeasurement state, while part of the information has been extracted and the rest is destroyed. Here, we propose a framework to characterize a quantum measurement by how much information it extracts and destroys, and how much information it leaves in the residual postmeasurement state. The concept is illustrated for several receivers discriminating coherent states.

Partially coherent axiconic surface plasmon polariton fields

Yahong Chen, Andreas Norrman, Sergey A. Ponomarenko, Ari T. Friberg

We introduce a class of structured polychromatic surface electromagnetic fields, reminiscent of conventional optical axicon fields, through a judicious superposition of partially correlated surface plasmon polaritons. We show that such partially coherent axiconic surface plasmon polariton fields are structurally stable and statistically highly versatile with regard to spectral density, polarization state, energy flow, and degree of coherence. These fields can be created by plasmon coherence engineering and may prove instrumental broadly in surface physics and in various nanophotonics applications.

Gauge invariant information concerning quantum channels

Łukasz Rudnicki, Zbigniew Puchała, Karol Zyczkowski

Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the complex spectrum of the superoperator to provide necessary conditions relevant for complete positivity of qubit channels and to express various metrics such as average gate fidelity.

Towards terahertz detection and calibration through spontaneous parametric down-conversion in the terahertz idler-frequency range generated by a 795 nm diode laser system

Vladimir V. Kornienko, Galiya Kh. Kitaeva, Florian Sedlmeir, Gerd Leuchs, Harald G. L. Schwefel

We study a calibration scheme for terahertz wave nonlinear-optical detectors based on spontaneous parametric down-conversion. Contrary to the usual low wavelength pump in the green, we report here on the observation of spontaneous parametric down-conversion originating from an in-growth poled lithium niobate crystal pumped with a continuous wave 50 mW, 795 nm diode laser system, phase-matched to a terahertz frequency idler wave. Such a system is more compact and allows for longer poling periods as well as lower losses in the crystal. Filtering the pump radiation by a rubidium-87 vapor cell allowed the frequency-angular spectra to be obtained down to similar to 0.5 THz or similar to 1 nm shift from the pump radiation line. The presence of an amplified spontaneous emission "pedestal" in the diode laser radiation spectrum significantly hampers the observation of spontaneous parametric down-conversion spectra, in contrast to conventional narrowband gas lasers. Benefits of switching to longer pump wavelengths are pointed out, such as collinear optical-terahertz phase-matching in bulk crystals. (c) 2018 Author(s).

Selective Coupling Enhances Harmonic Generation of Whispering-Gallery Modes

Luke S. Trainor, Florian Sedlmeir, Christian Peuntinger, Harald G. L. Schwefel

We demonstrate second-harmonic generation (SHG) in an x-cut congruent lithium niobate (LN) whispering-gallery mode (WGM) resonator. First, we show theoretically that independent control of the coupling of the pump and signal modes is optimal for high conversion rates. A coupling scheme based on our earlier work [F. Sedlmeir et al., Phys. Rev. Applied 7, 024029 (2017)] is then implemented experimentally to verify this improvement. Thereby, we are able to improve on the efficiency of SHG by more than an order of magnitude by selectively outcoupling using a LN prism, utilizing the birefringence of it and the resonator in kind. This method is also applicable to other nonlinear processes in WGM resonators.

Polarimetric purity and the concept of degree of polarization

José J. Gil, Andreas Norrman, Ari T. Friberg, Tero Setälä

The concept of degree of polarization for electromagnetic waves, in its general three-dimensional version, is revisited in the light of the implications of the recent findings on the structure of polarimetric purity and of the existence of nonregular states of polarization [J. J. Gil et al., Phys Rev. A 95, 053856 (2017)]. From the analysis of the characteristic decomposition of a polarization matrix R into an incoherent convex combination of (1) a pure state Rp, (2) a middle state Rm given by an equiprobable mixture of two eigenstates of R, and (3) a fully unpolarized state Ru−3D, it is found that, in general, Rm exhibits nonzero circular and linear degrees of polarization. Therefore, the degrees of linear and circular polarization of R cannot always be assigned to the single totally polarized component Rp. It is shown that the parameter P3D proposed formerly by Samson [J. C. Samson, Geophys. J. R. Astron. Soc. 34, 403 (1973)] takes into account, in a proper and objective form, all the contributions to polarimetric purity, namely, the contributions to the linear and circular degrees of polarization of R as well as to the stability of the plane containing its polarization ellipse. Consequently, P3D constitutes a natural representative of the degree of polarimetric purity. Some implications for the common convention for the concept of two-dimensional degree of polarization are also analyzed and discussed.

Simple factorization of unitary transformations

Hubert de Guise, Olivia Di Matteo, Luis Sanchez-Soto

We demonstrate a method for general linear optical networks that allows one to factorize any SU(n) matrix in terms of two SU(n−1) blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an efficient way, ending in a tidy arrangement of SU(2) transformations. The method hinges only on a linear relationship between input and output states, and can thus be applied to a variety of scenarios, such as microwaves, acoustics, and quantum fields.

A Holography-Based Modal Wavefront Sensor for the Precise Positioning of a Light Emitter Using a High-Resolution Computer-Generated Hologram

Florian Loosen, Johannes Stehr, Lucas Alber, Irina Harder, Norbert Lindlein

In certain applications, modal wavefront sensors (MWFSs) can outperform zonal wavefront sensors, which are widely used due to their high flexibility. In this paper, a holography-based MWFS as described is developed for the fast position control of a light emitter in a deep parabolic mirror. The light source is located in the vicinity of the focal point. Instead of Zernike polynomials, more complex phase functions, which are related to certain dislocations of the light source are used as detector modes. The performance of the sensor is verified with a test setup, where the test wavefront is generated by a spatial light modulator instead of a real parabolic mirror. The design and fabrication of the required high-resolution holographic element is described and an easy way of multiplexing several single mode sensors is demonstrated.

Mutual Unbiasedness in Coarse-Grained Continuous Variables

Daniel S. Tasca, Piero Sánchez, Stephen P. Walborn, Łukasz Rudnicki

The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of “standard” coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.

Broadband bright twin beams and their upconversion

Maria Chekhova, Semen Germanskiy, Dmitri Horoshko, Galiya Kitaeva, Mikhail Kolobov, Gerd Leuchs, Chris Phillips, Pavel Prudkovskii

We report on the observation of broadband (40 THz) bright twin beams through high-gain parametric downconversion in an aperiodically poled lithium niobate crystal. The output photon number is shown to scale exponentially with the pump power and not with the pump amplitude, as in homogeneous crystals. Photon number correlations and the number of frequency/temporal modes are assessed by spectral covariance measurements. By using sum-frequency generation on the surface of a non-phase-matched crystal, we measure a cross-correlation peak with the temporal width of 90 fs.

Quantum Error-Correcting Codes for Qudit Amplitude Damping

Markus Grassl, Linghang Kong, Zhaohui Wei, Zhang-Qi Yin, Bei Zeng

Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom or energy dissipation of a bosonic system at zero temperature. We discuss quantum error-correcting codes adapted to amplitude damping channels for higher dimensional systems (qudits). For multi-level atoms, we consider a natural kind<br>of decay process, and for bosonic systems,we consider the qudit amplitude damping channel obtained by truncating the Fock basis of the bosonic modes to a<br>certain maximum occupation number. We construct families of single-error-correcting quantum codes that can be used for both cases. Our codes have larger code dimensions than the previously known<br>single-error-correcting codes of the same lengths. Additionally, we present families of multi-error correcting codes for these two channels, as well as<br>generalizations of our construction technique to error-correcting codes for the qutrit V and Lambda channels.<br>

Printing of Large-Scale, Flexible, Long-Term Stable Dielectric Mirrors with Suppressed Side Interferences

Carina Bronnbauer, Arne Riecke, Marius Adler, Julian Hornich, Gerhard Schunk, Christoph J. Brabec, Karen Forberich

Dielectric mirrors are wavelength-selective mirrors which are based on thin film interference effects. Their optical band can precisely be adjusted in width, position, and reflectance by the refractive index of the applied materials, the layers' thicknesses, and the amount of deposited layers. Nowadays, they are a well-known light management tool for efficiency enhancement in, for example, semitransparent organic solar cells (OSCs) and light guiding in organic light-emitting diodes (OLEDs). However, most of the dielectric mirrors are still fabricated by lab-scale techniques such as spin-coating or physical vapor deposition under vacuum. Large-scale, fully printed (maximum 20 x 20 cm(2)) dielectric mirrors with adjustable reflectance characteristics are fabricated, using temperatures of maximum 50 degrees C and alcohol-based inks. According to the moderate processing conditions they can be easily deposited not only on rigid glass substrates but also on flexible foils. They show high stability against humidity, light irradiation, and temperature, positioning themselves as good candidates for applications in OLEDs and OSCs. Eventually, by simulations and experiments it is verified that a moderate degree of variations in layer thickness and surface roughness can suppress side interference fringes, while not impacting the main transmittance minimum or the main reflection maximum, respectively.

"Twisted' electrons

Hugo Larocque, Ido Kaminer, Vincenzo Grillo, Gerd Leuchs, Miles J. Padgett, Robert W. Boyd, Mordechai Segev, Ebrahim Karimi

Electrons have played a significant role in the development of many fields of physics during the last century. The interest surrounding them mostly involved their wave-like features prescribed by the quantum theory. In particular, these features correctly predict the behaviour of electrons in various physical systems including atoms, molecules, solid-state materials, and even in free space. Ten years ago, new breakthroughs were made, arising from the new ability to bestow orbital angular momentum (OAM) to the wave function of electrons. This quantity, in conjunction with the electron's charge, results in an additional magnetic property. Owing to these features, OAM-carrying, or twisted, electrons can effectively interact with magnetic fields in unprecedented ways and have motivated materials scientists to find new methods for generating twisted electrons and measuring their OAM content. Here, we provide an overview of such techniques along with an introduction to the exciting dynamics of twisted electrons.

Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, Luis Sanchez-Soto

We establish the multiparameter quantum Cramér-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright sources, the Cramér-Rao bound is independent of the source separation, which confirms that the Rayleigh resolution limit is just an artifact of the<br>conventional direct imaging and can be overcome with an adequate strategy. For the general case of unequally bright sources, the amount of information one can<br>gain about the separation falls to zero, but we show that there is always a quadratic improvement in an optimal detection in comparison with the intensity measurements. This advantage can be of utmost important in realistic scenarios, such as observational astronomy.

Quantum metrology at the limit with extremal Majorana constellations

F. Bouchard, P. de la Hoz, G. Bjork, R. W. Boyd, Markus Grassl, Z. Hradil, E. Karimi, A. B. Klimov, Gerd Leuchs, et al.

Quantum metrology allows for a tremendous boost in the accuracy of measurement of diverse physical parameters. The estimation of a rotation<br>constitutes a remarkable example of this quantum-enhanced precision. The recently introduced Kings of Quantumness are especially germane for this task<br>when the rotation axis is unknown, as they have a sensitivity independent of that axis and they achieve a Heisenberg-limit scaling. Here, we report the<br>experimental realization of these states by generating up to 21-dimensional orbital angular momentum states of single photons, and confirm their high metrological abilities.<br>

Fibonacci-Lucas SIC-POVMs

Markus Grassl, Andrew J. Scott

We present a conjectured family of SIC-POVMs which have an additional symmetry group whose size is growing with the dimension. The symmetry group is related to Fibonacci numbers, while the dimension is related to Lucas numbers. The conjecture is supported by exact solutions for dimensions d=4,8,19,48,124,323, as well as a numerical solution for dimension d=844.

Unraveling beam self-healing

Andrea Aiello, Girish S. Agarwal, Martin Paur, Bohumil Stoklasa, Zdenek Hradil, Jaroslav Rehacek, Pablo de la Hoz, Gerd Leuchs, Luis L. Sanchez-Soto

We show that, contrary to popular belief, diffraction-free beams not only may reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon Shack-Hartmann wave front reconstruction. We believe that these results can open new avenues in this field. (C) 2017 Optical Society of America

Efficient tomography with unknown detectors

L. Motka, M. Paur, J. Rehacek, Z. Hradil, L. L. Sanchez-Soto

We compare the two main techniques used for estimating the state of a physical system from unknown measurements: standard detector tomography and data-pattern tomography. Adopting linear inversion as a fair benchmark, we show that the difference between these two protocols can be traced back to the nonexistence of the reverse-order law for pseudoinverses. We capitalize on this fact to identify regimes where the data-pattern approach outperforms the standard one and vice versa. We corroborate these conclusions with numerical simulations of relevant examples of quantum state tomography.

Invariant Perfect Tensors

Youning Li, Muxin Han, Markus Grassl, Bei Zeng

Invariant tensors are states in the SU(2) tensor product representation that are invariant under the SU(2) action. They play an important role in the study of loop quantum gravity. On the other hand, perfect tensors are highly<br>entangled many-body quantum states with local density matrices maximally mixed. Recently, the notion of perfect tensors recently has attracted a lot of<br>attention in the fields of quantum information theory, condensed matter theory, and quantum gravity. In this work, we introduce the concept of an invariant perfect tensor (IPT), which is a $n$-valent tensor that is both invariant and perfect. We discuss the existence and construction of IPT. For bivalent tensors, the invariant perfect tensor is the unique singlet state for each local dimension. The trivalent invariant perfect tensor also exists and is uniquely given by Wigner's 3j symbol. However, we show that, surprisingly, there does not exist four-valent invariant perfect tensors for any dimension. On the contrary, when the dimension is large, almost all invariant tensors are perfect asymptotically, which is a consequence of the phenomenon of<br>concentration of measure for multipartite quantum states.

Towards optimal quantum tomography with unbalanced homodyning

Yong Siah Teo, Hyunseok Jeong, Luis L. Sanchez-Soto

Balanced homodyning, heterodyning and unbalanced homodyning are the three well-known sampling techniques used in quantum optics to characterize all possible photonic sources in continuous-variable quantum information theory. We show that for all quantum states and all observable-parameter tomography schemes, which includes the reconstructions of arbitrary operator moments and phase-space quasi-distributions, localized sampling with unbalanced homodyning is always tomographically more powerful (gives more accurate estimators) than delocalized sampling with heterodyning. The latter is recently known to often give more accurate parameter reconstructions than conventional marginalized sampling with balanced homodyning. This result also holds for realistic photodetectors with subunit efficiency. With examples from first- through fourth-moment tomography, we demonstrate that unbalanced homodyning can outperform balanced homodyning when heterodyning fails to do so. This new benchmark takes us one step towards optimal continuous-variable tomography with conventional photodetectors and minimal experimental components.

Focusing characteristics of a 4 pi parabolic mirror light-matter interface

Lucas Alber, Martin Fischer, Marianne Bader, Klaus Mantel, Markus Sondermann, Gerd Leuchs

Background: Focusing with a 4 pi parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror's fabrication process and might introduce errors that reduce the focusing quality. Methods: To determine these errors, we experimentally examine the focusing properties of a 4p parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single Yb-174(+) ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap. Results: We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface. Conclusion: Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4p parabolic mirror.

Coarse graining the phase space of N qubits

Olivia Di Matteo, Luis Sanchez-Soto, Gerd Leuchs, Markus Grassl

We develop a systematic coarse graining procedure for systems of N qubits. We exploit the underlying geometrical structures of the associated discrete<br>phase space to produce a coarse-grained version with reduced effective size. Our coarse-grained spaces inherit key properties of the original ones. In<br>particular, our procedure naturally yields a subset of the original measurement operators, which can be used to construct a coarse discrete Wigner function. These operators also constitute a systematic choice of incomplete measurements for the tomographer wishing to probe an intractably large system.

Small sets of complementary observables

Markus Grassl, D. McNulty, L. Mišta, T. Paterek

Two observables are called complementary if preparing a physical object in an eigenstate of one of them yields a completely random result in a measurement of<br>the other. We investigate small sets of complementary observables that cannot be extended by yet another complementary observable. We construct explicit<br>examples of the unextendible sets up to dimension $16$ and conjecture certain small sets to be unextendible in higher dimensions. Our constructions provide<br>three complementary measurements, only one observable away from the ultimate minimum of two observables in the set. Almost all of our examples in finite dimension allow to discriminate pure states from some mixed states, and shed light on the complex topology of the Bloch space of higher-dimensional quantum systems.<br>

Shifting the phase of a coherent beam with a Yb-174(+) ion: influence of the scattering cross section

Martin Fischer, Bharath Srivathsan, Lucas Alber, Markus Weber, Markus Sondermann, Gerd Leuchs

We discuss and measure the phase shift imposed onto a radially polarized light beam when focusing it onto an Yb-174(+) ion. In the derivation of the expected phase shifts, we include the properties of the involved atomic levels. Furthermore, we emphasize the importance of the scattering cross section and its relation to the efficiency for coupling the focused light to an atom. The phase shifts found in the experiment are compatible with the expected ones when accounting for known deficiencies of the focusing optics and the motion of the trapped ion at the Doppler limit of laser cooling (Hensch and Schawlow in Opt Commun 13:68-69,1975).

Generic method for lossless generation of arbitrarily shaped photons

Denis Sych, Valentin Averchenko, Gerd Leuchs

We put forward a generic method that enables lossless generation of pure single photons with arbitrary shape over any degree of freedom or several degrees of freedom simultaneously. The method exploits pairs of entangled photons. One of the photons is the subject for lossy shaping manipulations followed by a specially designed mode-equalizing measurement. A successful measurement outcome heralds the losslessly shaped second photon. The method has three crucial ingredients that define the quantum state of the shaped photon: the initial bipartite state of the photons, modulation of the first photon, and its mode-equalizing detection. We provide a specific recipe with a combination of these ingredients for achieving any desired pure state of the shaped photon.

Fundamental precision limit of a Mach-Zehnder interferometric sensor when one of the inputs is the vacuum

Masahiro Takeoka, Kaushik P. Seshadreesan, Chenglong You, Shuro Izumi, Jonathan P. Dowling

In the lore of quantum metrology, one often hears (or reads) the following no-go theorem: If you put a vacuum into one input port of a balanced Mach-Zehnder interferometer, then no matter what you put into the other input port, and nomatter what your detection scheme, the sensitivity can never be better than the shot-noise limit (SNL). Often the proof of this theorem is cited to be inC. Caves, Phys. Rev. D23, 1693 (1981), but upon further inspection, no such claim is made there. Quantum-Fisher-information-based arguments suggestive of this no-go theorem appear elsewhere in the literature, but are not stated in their full generality. Here we thoroughly explore this no-go theorem and give a rigorous statement: the no-go theorem holds whenever the unknown phase shift is split between both of the arms of the interferometer, but remarkably does not hold when only one arm has the unknown phase shift. In the latter scenario, we provide an explicit measurement strategy that beats the SNL. We also point out that these two scenarios are physically different and correspond to different types of sensing applications.

Complementarity and Polarization Modulation in Photon Interference

Andreas Norrman, Kasimir Blomstedt, Tero Setala, Ari T. Friberg

We derive two general complementarity relations for the distinguishability and visibility of genuine vector-light quantum fields in double-pinhole photon interference involving polarization modulation. The established framework reveals an intrinsic aspect of wave-particle duality of the photon, not previously reported, thus providing deeper insights into foundational quantum interference physics.

Plasmon coherence determination by nanoscattering

Yahong Chen, Andreas Norrman, Sergey A. Ponomarenko, Ari T. Friberg

We present a simple and robust protocol to recover the second-order field correlations of polychromatic, statistically stationary surface plasmon polaritons (SPPs) from a spectrum measurement in the far zone of a dipolar nanoscatterer. The recovered correlations carry comprehensive information about the spectral, spatial, and temporal coherence of the SPPs. We also introduce and exemplify for the first time, to the best of our knowledge, the two-point Stokes parameters associated with partially coherent SPP fields. (C) 2017 Optical Society of America

Some results on the structure of constacyclic codes and new linear codes over GF(7) from quasi-twisted codes

Nuh Aydin, Nicholas Connolly, Markus Grassl

One of the most important and challenging problems in coding theory is to construct codes with good parameters. There are various methods to construct codes with the best possible parameters. A promising and fruitful approach has been to focus on the class of quasi-twisted (QT) codes which includes constacyclic codes as a special case. This class of codes is known to contain many codes with good parameters. Although constacyclic codes and QT codes have been the subject of numerous studies and computer searches over the last few decades, we have been able to discover a new fundamental result about the structure of constacyclic codes which was instrumental in our comprehensive search method for new QT codes over GF(7). We have been able to find 41 QT codes with better parameters than the previously best known linear codes. Furthermore, we derived a number of additional new codes via Construction X as well as standard constructions, such as shortening and puncturing.

Experimental detection of entanglement polytopes via local filters

Yuan-Yuan Zhao, Markus Grassl, Bei Zeng, Guo-Yong Xiang, Chao Zhang, Chuan-Feng Li, Guang-Can Guo

Quantum entanglement, resulting in correlations between subsystems that are stronger than any possible classical correlation, is one of the mysteries of quantum mechanics. Entanglement cannot be increased by any local operation, and for a sufficiently large many-body quantum system there exist infinitely many different entanglement classes, i. e., states that are not related by stochastic local operations and classical communications. On the other hand, the method of entanglement polytopes results in finitely many coarse-grained types of entanglement that can be detected by only measuring single-particle spectra. We find, however, that with high probability the local spectra lie in more than one polytope, hence providing only partial information about the entanglement type. To overcome this problem, we propose to additionally use so-called local filters, which are non-unitary local operations. We experimentally demonstrate the detection of entanglement polytopes in a four-qubit system. Using local filters we can distinguish the entanglement type of states with the same single particle spectra, but which belong to different polytopes.

Extracting the physical sector of quantum states

D. Mogilevtsev, Y. S. Teo, J. Rehacek, Z. Hradil, J. Tiedau, R. Kruse, G. Harder, C. Silberhorn, L. L. Sanchez-Soto

The physical nature of any quantum source guarantees the existence of an effective Hilbert space of finite dimension, the physical sector, in which its state is completely characterized with arbitrarily high accuracy. The extraction of this sector is essential for state tomography. We show that the physical sector of a state, defined in some pre-chosen basis, can be systematically retrieved with a procedure using only data collected from a set of commuting quantum measurement outcomes, with no other assumptions about the source. We demonstrate the versatility and efficiency of the physical-sector extraction by applying it to simulated and experimental data for quantum light sources, as well as quantum systems of finite dimensions.

Lempel-Ziv Complexity of Photonic Quasicrystals

Juan J. Monzon, Angel Felipe, Luis L. Sanchez-Soto

The properties of one-dimensional photonic quasicrystals ultimately rely on their nontrivial long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. Here, we assess the quasicrystal structural features in terms of the Lempel-Ziv complexity. This is an easily calculable quantity that has proven to be useful for describing patterns in a variety of systems. One feature of great practical relevance is that it provides a reliable measure of how hard it is to create the structure. Using the generalized Fibonacci quasicrystals as our thread, we give analytical fitting formulas for the dependence of the optical response with the complexity.

Optimally cloned binary coherent states

C. R. Mueller, G. Leuchs, Ch. Marquardt, U. L. Andersen

Binary coherent state alphabets can be represented in a two-dimensional Hilbert space. We capitalize this formal connection between the otherwise distinct domains of qubits and continuous variable states to map binary phase-shift keyed coherent states onto the Bloch sphere and to derive their quantum-optimal clones. We analyze the Wigner function and the cumulants of the clones, and we conclude that optimal cloning of binary coherent states requires a nonlinearity above second order. We propose several practical and near-optimal cloning schemes and compare their cloning fidelity to the optimal cloner.

Free-space quantum links under diverse weather conditions

D. Vasylyev, A. A. Semenov, W. Vogel, K. Guenthner, A. Thurn, O. Bayraktar, Ch. Marquardt

Free-space optical communication links are promising channels for establishing secure quantum communication. Here we study the transmission of nonclassical light through a turbulent atmospheric link under diverse weather conditions, including rain or haze. To include these effects, the theory of light transmission through atmospheric links in the elliptic-beam approximation presented by Vasylyev et al. [D. Vasylyev et al., Phys. Rev. Lett. 117, 090501 (2016)] is further generalized. It is demonstrated, with good agreement between theory and experiment, that low-intensity rain merely contributes additional deterministic losses, whereas haze also introduces additional beam deformations of the transmitted light. Based on these results, we study theoretically the transmission of quadrature squeezing and Gaussian entanglement under these weather conditions.

High-dimensional intracity quantum cryptography with structured photons

Alicia Sit, Frederic Bouchard, Robert Fickler, Jeremie Gagnon-Bischoff, Hugo Larocque, Khabat Heshami, Dominique Elser, Christian Peuntinger, Kevin Guenthner, et al.

Quantum key distribution (QKD) promises information-theoretically secure communication and is already on the verge of commercialization. The next step will be to implement high-dimensional protocols in order to improve noise resistance and increase the data rate. Hitherto, no experimental verification of high-dimensional QKD in the singlephoton regime has been conducted outside of the laboratory. Here, we report the realization of such a single-photon QKD system in a turbulent free-space link of 0.3 km over the city of Ottawa, taking advantage of both the spin and orbital angular momentum photonic degrees of freedom. This combination of optical angular momenta allows us to create a 4-dimensional quantum state; wherein, using a high-dimensional BB84 protocol, a quantum bit error rate of 11% was attained with a corresponding secret key rate of 0.65 bits per sifted photon. In comparison, an error rate of 5% with a secret key rate of 0.43 bits per sifted photon is achieved for the case of 2-dimensional structured photons. We thus demonstrate that, even through moderate turbulence without active wavefront correction, high-dimensional photon states are advantageous for securely transmitting more information. This opens the way for intracity high-dimensional quantum communications under realistic conditions. (C) 2017 Optical Society of America

Free-space propagation of high-dimensional structured optical fields in an urban environment

Martin P. J. Lavery, Christian Peuntinger, Kevin Guenthner, Peter Banzer, Dominique Elser, Robert W. Boyd, Miles J. Padgett, Christoph Marquardt, Gerd Leuchs

Spatially structured optical fields have been used to enhance the functionality of a wide variety of systems that use light for sensing or information transfer. As higher-dimensional modes become a solution of choice in optical systems, it is important to develop channel models that suitably predict the effect of atmospheric turbulence on these modes. We investigate the propagation of a set of orthogonal spatial modes across a free-space channel between two buildings separated by 1.6 km. Given the circular geometry of a common optical lens, the orthogonal mode set we choose to implement is that described by the Laguerre-Gaussian (LG) field equations. Our study focuses on the preservation of phase purity, which is vital for spatial multiplexing and any system requiring full quantum-state tomography. We present experimental data for the modal degradation in a real urban environment and draw a comparison to recognized theoretical predictions of the link. Our findings indicate that adaptations to channel models are required to simulate the effects of atmospheric turbulence placed on high-dimensional structured modes that propagate over a long distance. Our study indicates that with mitigation of vortex splitting, potentially through precorrection techniques, one could overcome the challenges in a real point-to-point free-space channel in an urban environment.

Quantum-limited measurements of optical signals from a geostationary satellite

Kevin Guenthner, Imran Khan, Dominique Elser, Birgit Stiller, Oemer Bayraktar, Christian R. Mueller, Karen Saucke, Daniel Troendle, Frank Heine, et al.

The measurement of quantum signals that travel through long distances is fundamentally and technologically interesting. We present quantum-limited coherent measurements of optical signals that are sent from a satellite in geostationary Earth orbit to an optical ground station. We bound the excess noise that the quantum states could have acquired after having propagated 38,600 km through Earth's gravitational potential, as well as its turbulent atmosphere. Our results indicate that quantum communication is feasible, in principle, in such a scenario, highlighting the possibility of a global quantum key distribution network for secure communication. (C) 2017 Optical Society of America

Quantum communication with coherent states of light

Imran Khan, Dominique Elser, Thomas Dirmeier, Christoph Marquardt, Gerd Leuchs

Quantum communication offers long-term security especially, but not only, relevant to government and industrial users. It is worth noting that, for the first time in the history of cryptographic encoding, we are currently in the situation that secure communication can be based on the fundamental laws of physics ( information theoretical security) rather than on algorithmic security relying on the complexity of algorithms, which is periodically endangered as standard computer technology advances. On a fundamental level, the security of quantum key distribution (QKD) relies on the non-orthogonality of the quantum states used. So even coherent states are well suited for this task, the quantum states that largely describe the light generated by laser systems. Depending on whether one uses detectors resolving single or multiple photon states or detectors measuring the field quadratures, one speaks of, respectively, a discrete- or a continuous-variable description. Continuous-variable QKD with coherent states uses a technology that is very similar to the one employed in classical coherent communication systems, the backbone of today's Internet connections. Here, we review recent developments in this field in two connected regimes: (i) improving QKD equipment by implementing front-end telecom devices and (ii) research into satellite QKD for bridging long distances by building upon existing optical satellite links. This article is part of the themed issue 'Quantum technology for the 21st century'.

Temporal and spectral properties of quantum light

B. Stiller, U. Seyfarth, G. Leuchs, C. Fabre, V. Sandoghdar, N. Treps, L.F. Cugliandolo

Orbital angular momentum modes of high-gain parametric down-conversion

Lina Beltran, Gaetano Frascella, Angela M. Perez, Robert Fickler, Polina R. Sharapova, Mathieu Manceau, Olga V. Tikhonova, Robert W. Boyd, Gerd Leuchs, et al.

Light beams with orbital angular momentum (OAM) are convenient carriers of quantum information. They can. also be. used for imparting rotational motion to particles and providing. high resolution in imaging. Due to the conservation of OAM in parametric down-conversion (PDC), signal and idler photons generated at low gain have perfectly anti-correlated OAM values. It is interesting to study the OAM properties of high-gain PDC, where the same OAM modes can be populated with large, but correlated, numbers of photons. Here we investigate the OAM spectrum of high-gain PDC and show that the OAM mode content can be controlled by varying the pump power and the configuration of the source. In our experiment, we use a source consisting of two nonlinear crystals separated by an air gap. We discuss the OAM properties of PDC radiation emitted by this source and suggest possible modifications.

New self-dual additive F_4-codes constructed from circulant graphs

Markus Grassl, Masaaki Harada

In order to construct quantum [[n, 0, d]] codes for (n, d) = (56, 15), (57, 15), (58, 16), (63, 16), (67, 17), (70, 18), (71, 18), (79, 19), (83, 20), (87, 20), (89, 21), (95, 20), we construct self-dual additive F-4-codes of length n and minimum weight d from circulant graphs. The quantum codes with these parameters are constructed for the first time. (C) 2016 Elsevier B.V. All rights reserved.

Optimal measurements for resolution beyond the Rayleigh limit

J. Rehacek, M. Paur, B. Stoklasa, Z. Hradil, L. L. Sanchez-Soto

We establish the conditions to attain the ultimate resolution predicted by quantum estimation theory for the case of two incoherent point sources using a linear imaging system. The solution is closely related to the spatial symmetries of the detection scheme. In particular, for real symmetric point spread functions, any complete set of projections with definite parity achieves the goal. (C) 2017 Optical Society of America

Roadmap on structured light

Halina Rubinsztein-Dunlop, Andrew Forbes, M. V. Berry, M. R. Dennis, David L. Andrews, Masud Mansuripur, Cornelia Denz, Christina Alpmann, Peter Banzer, et al.

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

Multiphoton Effects Enhanced due to Ultrafast Photon-Number Fluctuations

Kirill Yu. Spasibko, Denis A. Kopylov, Victor L. Krutyanskiy, Tatiana V. Murzina, Gerd Leuchs, Maria V. Chekhova

The rate of an n-photon effect generally scales as the nth order autocorrelation function of the incident light, which is high for light with strong photon-number fluctuations. Therefore, "noisy" light sources are much more efficient for multiphoton effects than coherent sources with the same mean power, pulse duration, and repetition rate. Here we generate optical harmonics of the order of 2-4 from a bright squeezed vacuum, a state of light consisting of only quantum noise with no coherent component. We observe up to 2 orders of magnitude enhancement in the generation of optical harmonics due to ultrafast photon-number fluctuations. This feature is especially important for the nonlinear optics of fragile structures, where the use of a noisy pump can considerably increase the effect without overcoming the damage threshold.

Dimensionality of random light fields

Andreas Norrman, Ari T. Friberg, Jose J. Gil, Tero Setala

Background: The spectral polarization state and dimensionality of random light are important concepts in modern optical physics and photonics. Methods: By use of space-frequency domain coherence theory, we establish a rigorous classification for the electricfield vector to oscillate in one, two, or three spatial dimensions. Results: We also introduce a new measure, the polarimetric dimension, to quantify the dimensional character of light. The formalism is utilized to show that polarized three-dimensional light does not exist, while an evanescent wave generated in total internal reflection generally is a genuine three-dimensional light field. Conclusions: The framework we construct advances the polarization theory of random light and it could be beneficial for near-field optics and polarization-sensitive applications involving complex-structured light fields.

Experimental demonstration of negative-valued polarization quasiprobability distribution

K. Yu. Spasibko, M. V. Chekhova, F. Ya. Khalili

Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for position and momentum. Most notably, they both give correct one-dimensional marginal probability distributions and therefore represent the natural choice for the probability distributions in classical hidden-variable models. In this context, negativity of the Wigner function is considered as proof of nonclassicality for a quantum state. On the contrary, the polarization quasiprobability distribution demonstrates negativity for all quantum states. This feature comes from the discrete nature of Stokes variables; however, it was not observed in previous experiments, because they were performed with photon-number averaging detectors. Here we reconstruct the polarization quasiprobability distribution of a coherent state with photon-number resolving detectors, which allows us to directly observe for the first time its negativity. Furthermore we derive a theoretical polarization quasiprobability distribution for any linearly polarized quantum state.

Free space excitation of coupled Anderson-localized modes in photonic crystal waveguides with polarization tailored beam

Ali Mahdavi, Paul Roth, Jolly Xavier, Taofiq K. Paraiso, Peter Banzer, Frank Vollmer

We experimentally demonstrate free space excitation of coupled Anderson-localized modes in photonic crystal (PhC) line-defect waveguides (W1) with polarization tailored beams. The corresponding light beam is tightly focused on a pristine W1, and out-of-plane scattering is imaged. By integrating the scattering spectra along the guide, at the W1 modal cut-off, Anderson-localized cavities are observed due to residual W1 fabrication-disorder. Their spectral lines exhibit high quality Q factors up to 2 x 10(5). The incident beam polarization and scattering intensities of the localized modes characterize the efficiency of free-space coupling. The coupling is studied for linearly and radially polarized input beams and for different input coupling locations along the W1 guide. The proposed coupling scheme is particularly attractive for excitation of PhC waveguide modes and Anderson-localized cavities by beam steering and scanning microscopy for sensing applications. Published by AIP Publishing.

Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer

Mathieu Manceau, Gerd Leuchs, Farid Khalili, Maria Chekhova

In an unseeded SU(1,1) interferometer composed of two cascaded degenerate parametric amplifiers, with direct detection at the output, we demonstrate a phase sensitivity overcoming the shot noise limit by 2.3 dB. The interferometer is strongly unbalanced, with the parametric gain of the second amplifier exceeding the gain of the first one by a factor of 2, which makes the scheme extremely tolerant to detection losses. We show that by increasing the gain of the second amplifier, the phase supersensitivity of the interferometer can be preserved even with detection losses as high as 80%. This finding can considerably improve the state-of-the-art interferometry, enable sub-shot-noise phase sensitivity in spectral ranges with inefficient detection, and allow extension to quantum imaging.

Discrete phase-space structures and Wigner functions for N qubits

C. Munoz, A. B. Klimov, L. Sanchez-Soto

We further elaborate on a phase-space picture for a system of N qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and different entanglement properties. We discuss the construction of discrete covariant Wigner functions for these bundles and provide several illuminating examples.

Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing

Mathieu Manceau, Farid Khalili, Maria Chekhova

The sensitivity properties of an SU(1,1) interferometer made of two cascaded parametric amplifiers, as well as of an ordinary SU(2) interferometer preceded by a squeezer and followed by an anti-squeezer, are theoretically investigated. Several possible experimental configurations are considered, such as the absence or presence of a seed beam, direct or homodyne detection scheme. In all cases we formulate the optimal conditions to achieve phase super-sensitivity, meaning a sensitivity overcoming the shotnoise limit. Weshow that for a given gain of the first parametric amplifier, unbalancing the interferometer by increasing the gain of the second amplifier improves the interferometer properties. In particular, a broader super-sensitivity phase range and a better overall sensitivity can be achieved by gain unbalancing.

Linear and angular momenta in tightly focused vortex segmented beams of light

Martin Neugebauer, Andrea Aiello, Peter Banzer

We investigate the linear momentum density of light, which can be decomposed into spin and orbital parts, in the complex three-dimensional field distributions of tightly focused vortex segmented beams. The chosen angular spectrum exhibits two spatially separated vortices of opposite charge and orthogonal circular polarization to generate phase vortices in a meridional plane of observation. In the vicinity of those vortices, regions of negative orbital linear momentum occur. Besides these phase vortices, the occurrence of transverse orbital angular momentum manifests in a vortex charge-dependent relative shift of the energy density and linear momentum density.

Superiority of heterodyning over homodyning: An assessment with quadrature moments

Y. S. Teo, C. R. Mueller, H. Jeong, Z. Hradil, J. Rehacek, L. L. Sanchez-Soto

We examine the moment-reconstruction performance of both the homodyne and heterodyne (doublehomodyne) measurement schemes for arbitrary quantum states and introduce moment estimators that optimize the respective schemes for any given data. In the large-data limit, these estimators are as efficient as the maximum-likelihood estimators. We then illustrate the superiority of the heterodyne measurement for the reconstruction of the first and second moments by analyzing Gaussian states and many other significant nonclassical states. Finally, we present an extension of our theories to two-mode sources, which can be straightforwardly generalized to all other multimode sources.

Progress toward optimal quantum tomography with unbalanced homodyning

Y. S. Teo, H. Jeong, L. L. Sanchez-Soto

Balanced homodyning, heterodyning, and unbalanced homodyning are three well-known sampling techniques used in quantum optics to characterize photonic sources in the continuous-variable regime. We show that for all quantum states and all observable-parameter tomography schemes, which includes reconstructions of arbitrary operator moments and phase-space quasidistributions, localized sampling with unbalanced homodyning is always tomographically more powerful (gives more accurate estimators) than delocalized sampling with heterodyning. The latter is recently known to often give more accurate parameter reconstructions than conventional marginalized sampling with balanced homodyning. This result also holds for realistic photodetectors with subunit efficiency. With examples from first-through fourth-moment tomography, we demonstrate that unbalanced homodyning can outperform balanced homodyning when heterodyning fails to do so. This new benchmark takes us one step towards optimal continuous-variable tomography with conventional photodetectors and minimal experimental components.

Polarization-Selective Out-Coupling of Whispering-Gallery Modes

Florian Sedlmeir, Matthew R. Foreman, Ulrich Vogl, Richard Zeltner, Gerhard Schunk, Dmitry V. Strekalov, Christoph Marquardt, Gerd Leuchs, Harald G. L. Schwefel

Whispering-gallery mode (WGM) resonators are an important platform for linear, nonlinear, and quantum optical experiments. In such experiments, independent control of in-coupling and out-coupling rates to different modes can lead to higher conversion efficiencies and greater flexibility in the generation of nonclassical states based on parametric down-conversion. In this work, we introduce a scheme that enables selective out-coupling of WGMs belonging to a specific polarization family, while the orthogonally polarized modes remain largely unperturbed. Our technique utilizes material birefringence in both the resonator and the coupler such that a negative (positive) birefringence allows for polarization-selective coupling to TE (TM) WGMs. We formulate a refined coupling condition suitable for describing the case where the refractive indices of the resonator and the coupler are almost the same, from which we derive a criterion for polarization-selective coupling. Finally, we experimentally demonstrate our proposed method using a lithium niobate disk resonator coupled to a lithium niobate prism, where we show a 22-dB suppression of coupling to TM modes relative to TE modes.

Temporal shaping of single photons enabled by entanglement

Valentin Averchenko, Denis Sych, Gerhard Schunk, Ulrich Vogl, Christoph Marquardt, Gerd Leuchs

We present a method to produce pure single photons with an arbitrary designed temporal shape in a heralded way. As an indispensable resource, the method uses pairs of time-energy entangled photons. One photon of a pair undergoes temporal amplitude-phase modulation according to the desired shape. Subsequent frequency-resolved detection of the modulated photon heralds its entangled counterpart in a pure quantum state. The temporal shape of the heralded photon is indirectly affected by the modulation in the heralding arm. We derive conditions for which the shape of the heralded photon is given by the modulation function. The method can be implemented with various sources of time-energy entangled photons. In particular, using entangled photons from parametric down-conversion the method provides a simple means to generate pure shaped photons with an unprecedented broad range of temporal durations, from tenths of femtoseconds to microseconds. This shaping of single photons will push forward the implementation of scalable multidimensional quantum information protocols, efficient photon-matter coupling, and quantum control at the level of single quanta.

Characterization and shaping of the time-frequency Schmidt mode spectrum of bright twin beams generated in gas-filled hollow-core photonic crystal fibers

M. A. Finger, N. Y. Joly, P. St. J. Russell, M. V. Chekhova

We vary the time-frequency mode structure of ultrafast pulse-pumped modulational instability (MI) twin beams in an argon-filled hollow-core kagome-style photonic crystal fiber by adjusting the pressure, pump pulse chirp, fiber length, and parametric gain. Compared to solid-core systems, the pressure-dependent dispersion landscape brings increased flexibility to the tailoring of frequency correlations, and we demonstrate that the pump pulse chirp can be used to tune the joint spectrum of femtosecond-pumped.(3) sources. We also characterize the resulting mode content, not only by measuring the multimode second-order correlation function g((2)), but also by directly reconstructing the shapes and weights of time-frequency Schmidt (TFS) modes. We show that the number of modes directly influences the shot-to-shot pulse-energy and spectral-shape fluctuations in MI. Using this approach we control and monitor the number of TFS modes within the range from 1.3 to 4 using only a single fiber.

Unconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels

Masahiro Takeoka, Kaushik P. Seshadreesan, Mark M. Wilde

We consider quantum key distribution (QKD) and entanglement distribution using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. A practical implication of our result is that the capacity region demonstrated drastically improves upon rates achievable using a naive time-sharing strategy, which has been employed in previously demonstrated network QKD systems. We show a simple example of a broadcast QKD protocol overcoming the limit of the point-to-point strategy. Our result is thus an important step toward opening a new framework of network channel-based quantum communication technology.

New self-dual additive F4-codes constructed from circulant graphs

Markus Grassl, Masaaki Harada

In order to construct quantum [[n,0,d]] codes for (n,d)=(56,15), (57,15), (58,16), (63,16), (67,17), (70,18), (71,18), (79,19), (83,20), (87,20), (89,21), (95,20), we construct self-dual additive F4-codes of length n and minimum weight d from circulant graphs. The quantum codes with these parameters are constructed for the first time.

Autonomous absolute calibration of an ICCD camera in single-photon detection regime

Luo Qi, Felix Just, Gerd Leuchs, Maria V. Chekhova

Intensified charge coupled device (ICCD) cameras are widely used in vari-ous applications such as microscopy, astronomy, spectroscopy. Often they are used as single-photon detectors, with thresholding being an essential part of the readout. In this paper, we measure the quantum efficiency of an ICCD camera in the single-photon de-tection mode using the Klyshko absolute calibration technique. The quantum efficiency is obtained as a function of the threshold value and of the wavelength of the detected light. In addition, we study the homogeneity of the photon sensitivity over the camera chip area. The experiment is performed in the autonomous regime, without using any additional detectors. We therefore demonstrate the self-calibration of an ICCD camera.

Engineering the Frequency Spectrum of Bright Squeezed Vacuum via Group Velocity Dispersion in an SU(1,1) Interferometer

Samuel Lemieux, Mathieu Manceau, Polina R. Sharapova, Olga V. Tikhonova, Robert W. Boyd, Gerd Leuchs, Maria V. Chekhova

Bright squeezed vacuum, a promising tool for quantum information, can be generated by high-gain parametric down-conversion. However, its frequency and angular spectra are typically quite broad, which is undesirable for applications requiring single-mode radiation. We tailor the frequency spectrum of high-gain parametric down-conversion using an SU(1,1) interferometer consisting of two nonlinear crystals with a dispersive medium separating them. The dispersive medium allows us to select a narrow band of the frequency spectrum to be exponentially amplified by high-gain parametric amplification. The frequency spectrum is thereby narrowed from (56.5±0.1) to (1.22±0.02)  THz and, in doing so, the number of frequency modes is reduced from approximately 50 to 1.82±0.02. Moreover, this method provides control and flexibility over the spectrum of the generated light through the timing of the pump.

Hybrid photonic-crystal fiber for single-mode phase matched generation of third harmonic and photon triplets

Andrea Cavanna, Felix Just, Xin Jiang, Gerd Leuchs, Maria V. Chekhova, Philip St. J. Russell, Nicolas Y. Joly

All-fiber systems for third harmonic generation are of great interest because they can be used for the inverse process, namely, the generation of entangled photon triplets. Usually, chromatic dispersion prevents phase matching between the incident and generated radiation when they are both guided in an LP01-like mode. Here, we present a hybrid photonic crystal fiber that has been designed for phase matched third harmonic generation from 1596 to 532 nm in single-lobed modes. The third harmonic radiation is guided by an all-solid bandgap microstructure, while the pump frequency is confined by conventional total internal reflection. The fiber is also suitable for the generation of photon triplet states.

Nonlinear interferometers in quantum optics

M. V. Chekhova, Z. Y. Ou

We review the main works in the field of nonlinear interferometers, which has been developing ever since the start of nonlinear optics and has seen growing interest in recent years due to the applications in quantum information and quantum metrology. Because the class of schemes that are referred to as nonlinear interferometers is too broad, we restrict the consideration to the cases in which crystals, fibers, or atomic systems producing the nonlinear effect are placed inside the interferometer, and only linear phase shifts are imposed. As a nonlinear effect, we consider four-wave mixing and parametric down-conversion, at both low and high gain.

The many facets of the Fabry-Perot

Luis L. Sanchez-Soto, Juan J. Monzon, Gerd Leuchs

Local Sampling of the Wigner Function at Telecom Wavelength with Loss-Tolerant Detection of Photon Statistics

G. Harder, Ch Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, L. L. Sanchez-Soto

We report the experimental point-by-point sampling of the Wigner function for nonclassical states created in an ultrafast pulsed type-II parametric down-conversion source. We use a loss-tolerant time-multiplexed detector based on a fiber-optical setup and a pair of photon-number-resolving avalanche photodiodes. By capitalizing on an expedient data-pattern tomography, we assess the properties of the light states with outstanding accuracy. The method allows us to reliably infer the squeezing of genuine two-mode states without any phase reference.

Influence of the substrate material on the knife-edge based profiling of tightly focused light beams

C. Huber, S. Orlov, P. Banzer, G. Leuchs

The performance of the knife-edge method as a beam profiling technique for tightly focused light beams depends on several parameters, such as the material and height of the knife-pad as well as the polarization and wavelength of the focused light beam under study. Here we demonstrate that the choice of the substrate the knife-pads are fabricated on has a crucial influence on the reconstructed beam projections as well. We employ an analytical model for the interaction of the knife-pad with the beam and report good agreement between our numerical and experimental results. Moreover, we simplify the analytical model and demonstrate, in which way the underlying physical effects lead to the apparent polarization dependent beam shifts and changes of the beamwidth for different substrate materials and heights of the knife-pad. (C) 2016 Optical Society of America

Free-Space Quantum Signatures Using Heterodyne Measurements

Callum Croal, Christian Peuntinger, Bettina Heim, Imran Khan, Christoph Marquardt, Gerd Leuchs, Petros Wallden, Erika Andersson, Natalia Korolkova

Efficient single-photon absorption by a trapped moving atom

N. Trautmann, G. Alber, G. Leuchs

Spontaneous generation of singularities in paraxial optical fields

Andrea Aiello

In nonrelativistic quantum mechanics, the spontaneous generation of singularities in smooth and finite wave functions is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schrodinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields that develop a spatial singularity in the focal point of a weakly focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mechanism may stimulate fruitful research for diverse technological and scientific applications. (C) 2016 Optical Society of America

Resonant photo-ionization of Yb+ to Yb2+

Simon Heugel, Martin Fischer, Vladimir Elman, Robert Maiwald, Markus Sondermann, Gerd Leuchs

We demonstrate the controlled creation of a Yb-174(2+) ion by photo-ionizing Yb-174(+) with weak continuous-wave lasers at ultraviolet wavelengths. The photo-ionization is performed by resonantly exciting transitions of the Yb-174(+) ion in three steps. Starting from an ion crystal of two laser-cooled Yb-174(+) ions localized in a radio-frequency trap, the verification of the ionization process is performed by characterizing the properties of the resulting mixed-species ion-crystal. The obtained results facilitate fundamental studies of physics involving Yb2+ ions.

Unveiling the optical properties of a metamaterial synthesized by electron-beam-induced deposition

P. Wozniak, K. Hoeflich, G. Broenstrup, P. Banzer, S. Christiansen, G. Leuchs

Direct writing using a focused electron beam allows for fabricating truly three-dimensional structures of sub-wavelength dimensions in the visible spectral regime. The resulting sophisticated geometries are perfectly suited for studying light-matter interaction at the nanoscale. Their overall optical response will strongly depend not only on geometry but also on the optical properties of the deposited material. In the case of the typically used metal-organic precursors, the deposits show a substructure of metallic nanocrystals embedded in a carbonaceous matrix. Since gold-containing precursor media are especially interesting for optical applications, we experimentally determine the effective permittivity of such an effective material. Our experiment is based on spectroscopic measurements of planar deposits. The retrieved permittivity shows a systematic dependence on the gold particle density and cannot be sufficiently described using the common Maxwell-Garnett approach for effective medium.

Ring-shaped spectra of parametric downconversion and entangled photons that never meet

Kirill Yu. Spasibko, Denis A. Kopylov, Tatiana V. Murzina, Gerd Leuchs, Maria V. Chekhova

We report on the observation of an unusual type of parametric downconversion. In the regime where collinear degenerate emission is in the anomalous range of group-velocity dispersion, its spectrum is restricted in both angle and wavelength. Detuning from exact collinear-degenerate phase-matching leads to a ring shape of the wavelength-angular spectrum, suggesting a new type of spatiotemporal coherence and entanglement of photon pairs. By imposing a phase varying in a specific way in both angle and wavelength, one can obtain an interesting state of an entangled photon pair, with the two photons being never at the same point at the same time. (C) 2016 Optical Society of America

Detecting the spatial quantum uncertainty of bosonic systems

Vanessa Chille, Nicolas Treps, Claude Fabre, Gerd Leuchs, Christoph Marquardt, Andrea Aiello

Attacks on practical quantum key distribution systems (and how to prevent them)

Nitin Jain, Birgit Stiller, Imran Khan, Dominique Elser, Christoph Marquardt, Gerd Leuchs

With the emergence of an information society, the idea of protecting sensitive data is steadily gaining importance. Conventional encryption methods may not be sufficient to guarantee data protection in the future. Quantum key distribution (QKD) is an emerging technology that exploits fundamental physical properties to guarantee perfect security in theory. However, it is not easy to ensure in practice that the implementations of QKD systems are exactly in line with the theoretical specifications. Such theory-practice deviations can open loopholes and compromise security. Several such loopholes have been discovered and investigated in the last decade. These activities have motivated the proposal and implementation of appropriate countermeasures, thereby preventing future attacks and enhancing the practical security of QKD. This article introduces the so-called field of quantum hacking by summarising a variety of attacks and their prevention mechanisms.

Towards Laser-based Photonic Chip Integrated Quantum Random Number Generators

M. Sabuncu

Lasers are recently being used more frequently in random number generators. The world record in random number generation was broken by the help of lasers. The world's fastest quantum random number generators utilize lasers to tap into the random fluctuations in order to extract true random bit sequences. We investigate a system based on a Nd:YAG laser that potentially generates true random bits at Gbit/s rates. As photonic on chip technologies progress we foresee laser based high speed random number generators integrated on chips. Such a photonic chip will create a revolution in the technology of security devices that employ quantum cryptography techniques for secure communication.

Optical Polarization Mobius Strips and Points of Purely Transverse Spin Density

Thomas Bauer, Martin Neugebauer, Gerd Leuchs, Peter Banzer

Tightly focused light beams can exhibit complex and versatile structured electric field distributions. The local field may spin around any axis including a transverse axis perpendicular to the beams' propagation direction. At certain focal positions, the corresponding local polarization ellipse can even degenerate into a perfect circle, representing a point of circular polarization or C point. We consider the most fundamental case of a linearly polarized Gaussian beam, where-upon tight focusing-those C points created by transversely spinning fields can form the center of 3D optical polarization topologies when choosing the plane of observation appropriately. Because of the high symmetry of the focal field, these polarization topologies exhibit nontrivial structures similar to Mobius strips. We use a direct physical measure to find C points with an arbitrarily oriented spinning axis of the electric field and experimentally investigate the fully three-dimensional polarization topologies surrounding these C points by exploiting an amplitude and phase reconstruction technique.

Lateral spin transport in paraxial beams of light

Martin Neugebauer, Simon Grosche, Sergej Rothau, Gerd Leuchs, Peter Banzer

We investigate the lateral transport of (longitudinal) spin angular momentum in a special polarization tailored light beam composed of a superposition of a y-polarized zero-order and an x-polarized first-order Hermite-Gaussian mode. This phenomenon is linked to the relative Gouy phase shift between the individual modes upon propagation, but can also be interpreted as a geometric phase effect. Experimentally, we demonstrate the implementation of such a mode and measure the spin density upon propagation. (C) 2016 Optical Society of America

Operational meaning of quantum measures of recovery

Tom Cooney, Christoph Hirche, Ciara Morgan, Jonathan P. Olson, Kaushik P. Seshadreesan, John Watrous, Mark M. Wilde

Several information measures have recently been defined that capture the notion of recoverability. In particular, the fidelity of recovery quantifies how well one can recover a system A of a tripartite quantum state, defined on systems ABC, by acting on system C alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. The quantum interactive proof system giving this operational meaning requires four messages exchanged between the prover and verifier, but by forcing the prover to perform actions in superposition, we construct a different proof system that requires only two messages. The result is that the associated decision problem is in QIP(2) and another argument establishes it as hard for QSZK (both classes contain problems believed to be difficult to solve for a quantum computer). We finally prove that the regularized relative entropy of recovery is equal to the optimal type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the type I error is constrained to be no larger than a constant.

A Classical Analog of Random Quantum States

Denis Sych

Polarization-controlled directional scattering for nanoscopic position sensing

Martin Neugebauer, Pawel Wozniak, Ankan Bag, Gerd Leuchs, Peter Banzer

Controlling the propagation and coupling of light to sub-wavelength antennas is a crucial prerequisite for many nanoscale optical devices. Recently, the main focus of attention has been directed towards high-refractive-index materials such as silicon as an integral part of the antenna design. This development is motivated by the rich spectral properties of individual high-refractive-index nanoparticles. Here we take advantage of the interference of their magnetic and electric resonances to achieve strong lateral directionality. For controlled excitation of a spherical silicon nanoantenna, we use tightly focused radially polarized light. The resultant directional emission depends on the antenna's position relative to the focus. This approach finds application as a novel position sensing technique, which might be implemented in modern nanometrology and super-resolution microscopy set-ups. We demonstrate in a proof-of-concept experiment that a lateral resolution in the Angstrom regime can be achieved.

Frequency tuning of single photons from a whispering-gallery mode resonator to MHz-wide transitions

G. Schunk, U. Vogl, F. Sedlmeir, D. V. Strekalov, A. Otterpohl, V. Averchenko, H. G. L. Schwefel, G. Leuchs, Ch. Marquardt

Chiral optical response of planar and symmetric nanotrimers enabled by heteromaterial selection

Peter Banzer, Pawel Wozniak, Uwe Mick, Israel De Leon, Robert W. Boyd

Implementing a neutral-atom controlled-phase gate with a single Rydberg pulse

Rui Han, Hui Khoon Ng, Berthold-Georg Englert

One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on actual experimental scenarios, a gate fidelity higher than 0.99 is achievable. Copyright (C) EPLA, 2016

Quantum technology: from research to application

Wolfgang P. Schleich, Kedar S. Ranade, Christian Anton, Markus Arndt, Markus Aspelmeyer, Manfred Bayer, Gunnar Berg, Tommaso Calarco, Harald Fuchs, et al.

The term quantum physics refers to the phenomena and characteristics of atomic and subatomic systems which cannot be explained by classical physics. Quantum physics has had a long tradition in Germany, going back nearly 100 years. Quantum physics is the foundation of many modern technologies. The first generation of quantum technology provides the basis for key areas such as semiconductor and laser technology. The "new" quantum technology, based on influencing individual quantum systems, has been the subject of research for about the last 20 years. Quantum technology has great economic potential due to its extensive research programs conducted in specialized quantum technology centres throughout the world. To be a viable and active participant in the economic potential of this field, the research infrastructure in Germany should be improved to facilitate more investigations in quantum technology research.

Efficient microwave to optical photon conversion: an electro-optical realization

Alfredo Rueda, Florian Sedlmeir, Michele C. Collodo, Ulrich Vogl, Birgit Stiller, Gerhard Schunk, Dmitry V. Strekalov, Christoph Marquardt, Johannes M. Fink, et al.

Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme, this is impossible because both up-and down-converted sidebands are necessarily present. Here, we demonstrate true single-sideband up-or down-conversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a 3 orders of magnitude improvement of the electro-optical conversion efficiency, reaching 0.1% photon number conversion for a 10 GHz microwave tone at 0.42 mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for nonclassical state conversion and communication. Our conversion bandwidth is larger than 1 MHz and is not fundamentally limited. (C) 2016 Optical Society of America

The duality principle in the presence of postselection

Jonathan Leach, Eliot Bolduc, Filippo M. Miatto, Kevin Piche, Gerd Leuchs, Robert W. Boyd

The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility V of interference fringes and predictability P of paths within a two-alternative system, which are bound by the inequality V-2 + P-2 <= 1. However, if such a system is coupled to its environment, it becomes possible to obtain conditional measures of visibility and predictability, i.e. measures that are conditioned on the state of the environment. We show that in this case, the predictability and visibility values can lead to an apparent violation of the duality principle. We experimentally realize this apparent violation in a controlled manner by enforcing a fair-sampling-like loophole via postselection. This work highlights some of the subtleties that one can encounter while interpreting familiar quantities such as which-alternative information and visibility. While we concentrated on an extreme example, it is of utmost importance to realise that such subtleties might also be present in cases where the results are not obviously violating an algebraic bound, making them harder (but not any less crucial) to detect.

Nonlinear interferometer for tailoring the frequency spectrum of bright squeezed vacuum

T. Sh. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, M. V. Chekhova

We propose a method for tailoring the frequency spectrum of bright squeezed vacuum by generating it in a nonlinear interferometer, consisting of two down-converting nonlinear crystals separated by a dispersive medium. Due to a faster dispersive spreading of higher order Schmidt modes, the spectral width of the radiation at the output is reduced as the length of the dispersive medium is increased. Preliminary results show 30% spectral narrowing.

Low-noise macroscopic twin beams

Timur Sh. Iskhakov, Vladyslav C. Usenko, Radim Filip, Maria V. Chekhova, Gerd Leuchs

Applying a multiphoton-subtraction technique to the two-color macroscopic squeezed vacuum state of light generated via high-gain parametric down-conversion we conditionally prepare a different state of light: bright multimode low-noise twin beams. A lower noise in the sum of the photon numbers opens a possibility to encode information into this variable while keeping the nonclassical character of the state. The obtained results demonstrate up to eightfold suppression of noise in each beam while preserving and even moderately improving the nonclassical photon-number correlations between the beams. The prepared low-noise macroscopic state, containing up to 2000 photons per mode, is not among the Gaussian states achievable through nonlinear optical processes. Apart from that, we suggest a method for measuring quantum efficiency, which is based on the Fano factor measurement. The proposed technique substantially improves the usefulness of twin beams for quantum communication and metrology.

The ubiquitous photonic wheel

Andrea Aiello, Peter Banzer

Evading Vacuum Noise: Wigner Projections or Husimi Samples?

C. R. Mueller, C. Peuntinger, T. Dirmeier, I. Khan, U. Vogl, Ch. Marquardt, G. Leuchs, L. L. Sanchez-Soto, Y. S. Teo, et al.

Optical trapping of nanoparticles by full solid-angle focusing

Vsevolod Salakhutdinov, Markus Sondermann, Luigi Carbone, Elisabeth Giacobino, Alberto Bramati, Gerd Leuchs

Multimode theory of single-photon subtraction

V. Averchenko, C. Jacquard, V. Thiel, C. Fabre, N. Treps

Parsing polarization squeezing into Fock layers

Christian R. Mueller, Lars S. Madsen, Andrei B. Klimov, Luis L. Sanchez-Soto, Gerd Leuchs, Christoph Marquardt, Ulrik L. Andersen

We investigate polarization squeezing in squeezed coherent states with varying coherent amplitudes. In contrast to the traditional characterization based on the full Stokes parameters, we experimentally determine the Stokes vector of each excitation subspace separately. Only for states with a fixed photon number do the methods coincide; when the photon number is indefinite, we parse the state in Fock layers, finding that substantially higher squeezing can be observed in some of the single layers. By capitalizing on the properties of the Husimi Q function, we map this notion onto the Poincare space, providing a full account of the measured squeezing.

Tunable optical parametric generator based on the pump spatial walk-off

Andrea Cavanna, Felix Just, Polina R. Sharapova, Michael Taheri, Gerd Leuchs, Maria V. Chekhova

We suggest a novel optical parametric generator (OPG) in which one of the downconverted beams is spontaneously generated along the Poynting vector of the pump beam. In this configuration, the generation takes advantage of the walk-off of the extraordinary pump, rather than being degraded by it. As a result, the generated signal and idler beams are bright due to a high conversion efficiency, spatially nearly single mode due to the preferred direction of the Poynting vector, tunable over a wide range of wavelengths and broadband. The two beams are also correlated in frequency and in the photon number per pulse. Furthermore, due to their thermal statistics, these beams can be used as a pump to efficiently generate other nonlinear processes. (C) 2016 Optical Society of America

Measuring the modulus of the spatial coherence function using an error tolerant phase shifting algorithm and a continuous lateral shearing interferometer

Irina Harder, Martin Eisner, Reinhard Voelkel, Sergej Rothau, Johannes Schwider, Peter Schwider

The modulus of the degree of coherence can be derived from interference patterns either by using fringes and next neighbour operations or by using several interferograms produced through phase shifting. Here the latter approach will be followed by using a lateral shearing interferometer exploiting a diffractive grating wedge providing a linearly progressive shear. Phase shifting methods offer pixel-oriented evaluations but suffer from instabilities and drifts which is the reason for the derivation of an error immune algorithm. This algorithm will use five pi/2-steps of the reference phase also for the calculation of the modulus of the coherence function. (C) 2016 Optical Society of America

Progress towards practical device-independent quantum key distribution with spontaneous parametric down-conversion sources, on-off photodetectors, and entanglement swapping

Kaushik P. Seshadreesan, Masahiro Takeoka, Masahide Sasaki

Device-independent quantum key distribution (DIQKD) guarantees unconditional security of a secret key without making assumptions about the internal workings of the devices used for distribution. It does so using the loophole-free violation of a Bell's inequality. The primary challenge in realizing DIQKD in practice is the detection loophole problem that is inherent to photonic tests of Bell' s inequalities over lossy channels. We revisit the proposal of Curty and Moroder [Phys.Rev.A 84, 010304(R) (2011)] to use a linear optics-based entanglement-swapping relay (ESR) to counter this problem. We consider realistic models for the entanglement sources and photodetectors: more precisely, (a) polarization-entangled states based on pulsed spontaneous parametric down-conversion sources with infinitely higher-order multiphoton components and multimode spectral structure, and (b) on-off photodetectors with nonunit efficiencies and nonzero dark-count probabilities. We show that the ESR-based scheme is robust against the above imperfections and enables positive key rates at distances much larger than what is possible otherwise.

Quantum-polarization state tomography

Oemer Bayraktar, Marcin Swillo, Carlota Canalias, Gunnar Bjork

We propose and demonstrate a method for quantum-state tomography of qudits encoded in the quantum polarization of N-photon states. This is achieved by distributing N photons nondeterministically into three paths and their subsequent projection, which for N = 1 is equivalent to measuring the Stokes (or Pauli) operators. The statistics of the recorded N-fold coincidences determines the unknown N-photon polarization state uniquely. The proposed, fixed setup manifestly rules out any systematic measurement errors due to moving components and allows for simple switching between tomography of different states, which makes it ideal for adaptive tomography schemes.

Tighter spots of light with superposed orbital-angular-momentum beams

Pawel Wozniak, Peter Banzer, Frederic Bouchard, Ebrahim Karimi, Gerd Leuchs, Robert W. Boyd

The possibility of focusing light to an ever tighter spot has important implications for many applications and fields of optics research, such as nano-optics and plasmonics, laser-scanning microscopy, optical data storage, and many more. The size of lateral features of the field at the focus depends on several parameters, including the numerical aperture of the focusing system, but also the wavelength and polarization, phase and intensity distribution of the input beam. Here, we study the smallest achievable focal feature sizes of coherent superpositions of two copropagating beams carrying opposite orbital angular momentum. We investigate the feature sizes for this class of beams not only in the scalar limit, but also use a fully vectorial treatment to discuss the case of tight focusing. Both our numerical simulations and our experimental results confirm that lateral feature sizes considerably smaller than those of a tightly focused Gaussian light beam can be observed. These findings may pave the way for improving the resolution of imaging systems or may find applications in nano-optics experiments.

Integrated plasmonic metasurfaces for spectropolarimetry

Wei Ting Chen, Peter Torok, Matthew R. Foreman, Chun Yen Liao, Wei-Yi Tsai, Pei Ru Wu, Din Ping Tsai

Plasmonic metasurfaces enable simultaneous control of the phase, momentum, amplitude and polarization of light and hence promise great utility in realization of compact photonic devices. In this paper, we demonstrate a novel chip-scale device suitable for simultaneous polarization and spectral measurements through use of six integrated plasmonic metasurfaces (IPMs), which diffract light with a given polarization state and spectral component into well-defined spatial domains. Full calibration and characterization of our device is presented, whereby good spectral resolution and polarization accuracy over a wavelength range of 500-700 nm is shown. Functionality of our device in a Muller matrix modality is demonstrated through determination of the polarization properties of a commercially available variable waveplate. Our proposed IPM is robust, compact and can be fabricated with a single photolithography step, promising many applications in polarization imaging, quantum communication and quantitative sensing.

Experimental generation of amplitude squeezed vector beams

Vanessa Chille, Stefan Berg-Johansen, Marion Semmler, Peter Banzer, Andrea Aiello, Gerd Leuchs, Christoph Marquardt

We present an experimental method for the generation of amplitude squeezed high-order vector beams. The light is modified twice by a spatial light modulator such that the vector beam is created by means of a collinear interferometric technique. A major advantage of this approach is that it avoids systematic losses, which are detrimental as they cause decoherence in continuous-variable quantum systems. The utilisation of a spatial light modulator (SLM) gives the flexibility to switch between arbitrary mode orders. The conversion efficiency with our setup is only limited by the efficiency of the SLM. We show the experimental generation of Laguerre-Gauss (LG) modes with radial indices 0 or 1 and azimuthal indices up to 3 with complex polarization structures and a quantum noise reduction up to -0.9dB +/- 0.1dB. The corresponding polarization structures are studied in detail by measuring the spatial distribution of the Stokes parameters. (C) 2016 Optical Society of America

Achieving the ultimate optical resolution

Martin Paur, Bohumil Stoklasa, Zdenek Hradil, Luis L. Sanchez-Soto, Jaroslav Rehacek

Optical resolution from Fisher information

L. Motka, B. Stoklasa, M. D'Angelo, P. Facchi, A. Garuccio, Z. Hradil, S. Pascazio, F. V. Pepe, Y. S. Teo, et al.

Single-mode squeezing in arbitrary spatial modes

Marion Semmler, Stefan Berg-Johansen, Vanessa Chille, Christian Gabriel, Peter Banzer, Andrea Aiello, Christoph Marquardt, Gerd Leuchs

As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light. (C) 2016 Optical Society of America

Demonstration of local teleportation using classical entanglement

Diego Guzman-Silva, Robert Bruening, Felix Zimmermann, Christian Vetter, Markus Graefe, Matthias Heinrich, Stefan Nolte, Michael Duparre, Andrea Aiello, et al.

Teleportation describes the transmission of information without transport of neither matter nor energy. For many years, however, it has been implicitly assumed that this scheme is of inherently nonlocal nature, and therefore exclusive to quantum systems. Here, we experimentally demonstrate that the concept of teleportation can be readily generalized beyond the quantum realm. We present an optical implementation of the teleportation protocol solely based on classical entanglement between spatial and modal degrees of freedom, entirely independent of nonlocality. Our findings could enable novel methods for distributing information between different transmission channels and may provide the means to leverage the advantages of both quantum and classical systems to create a robust hybrid communication infrastructure.

Practical Receiver for Optimal Discrimination of Binary Coherent Signals

Denis Sych, Gerd Leuchs

Unconstrained distillation capacities of a pure-loss bosonic broadcast channel

Masahiro Takeoka, Kaushik P. Seshadreesan, Mark M. Wilde

Dielectric tuning and coupling of whispering gallery modes using an anisotropic prism

Matthew R. Foreman, Florian Sedlmeir, Harald G. L. Schwefel, Gerd Leuchs

Nonlinear and quantum optics with whispering gallery resonators

Dmitry V. Strekalov, Christoph Marquardt, Andrey B. Matsko, Harald G. L. Schwefel, Gerd Leuchs

Spatially-controlled laser-induced decoration of 2D and 3D substrates with plasmonic nanoparticles

M. Y. Bashouti, A. V. Povolotckaia, A. V. Povolotskiy, S. P. Tunik, S. H. Christiansen, G. Leuchs, A. A. Manshina

We demonstrate a new approach which can be used for targeted imparting of plasmonic properties for a wide range of different substrates (transparent and non-transparent) which may have any 2D or 3D topological structure created independently in a prior step with some other technology.

30 years of squeezed light generation

Ulrik L. Andersen, Tobias Gehring, Christoph Marquardt, Gerd Leuchs

Squeezed light generation has come of age. Significant advances on squeezed light generation have been made over the last 30 years-from the initial, conceptual experiment in 1985 till today's top-tuned, application-oriented setups. Here we review the main experimental platforms for generating quadrature squeezed light that have been investigated in the last 30 years.

Exotic looped trajectories of photons in three-slit interference

Omar S. Magana-Loaiza, Israel De Leon, Mohammad Mirhosseini, Robert Fickler, Akbar Safari, Uwe Mick, Brian McIntyre, Peter Banzer, Brandon Rodenburg, et al.

Heralded source of bright multi-mode mesoscopic sub-Poissonian light

T. Sh. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, G. Leuchs

In a direct detection scheme, we observed 7.8 dB of twin-beam squeezing for multi-mode two-color squeezed vacuum generated via parametric downconversion. Applying postselection, we conditionally prepared a sub-Poissonian state of light containing 6.3 . 10(5) photons per pulse on the average with the Fano factor 0.63 +/- 0.01. The scheme can be considered as the heralded preparation of pulses with the mean energy varying between tens and hundreds of fJ and the uncertainty considerably below the shot-noise level. Such pulses can be used in metrology (for instance, for radiometer calibration), as well as for probing multi-mode non-linear optical effects. (C) 2016 Optical Society of America

New self-dual additive F4-codes constructed from circulant graphs

Markus Grassl, Masaaki Harada

In order to construct quantum [[n,0,d]] codes for (n,d)=(56,15), (57,15), (58,16), (63,16), (67,17), (70,18), (71,18), (79,19), (83,20), (87,20), (89,21), (95,20), we construct self-dual additive F4-codes of length n and minimum weight d from circulant graphs. The quantum codes with these parameters are constructed for the first time.

Intensity-intensity correlations determined by dimension of quantum state in phase space: P-distribution

Gerd Leuchs, Roy J. Glauber, Wolfgang P Schleich

Strong, spectrally-tunable chirality in diffractive metasurfaces

Israel De Leon, Matthew J. Horton, Sebastian A. Schulz, Jeremy Upham, Peter Banzer, Robert W. Boyd

Metamaterials and metasurfaces provide a paradigm-changing approach for manipulating light. Their potential has been evinced by recent demonstrations of chiral responses much greater than those of natural materials. Here, we demonstrate theoretically and experimentally that the extrinsic chiral response of a metasurface can be dramatically enhanced by near-field diffraction effects. At the core of this phenomenon are lattice plasmon modes that respond selectively to the illumination’s polarization handedness. The metasurface exhibits sharp features in its circular dichroism spectra, which are tunable over a broad bandwidth by changing the illumination angle over a few degrees. Using this property, we demonstrate an ultra-thin circular-polarization sensitive spectral filter with a linewidth of ~10 nm, which can be dynamically tuned over a spectral range of 200 nm. Chiral diffractive metasurfaces, such as the one proposed here, open exciting possibilities for ultra-thin photonic devices with tunable, spin-controlled functionality.

Dimension of quantum phase space measured by photon correlations

Gerd Leuchs, Roy J. Glauber, Wolfgang P Schleich

Microconstriction Arrays for High-Throughput Quantitative Measurements of Cell Mechanical Properties

Janina R. Lange, Julian Steinwachs, Thorsten Kolb, Lena A. Lautscham, Irina Harder, Graeme Whyte, Ben Fabry

We describe a method for quantifying the mechanical properties of cells in suspension with a microfluidic device consisting of a parallel array of micron-sized constrictions. Using a high-speed charge-coupled device camera, we measure the flow speed, cell deformation, and entry time into the constrictions of several hundred cells per minute during their passage through the device. From the flow speed and the occupation state of the microconstriction array with cells, the driving pressure across each constriction is continuously computed. Cell entry times into microconstrictions decrease with increased driving pressure and decreased cell size according to a power law. From this power-law relationship, the cell elasticity and fluidity can be estimated. When cells are treated with drugs that depolymerize or stabilize the cytoskeleton or the nucleus, elasticity and fluidity data from all treatments collapse onto a master curve. Power-law rheology and collapse onto a master curve are predicted by the theory of soft glassy materials and have been previously shown to describe the mechanical behavior of cells adhering to a substrate. Our finding that this theory also applies to cells in suspension provides the foundation for a quantitative high-throughput measurement of cell mechanical properties with microfluidic devices.

Goos-Hanchen and Imbert-Fedorov shifts for astigmatic Gaussian beams

Marco Ornigotti, Andrea Aiello

In this work we investigate the role of the beam astigmatism in the Goos-Hanchen and Imbert-Fedorov shift. As a case study, we consider a Gaussian beam focused by an astigmatic lens and we calculate explicitly the corrections to the standard formulas for beam shifts due to the astigmatism induced by the lens. Our results show that the different focusing in the longitudinal and transverse direction introduced by an astigmatic lens may enhance the angular part of the shift.

Selective switching of individual multipole resonances in single dielectric nanoparticles

Pawel Wozniak, Peter Banzer, Gerd Leuchs

Following Mie theory, nanoparticles made of a high-refractive-index dielectric, such as silicon, exhibit a resonator-like behavior and very rich resonance spectra. Which electric or magnetic particle mode is excited depends on the wavelength, the refractive-index contrast relative to the environment, and the geometry of the nanoparticle itself. In addition, the spatial structure of the impinging light field plays a major role in the excitation of the nanoparticle resonances. Here, it is shown that, by tailoring the excitation field, individual multipole resonances can be selectively addressed while suppressing the excitation of other particle modes. This enables a detailed study of selected individual resonances without interference by the other modes.

Practical implementation of mutually unbiased bases using quantum circuits

U. Seyfarth, L. L. Sanchez-Soto, G. Leuchs

The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits. We also analyze the quantum circuits implementing the various entanglement classes.

Thermal characterisation of (bio)polymers with a temperature-stabilised whispering gallery mode microsensor

Eugene Kim, Matthew R. Foreman, Martin D. Baaske, Frank Vollmer

In this work, we theoretically and experimentally investigate the thermal response of whispering gallery mode microresonators operating in an aqueous glycerol medium. Thermal stabilisation of the resonance wavelength is realised by appropriate choice of the resonator radius and glycerol concentration, with a 60 fold reduction in thermal sensitivity demonstrated. Finally, we employ our stabilised system to determine the thermal dependence of the molecular polarisability of adsorbed bovine serum albumin molecules and the refractive index of dextran and poly(diallyldimethylammonium chloride) coatings. (C) 2015 AIP Publishing LLC.

Measuring the Transverse Spin Density of Light

Martin Neugebauer, Thomas Bauer, Andrea Aiello, Peter Banzer

We generate tightly focused optical vector beams whose electric fields spin around an axis transverse to the beams' propagation direction. We experimentally investigate these fields by exploiting the directional near-field interference of a dipolelike plasmonic field probe placed adjacent to a dielectric interface. This directionality depends on the transverse electric spin density of the excitation field. Near-to far-field conversion mediated by the dielectric interface enables us to detect the directionality of the emitted light in the far field and, therefore, to measure the transverse electric spin density with nanoscopic resolution. Finally, we determine the longitudinal electric component of Belinfante's elusive spin momentum density, a solenoidal field quantity often referred to as "virtual."

Giant narrowband twin-beam generation along the pump-energy propagation direction

Angela M. Perez, Kirill Yu Spasibko, Polina R. Sharapova, Olga V. Tikhonova, Gerd Leuchs, Maria V. Chekhova

Walk-off effects, originating from the difference between the group and phase velocities, limit the efficiency of nonlinear optical interactions. While transverse walk-off can be eliminated by proper medium engineering, longitudinal walk-off is harder to avoid. In particular, ultrafast twin-beam generation via pulsed parametric down-conversion and four-wave mixing is only possible in short crystals or fibres. Here we show that in high-gain parametric down-conversion, one can overcome the destructive role of both effects and even turn them into useful tools for shaping the emission. In our experiment, one of the twin beams is emitted along the pump Poynting vector or its group velocity matches that of the pump. The result is markedly enhanced generation of both twin beams, with the simultaneous narrowing of angular and frequency spectrum. The effect will enable efficient generation of ultrafast twin photons and beams in cavities, waveguides and whispering-gallery mode resonators.

Projective filtering of the fundamental eigenmode from spatially multimode radiation

A. M. Perez, P. R. Sharapova, S. S. Straupe, F. M. Miatto, O. V. Tikhonova, G. Leuchs, M. V. Chekhova

Lossless filtering of a single coherent (Schmidt) mode from spatially multimode radiation is a problem crucial for optics in general and for quantum optics in particular. It becomes especially important in the case of nonclassical light that is fragile to optical losses. An example is bright squeezed vacuum generated via high-gain parametric down conversion or four-wave mixing. Its highly multiphoton and multimode structure offers a huge increase in the information capacity provided that each mode can be addressed separately. However, the nonclassical signature of bright squeezed vacuum, photon-number correlations, are highly susceptible to losses. Here we demonstrate lossless filtering of a single spatial Schmidt mode by projecting the spatial spectrum of bright squeezed vacuum on the eigenmode of a single-mode fiber. Moreover, we show that the first Schmidt mode can be captured by simply maximizing the fiber-coupled intensity. Importantly, the projection operation does not affect the targeted mode and leaves it usable for further applications.

Whispering gallery mode sensors (vol 7, pg 168, 2015)

Matthew R. Foreman, Jon D. Swaim, Frank Vollmer

Classically entangled optical beams for high-speed kinematic sensing

Stefan Berg-Johansen, Falk Toeppel, Birgit Stiller, Peter Banzer, Marco Ornigotti, Elisabeth Giacobino, Gerd Leuchs, Andrea Aiello, Christoph Marquardt

Tracking the kinematics of fast-moving objects is an important diagnostic tool for science and engineering. Here, we demonstrate an approach to positional and directional sensing based on the concept of classical entanglement in vector beams of light [Found. Phys. 28, 361 -374 (1998)]. The measurement principle relies on the intrinsic correlations existing in such beams between transverse spatial modes and polarization. The latter can be determined from intensity measurements with only a few fast photodiodes, greatly outperforming the bandwidth of current CCD/CMOS devices. In this way, our setup enables two-dimensional real-time sensing with temporal resolution in the GHz range. We expect the concept to open up new directions in metrology and sensing. (C) 2015 Optical Society of America

Near-infrared single-photon spectroscopy of a whispering gallery mode resonator using energy-resolving transition edge sensors

Michael Foertsch, Thomas Gerrits, Martin J. Stevens, Dmitry Strekalov, Gerhard Schunk, Josef U. Fuerst, Ulrich Vogl, Florian Sedlmeir, Harald G. L. Schwefel, et al.

We demonstrate a method to perform spectroscopy of near-infrared single photons without the need of dispersive elements. This method is based on a photon energy resolving transition edge sensor and is applied for the characterization of widely wavelength tunable narrow-band single photons emitted from a crystalline whispering gallery mode resonator. We measure the emission wavelength of the generated signal and idler photons with an uncertainty of up to 2 nm.

Quantum-like nonseparable structures in optical beams

Andrea Aiello, Falk Toeppel, Christoph Marquardt, Elisabeth Giacobino, Gerd Leuchs

When two or more degrees of freedom become coupled in a physical system, a number of observables of the latter cannot be represented by mathematical expressions separable with respect to the different degrees of freedom. In recent years it appeared clear that these expressions may display the same mathematical structures exhibited by multiparty entangled states in quantum mechanics. In this work, we investigate the occurrence of such structures in optical beams, a phenomenon that is often referred to as 'classical entanglement'. We present a unified theory for different kinds of light beams exhibiting classical entanglement and we indicate several possible extensions of the concept. Our results clarify and shed new light upon the physics underlying this intriguing aspect of classical optics.

Risk Analysis of Trojan-Horse Attacks on Practical Quantum Key Distribution Systems

Nitin Jain, Birgit Stiller, Imran Khan, Vadim Makarov, Christoph Marquardt, Gerd Leuchs

An eavesdropper Eve may probe a quantum key distribution (QKD) system by sending a bright pulse from the quantum channel into the system and analyzing the back-reflected pulses. Such Trojan-horse attacks can breach the security of the QKD system, if appropriate safeguards are not installed or if they can be fooled by the Eve. We present a risk analysis of such attacks based on extensive spectral measurements, such as transmittance, reflectivity, and detection sensitivity of some critical components used in a typical QKD systems. Our results indicate the existence of wavelength regimes, where the attacker gains considerable advantage as compared to launching an attack at 1550 nm. We also propose countermeasures to reduce the risk of such attacks.

Intracavity Squeezing Can Enhance Quantum-Limited Optomechanical Position Detection through Deamplification

V. Peano, H. G. L. Schwefel, Ch. Marquardt, F. Marquardt

It has been predicted and experimentally demonstrated that by injecting squeezed light into an optomechanical device, it is possible to enhance the precision of a position measurement. Here, we present a fundamentally different approach where the squeezing is created directly inside the cavity by a nonlinear medium. Counterintuitively, the enhancement of the signal-to-noise ratio works by deamplifying precisely the quadrature that is sensitive to the mechanical motion without losing quantum information. This enhancement works for systems with a weak optomechanical coupling and/or strong mechanical damping. This can allow for larger mechanical bandwidth of quantum-limited detectors based on optomechanical devices. Our approach can be straightforwardly extended to quantum nondemolition qubit detection.

Optimal Frames for Polarization State Reconstruction

Matthew R. Foreman, Alberto Favaro, Andrea Aiello

Complete determination of the polarization state of light requires at least four distinct projective measurements of the associated Stokes vector. Stability of state reconstruction, however, hinges on the condition number kappa of the corresponding instrument matrix. Optimization of redundant measurement frames with an arbitrary number of analysis states, m, is considered in this Letter in the sense of minimization of kappa. The minimum achievable kappa is analytically found and shown to be independent of m, except for m = 5 where this minimum is unachievable. Distribution of the optimal analysis states over the Poincare sphere is found to be described by spherical 2 designs, including the Platonic solids as special cases. Higher order polarization properties also play a key role in nonlinear, stochastic, and quantum processes. Optimal measurement schemes for nonlinear measurands of degree t are hence also considered and found to correspond to spherical 2t designs, thereby constituting a generalization of the concept of mutually unbiased bases.

Stars of the quantum Universe: extremal constellations on the Poincare sphere

Gunnar Bjork, Markus Grassl, Pablo de la Hoz, Gerd Leuchs, Luis L. Sanchez-Soto

The characterization of the polarization properties of a quantum state requires the knowledge of the joint probability distribution of the Stokes variables. This amounts to assessing all the moments of these variables, which are aptly encoded in a multipole expansion of the density matrix. The cumulative distribution of these multipoles encapsulates in a handy manner the polarization content of the state. We work out the extremal states for that distribution, finding that SU(2) coherent states are maximal to any order, so they are the most polarized allowed by quantum theory. The converse case of pure states minimizing that distribution, which can be seen as the most quantum ones, is investigated for a diverse range of number of photons. Exploiting the Majorana representation, the problem appears to be closely related to distributing a number of points uniformly over the surface of the Poincare sphere.

A robust quantum receiver for phase shift keyed signals

C. R. Mueller, Ch Marquardt

The impossibility of perfectly discriminating non-orthogonal quantum states imposes far-reaching consequences both on quantum and classical communication schemes. We propose and numerically analyze an optimized quantum receiver for the discrimination of phase encoded signals. Our scheme outperforms the standard quantum limit and approaches the Helstrom bound for any signal power. The discrimination is performed via an optimized, feedback-mediated displacement prior to a photon counting detector. We provide a detailed analysis of the influence of excess noise and technical imperfections on the average error probability. The results demonstrate the receiver's robustness and show that it can outperform any classical receiver over a wide range of realistic parameters.

Adjustable diffractive spiral phase plates

Walter Harm, Stefan Bernet, Monika Ritsch-Marte, Irina Harder, Norbert Lindlein

We report on the fabrication and the experimental demonstration of Moire diffractive spiral phase plates with adjustable helical charge. The proposed optical unit consists of two axially stacked diffractive elements of conjugate structure. The joint transmission function of the compound system corresponds to that of a spiral phase plate where the angle of mutual rotation about the central axis enables continuous adjustment of the helical charge. The diffractive elements are fabricated by gray-scale photolithography with a pixel size of 200 nm and 128 phase step levels in fused silica. We experimentally demonstrate the conversion of a TEM00 beam into approximated Laguerre-Gauss (LG) beams of variable helical charge, with a correspondingly variable radius of their ring-shaped intensity distribution. (C) 2015 Optical Society of America

Observation of optical polarization Mobius strips

Thomas Bauer, Peter Banzer, Ebrahim Karimi, Sergej Orlov, Andrea Rubano, Lorenzo Marrucci, Enrico Santamato, Robert W. Boyd, Gerd Leuchs

Mobius strips are three-dimensional geometrical structures, fascinating for their peculiar property of being surfaces with only one "side"-or, more technically, being "nonorientable" surfaces. Despite being easily realized artificially, the spontaneous emergence of these structures in nature is exceedingly rare. Here, we generate Mobius strips of optical polarization by tightly focusing the light beam emerging from a q-plate, a liquid crystal device that modifies the polarization of light in a space-variantmanner. Using a recently developed-method for the three-dimensional nanotomography of optical vector fields, we fully reconstruct the light polarization structure in the focal region, confirming the appearance of Mobius polarization structures. The preparation of such structured light modes may be important for complex light beam engineering and optical micro-and nanofabrication.

Entangling the Whole by Beam Splitting a Part

Callum Croal, Christian Peuntinger, Vanessa Chille, Christoph Marquardt, Gerd Leuchs, Natalia Korolkova, Ladislav Mista Jr.

A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.

A chaotic approach clears up imaging

Harald G. L. Schwefel, Hakan E. Tuereci

Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations

Vanessa Chille, Niall Quinn, Christian Peuntinger, Callum Croal, Ladislav Mista Jr., Christoph Marquardt, Gerd Leuchs, Natalia Korolkova

We provide experimental evidence of quantum features in bipartite states classified as entirely classical according to a conventional criterion based on the Glauber P function but possessing nonzero Gaussian quantum discord. Their quantum nature is experimentally revealed by acting locally on one part of the discordant state. We experimentally verify and investigate the effect of discord increase under the action of local loss and link it to the entanglement with the environment. Adding an environmental system purifying the state, we unveil the flow of quantum correlations within a global pure system using the Koashi-Winter inequality. For a discordant state generated by splitting a state in which the initial squeezing is destroyed by random displacements, we demonstrate the recovery of entanglement highlighting the role of system-environment correlations.

Classical polarization multipoles: paraxial versus nonparaxial

P. de la Hoz, G. Bjork, H. de Guise, A. B. Klimov, G. Leuchs, L. L. Sanchez-Soto

We discuss the polarization of paraxial and nonparaxial classical light fields by resorting to a multipole expansion of the corresponding polarization matrix. It turns out that only a dipolar term contributes when one considers SU(2) (paraxial) or SU(3) (nonparaxial) as fundamental symmetries. In this latter case, one can alternatively expand in SU(2) multipoles, and then both a dipolar and a quadrupolar component contribute, which explains the richer structure of this nonparaxial instance. These multipoles uniquely determine Wigner functions, in terms of which we examine some intriguing hallmarks arising in this classical scenario.

Towards an optical far-field measurement of higher-order multipole contributions to the scattering response of nanoparticles

Thomas Bauer, Sergej Orlov, Gerd Leuchs, Peter Banzer

We experimentally show an all-optical multipolar decomposition of the lowest-order eigenmodes of a single gold nanoprism using azimuthally and radially polarized cylindrical vector beams. By scanning the particle through these tailored field distributions, the multipolar character of the eigenmodes gets encoded into 2D-scanning intensity maps even for higher-order contributions to the eigenmode that are too weak to be discerned in the direct far-field scattering response. This method enables a detailed optical mode analysis of individual nanoparticles. (C) 2015 AIP Publishing LLC.

From transverse angular momentum to photonic wheels

Andrea Aiello, Peter Banzer, Martin Neugebauer, Gerd Leuchs

Scientists have known for more than a century that light possesses both linear and angular momenta along the direction of propagation. However, only recent advances in optics have led to the notion of spinning electromagnetic fields capable of carrying angular momenta transverse to the direction of motion. Such fields enable numerous applications in nano-optics, biosensing and near-field microscopy, including three-dimensional control over atoms, molecules and nanostructures, and allowing for the realization of chiral nanophotonic interfaces and plasmonic devices. Here, we report on recent developments of optics with light carrying transverse spin. We present both the underlying principles and the latest achievements, and also highlight new capabilities and future applications emerging from this young yet already advanced field of research.

Exploiting cellophane birefringence to generate radially and azimuthally polarised vector beams

Johnston Kalwe, Martin Neugebauer, Calvine Ominde, Gerd Leuchs, Geoffrey Rurimo, Peter Banzer

We exploit the birefringence of cellophane to convert a linearly polarised Gaussian beam into either a radially or azimuthally polarised beam. For that, we fabricated a low-cost polarisation mask consisting of four segments of cellophane. The fast axis of each segment is oriented appropriately in order to rotate the polarisation of the incident linearly polarised beam as desired. To ensure the correct operation of the polarisation mask, we tested the polarisation state of the generated beam by measuring the spatial distribution of the Stokes parameters. Such a device is very cost efficient and allows for the generation of cylindrical vector beams of high quality.

Extremal states for photon number and quadratures as gauges for nonclassicality

Z. Hradil, J. Rehacek, P. de la Hoz, G. Leuchs, L. L. Sanchez-Soto

Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertainty relation, as well as a couple of weaker inequalities obtained by relaxing some restrictions of the problem. We also find the intelligent states saturating that relation and complete their characterization by considering extra constraints on the second-order moments of the variables involved. Using these moments, we construct performance measures tailored to diagnose photon-added and Schrodinger-cat-like states, among others.

Two-photon spectral amplitude of entangled states resolved in separable Schmidt modes

A. Avella, G. Brida, M. Chekhova, M. Gramegna, A. Shurupov, M. Genovese

The ability to access high dimensionality in Hilbert spaces represents a demanding key-stone for state-of-the-art quantum information. The manipulation of entangled states in continuous variables, wavevector as well frequency, represents a powerful resource in this sense. The number of dimensions of the Hilbert space that can be used in practical information protocols can be determined by the number of Schmidt modes that it is possible to address one by one. In the case of wavevector variables, the Schmidt modes can be losslessly selected using single-mode fibre and a spatial light modulator, but no similar procedure exists for the frequency space. The aim of this work is to present a technique to engineer the spectral properties of biphoton light, emitted via ultrafast spontaneous parametric down conversion, in such a way that the two-photon spectral amplitude (TPSA) contains several non-overlapping Schmidt modes, each of which can be filtered losslessly in frequency variables. Such TPSA manipulation is operated by a fine balancing of parameters like the pump frequency, the shaping of pump pulse spectrum, the dispersion dependence of spontaneous parametric down-conversion crystals as well as their length. Measurements have been performed exploiting the group velocity dispersion induced by the passage of optical fields through dispersive media, operating a frequency-to-time two-dimensional Fourier transform of the TPSA. Exploiting this kind of measurement we experimentally demonstrate the ability to control the Schmidt modes structure in TPSA through the pump spectrum manipulation.

Phase retrieval from carrier frequency interferograms: reduction of the impact of space-variant disturbances

J. Schwider, V. Nercissian, K. Mantel

Phase "extraction" by using temporal phase shifting is sensitive to vibrations and drifts, producing systematic phase errors periodic with twice the fringe frequency. This error source may be avoided by evaluating only single carrier frequency interferograms, which makes the procedure immune against vibrations and drifts provided that the integration time is short enough to freeze the fringe pattern. However, the phases extracted from single interferograms in this way often show local irregularities depending on the mean phase of the interference pattern. Such local phase irregularities are caused by local disturbances in the light path like specks and dust particles on the optical components of the interferometer. Moreover, since digitized data are gathered, there is a nonlinear processing step involved which is also responsible for the generation of such irregularities. Here, it is proposed to use a set of suitably combined phase-ramped interferograms to reduce phase dependent irregularities. The proposed averaging technique also reduces edge ringing effects known from Fourier evaluation procedures. Since the imaging optics also contributes to the phase to be measured when tilted wavefronts are used, calibration is mandatory. The calibrated state is only valid if strict rules considering fringe number per diameter as well as the position of the wedge in the interferometer are maintained in the measuring process.

Quantum theory of an electromagnetic observer: Classically behaving macroscopic systems and the emergence of the classical world in quantum electrodynamics

L. I. Plimak, Misha Ivanov, A. Aiello, S. Stenholm

Quantum electrodynamics under conditions of distinguishability of interactingmatter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.

Extremal quantum states and their Majorana constellations

G. Bjork, A. B. Klimov, P. de la Hoz, M. Grassl, G. Leuchs, L. L. Sanchez-Soto

The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution of those multipoles and work out the corresponding extremal pure states. We find that SU(2) coherent states are maximal to any order whereas the converse case of minimal states (which can be seen as the most quantum ones) is investigated for a diverse range of the number of photons. Taking advantage of the Majorana representation, we recast the problem as that of distributing a number of points uniformly over the surface of the Poincare sphere.

Optical Tracking of Anomalous Diffusion Kinetics in Polymer Microspheres

Matthew R. Foreman, Frank Vollmer

In this Letter we propose the use of whispering gallery mode resonance tracking as a label-free optical means to monitor diffusion kinetics in glassy polymer microspheres. Approximate solutions to the governing diffusion equations are derived for the case of slow relaxation and small Stefan number. Transduction of physical changes in the polymer, including formation of a rubbery layer, swelling, and dissolution, into detectable resonance shifts are described using a perturbative approach. Concrete examples of poly(methyl methacrylate) and polystyrene spheres in water are considered.

Schmidt modes in the angular spectrum of bright squeezed vacuum

P. Sharapova, A. M. Perez, O. V. Tikhonova, M. V. Chekhova

We investigate both theoretically and experimentally strong correlations in macroscopic (bright) quantum states of light generated via unseeded parametric down-conversion and four-wave mixing. The states generated this way contain only quantum noise, without a classical component, and are referred to as bright squeezed vacuum (BSV). Their important advantage is the multimode structure, which offers a larger capacity for the encoding of quantum information. For the theoretical description of these states and their correlation features we introduce a generalized fully analytical approach, based on the concept of independent collective (Schmidt) modes and valid for the cases of both weak and strong nonlinear interaction. In experiment, we generate states of macroscopic BSV with up to 1010 photons per mode and examine large photon-number spatial correlations that are found to be very well described by our theoretical approach.

Raman-Free, Noble-Gas-Filled Photonic-Crystal Fiber Source for Ultrafast, Very Bright Twin-Beam Squeezed Vacuum

Martin A. Finger, Timur Sh. Iskhakov, Nicolas Y. Joly, Maria V. Chekhova, Philip St. J. Russell

We report a novel source of twin beams based on modulational instability in high-pressure argon-filled hollow-core kagome-style photonic-crystal fiber. The source is Raman-free and manifests strong photonnumber correlations for femtosecond pulses of squeezed vacuum with a record brightness of similar to 2500 photons per mode. The ultra-broadband (similar to 50 THz) twin beams are frequency tunable and contain one spatial and less than 5 frequency modes. The presented source outperforms all previously reported squeezed-vacuum twin-beam sources in terms of brightness and low mode content.

Interfacing transitions of different alkali atoms and telecom bands using one narrowband photon pair source

Gerhard Schunk, Ulrich Vogl, Dmitry V. Strekalov, Michael Foertsch, Florian Sedlmeir, Harald G. L. Schwefel, Manuela Goebelt, Silke Christiansen, Gerd Leuchs, et al.

Quantum information technology strongly relies on the coupling of optical photons with narrowband quantum systems, such as quantum dots, color centers, and atomic systems. This coupling requires matching the optical wavelength and bandwidth to the desired system, which presents a considerable problem for most available sources of quantum light. Here we demonstrate the coupling of alkali dipole transitions with a tunable source of photon pairs. Our source is based on spontaneous parametric downconversion in a triply resonant whispering gallery mode resonator. For this, we have developed novel wavelength-tuning mechanisms that allow a coarse tuning to either the cesium or rubidium wavelength, with subsequent continuous fine-tuning to the desired transition. As a demonstration of the functionality of the source, we performed a heralded single-photon measurement of the atomic decay. We present a major advance in controlling the spontaneous downconversion process, which makes our bright source of heralded single photons now compatible with a plethora of narrowband resonant systems. (C) 2015 Optical Society of America

Bright squeezed vacuum: Entanglement of macroscopic light beams

M. V. Chekhova, G. Leuchs, M. Zukowski

We discuss various methods to create macroscopic (bright) entangled light beams. As an example, bright squeezed vacuum is considered in detail. This state of light, obtained via high-gain parametric downconversion, manifests entanglement in both photon numbers and polarization. (C) 2014 Elsevier B.V. All rights reserved.

Time-Reversal-Symmetric Single-Photon Wave Packets for Free-Space Quantum Communication

N. Trautmann, G. Alber, G. S. Agarwal, G. Leuchs

Readout and retrieval processes are proposed for efficient, high-fidelity quantum state transfer between a matter qubit, encoded in the level structure of a single atom or ion, and a photonic qubit, encoded in a time-reversal-symmetric single-photon wave packet. They are based on controlling spontaneous photon emission and absorption of a matter qubit on demand in free space by stimulated Raman adiabatic passage. As these processes do not involve mode selection by high-finesse cavities or photon transport through optical fibers, they offer interesting perspectives as basic building blocks for free-space quantum-communication protocols.

New Constructions of Codes for Asymmetric Channels via Concatenation

Markus Grassl, Peter W. Shor, Graeme Smith, John Smolin, Bei Zeng

We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear single-error-correcting codes from ternary outer codes. We show that some of the Varshamov-Tenengol'ts-Constantin-Rao codes, a class of binary nonlinear codes for this channel, have a nice structure when viewed as ternary codes. In many cases, our ternary construction yields even better codes. For the nonbinary asymmetric channel, our methods construct linear codes for many lengths and distances which are superior to the linear codes of the same length capable of correcting the same number of symmetric errors.

Quantum uncertainty in the beam width of spatial optical modes

Vanessa Chille, Peter Banzer, Andrea Aiello, Gerd Leuchs, Christoph Marquardt, Nicolas Treps, Claude Fabre

We theoretically investigate the quantum uncertainty in the beam width of transverse optical modes and, for this purpose, define a corresponding quantum operator. Single mode states are studied as well as multimode states with small quantum noise. General relations are derived, and specific examples of different modes and quantum states are examined. For the multimode case, we show that the quantum uncertainty in the beam width can be completely attributed to the amplitude quadrature uncertainty of one specific mode, which is uniquely determined by the field under investigation. This discovery provides us with a strategy for the reduction of the beam width noise by an appropriate choice of the quantum state. (C) 2015 Optical Society of America

Goos-Hanchen and Imbert-Fedorov shifts for paraxial X-waves

Marco Ornigotti, Andrea Aiello, Claudio Conti

We present a theoretical analysis for the Goos-Hanchen and Imbert-Fedorov shifts experienced by an X-wave upon reflection from a dielectric interface. We show that the temporal chirp, as well as the bandwidth of the X-wave, directly affect the spatial shifts in a way that can be experimentally observed, while the angular shifts do not depend on the spectral features of the X-wave. A dependence of the spatial shifts on the spatial structure of the X-wave is also discussed. (C) 2015 Optical Society of America

Experimental Realization of Quantum Tomography of Photonic Qudits via Symmetric Informationally Complete Positive Operator-Valued Measures

N. Bent, H. Qassim, A. A. Tahir, D. Sych, G. Leuchs, L. L. Sanchez-Soto, E. Karimi, R. W. Boyd

Symmetric informationally complete positive operator-valued measures provide efficient quantum state tomography in any finite dimension. In this work, we implement state tomography using symmetric informationally complete positive operator-valued measures for both pure and mixed photonic qudit states in Hilbert spaces of orbital angular momentum, including spaces whose dimension is not power of a prime. Fidelities of reconstruction within the range of 0.81-0.96 are obtained for both pure and mixed states. These results are relevant to high-dimensional quantum information and computation experiments, especially to those where a complete set of mutually unbiased bases is unknown.

Loss-tolerant hybrid measurement test of CHSH inequality with weakly amplified N00N states

Falk Toeppel, Magdalena Stobinska

Although our understanding of Bell's theorem and experimental techniques to test it have improved over the last 40 years, thus far all Bell tests have suffered at least from the detection or the locality loophole. Most photonic Bell tests rely on inefficient discrete-outcome measurements, often provided by photon counting detection. One possible way to close the detection loophole in photonic Bell tests is to involve efficient continuous-variable measurements instead, such as homodyne detection. Here, we propose a test of the Clauser-Horne-Shimony-Holt inequality that applies photon counting and homodyne detection on weakly amplified two-photon N00N states. The scheme suggested is remarkably robust against experimental imperfections and suits the limits of current technology. As amplified quantum states are considered, our work also contributes to the exploration of entangled macroscopic quantum systems. Further, it may constitute an alternative platform for a loophole-free Bell test, which is also important for quantum-technological applications.

Cylindrically polarized Bessel-Gauss beams

Daena Madhi, Marco Ornigotti, Andrea Aiello

We present a study of radially and azimuthally polarized Bessel-Gauss (BG) beams in both the paraxial and nonparaxial regime. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for BG beams. We show that independently on the ratio between the Bessel aperture cone angle theta(0) and the Gaussian beam divergence theta(0), the nonparaxial corrections are alway very small and therefore negligible. The explicit expressions for the nonparaxial vector electric field components are also reported.

Highly efficient generation of single-mode photon pairs from a crystalline whispering-gallery-mode resonator source

Michael Foertsch, Gerhard Schunk, Josef U. Fuerst, Dmitry Strekalov, Thomas Gerrits, Martin J. Stevens, Florian Sedlmeir, Harald G. L. Schwefel, Sae Woo Nam, et al.

We report a highly efficient source of narrow-band photon pairs based on parametric down-conversion in a crystalline-whispering-gallery-mode resonator. Remarkably, each photon of a pair is detected in a single spatial and temporal mode, as witnessed by Glauber's autocorrelation function. We explore the phase-matching conditions in spherical geometries, and determine the requirements for single-mode operation. Understanding these conditions has allowed us to experimentally demonstrate a single-mode pair-detection efficiency of 1.13 x 10(6) pairs/s per mW pump power per 26.8 MHz bandwidth.

Whispering gallery mode sensors

Matthew R. Foreman, Jon D. Swaim, Frank Vollmer

We present a comprehensive overview of sensor technology exploiting optical whispering gallery mode (WGM) resonances. After a short introduction we begin by detailing the fundamental principles and theory of WGMs in optical microcavities and the transduction mechanisms frequently employed for sensing purposes. Key recent theoretical contributions to the modeling and analysis of WGM systems are highlighted. Subsequently we review the state of the art of WGM sensors by outlining efforts made to date to improve current detection limits. Proposals in this vein are numerous and range, for example, from plasmonic enhancements and active cavities to hybrid optomechanical sensors, which are already working in the shot noise limited regime. In parallel to furthering WGM sensitivity, efforts to improve the time resolution are beginning to emerge. We therefore summarize the techniques being pursued in this vein. Ultimately WGM sensors aim for real-world applications, such as measurements of force and temperature, or alternatively gas and biosensing. Each such application is thus reviewed in turn, and important achievements are discussed. Finally, we adopt a more forward-looking perspective and discuss the outlook of WGM sensors within both a physical and biological context and consider how they may yet push the detection envelope further. (C) 2015 Optical Society of America

Note on the helicity decomposition of spin and orbital optical currents

Andrea Aiello, M. V. Berry

In the helicity representation, the Poynting vector (current) for a monochromatic optical field, when calculated using either the electric or the magnetic field, separates into right-handed and left-handed contributions, with no cross-helicity contributions. Cross-helicity terms do appear in the orbital and spin contributions to the current. But when the electric and magnetic formulas are averaged ('electric-magnetic democracy'), these terms cancel, restoring the separation into right-handed and left-handed currents for orbital and spin separately.

Direct Schmidt number measurement of high-gain parametric down conversion

I. V. Dyakonov, P. R. Sharapova, T. Sh Iskhakov, G. Leuchs

In this work we estimate the transverse Schmidt number for the bipartite high-gain parametric down conversion state by means of second-order intensity correlation function measurement. Assuming that the number of modes is equal in both beams we determine the Schmidt number considering only one of the subsystems. The obtained results demonstrate that this approach is equally efficient over the whole propagation of the state from the near field to the far field regions of its emitter.

Quantum Uniqueness

Denis Sych, Gerd Leuchs

Classical physics allows for the existence of pairs of absolutely identical systems. Pairwise application of identical measurements to each of those systems always leads to exactly alike results irrespectively of the choice of measurements. Here we ask a question how the picture looks like in the quantum domain. Surprisingly, we get a counterintuitive outcome. Pairwise application of identical (but a priori unknown) measurements cannot always lead to exactly alike results. We interpret this as quantum uniqueness-a feature that has no classical analog.

Depolarized guided acoustic wave Brillouin scattering in hollow-core photonic crystal fibers

Wenjia Elser Nee Zhong, Birgit Stiller, Dominique Elser, Bettina Heim, Christoph Marquardt, Gerd Leuchs

By performing quantum-noise-limited optical heterodyne detection, we observe polarization noise in light after propagation through a hollow-core photonic crystal fiber (PCF). We compare the noise spectrum to the one of a standard fiber and find an increase of noise even though the light is mainly transmitted in air in a hollow-core PCF. Combined with our simulation of the acoustic vibrational modes in the hollow-core PCF, we are offering an explanation for the polarization noise with a variation of guided acoustic wave Brillouin scattering (GAWBS). Here, instead of modulating the strain in the fiber core as in a solid core fiber, the acoustic vibrations in hollow-core PCF influence the effective refractive index by modulating the geometry of the photonic crystal structure. This induces polarization noise in the light guided by the photonic crystal structure. (C) 2015 Optical Society of America

Dielectric Rod Waveguide Antenna as THz Emitter for Photomixing Devices

Alejandro Rivera-Lavado, Sascha Preu, Luis Enrique Garcia-Munoz, Andrey Generalov, Javier Montero-de-Paz, Gottfried Doehler, Dmitri Lioubtchenko, Mario Mendez-Aller, Florian Sedlmeir, et al.

We propose a dielectric rod waveguide antenna (DRW) integrated with a photomixer as a THz emitter. This represents a different approach as opposed to the classical solution of a substrate lens. Main goals are an inexpensive alternative to substrate lenses, reduction of both reflections on the semiconductor-air interface and scattering of terahertz-generated power into the substrate. A radiation pattern measured at 137 GHz is shown as a proof-of-concept. In order to increase radiated power, the improvement of the rod antenna is discussed. Finally, as an application example, evanescent coupling of the DRW into a high index whispering gallery mode resonator is shown.

Classical entanglement in polarization metrology

Falk Toeppel, Andrea Aiello, Christoph Marquardt, Elisabeth Giacobino, Gerd Leuchs

Quantum approaches relying on entangled photons have been recently proposed to increase the efficiency of optical measurements. We demonstrate here that, surprisingly, the use of classical light with entangled degrees of freedom can also bring outstanding advantages over conventional measurements in polarization metrology. Specifically, we show that radially polarized beams of light allow to perform real-time single-shot Mueller matrix polarimetry. Our results also indicate that quantum optical procedures requiring entanglement without nonlocality can be actually achieved in the classical optics regime.

The Hertz vector revisited: a simple physical picture

Marco Ornigotti, Andrea Aiello

The polarization potentials, also known as Hertz vectors, are useful auxiliary fields that permit the calculation of the fundamental electromagnetic fields in many cases of practical importance. In this article we show that in a vacuum a single Hertz vector written as the product of a scalar potential and a constant vector, naturally arises as consequence of the transversality of the electromagnetic fields. Thus, our treatment shines a new light on the physical meaning of a Hertz potential.

Detection of non-classical space-time correlations with a novel type of single-photon camera

Felix Just, Mykhaylo Filipenko, Andrea Cavanna, Thilo Michel, Thomas Gleixner, Michael Taheri, John Vallerga, Michael Campbell, Timo Tick, et al.

During the last decades, multi-pixel detectors have been developed capable of registering single photons. The newly developed hybrid photon detector camera has a remarkable property that it has not only spatial but also temporal resolution. In this work, we apply this device to the detection of non-classical light from spontaneous parametric down-conversion and use two-photon correlations for the absolute calibration of its quantum efficiency. (C) 2014 Optical Society of America

Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern

Gerhard Schunk, Josef U. Fuerst, Michael Foertsch, Dmitry V. Strekalov, Ulrich Vogl, Florian Sedlmeir, Harald G. L. Schwefel, Gerd Leuchs, Christoph Marquardt

Identifying the mode numbers in whispering-gallery mode resonators (WGMRs) is important for tailoring them to experimental needs. Here we report on a novel experimental mode analysis technique based on the combination of frequency analysis and far-field imaging for high mode numbers of large WGMRs. The radial mode numbers q and the angular mode numbers p = l-m are identified and labeled via far-field imaging. The polar mode numbers l are determined unambiguously by fitting the frequency differences between individual whispering gallery modes (WGMs). This allows for the accurate determination of the geometry and the refractive index at different temperatures of the WGMR. For future applications in classical and quantum optics, this mode analysis enables one to control the narrow-band phase-matching conditions in nonlinear processes such as second-harmonic generation or parametric down-conversion. (C) 2014 Optical Society of America

Trojan-horse attacks threaten the security of practical quantum cryptography

Nitin Jain, Elena Anisimova, Imran Khan, Vadim Makarov, Christoph Marquardt, Gerd Leuchs

A quantum key distribution (QKD) system may be probed by an eavesdropper Eve by sending in bright light from the quantum channel and analyzing the back-reflections. We propose and experimentally demonstrate a setup for mounting such a Trojan-horse attack. We show it in operation against the quantum cryptosystem Clavis2 from ID Quantique, as a proof-of-principle. With just a few back-reflected photons, Eve discerns Bob's (secret) basis choice, and thus the raw key bit in the Scarani-Acin-Ribordy-Gisin 2004 protocol, with higher than 90% probability. This would clearly breach the security of the cryptosystem. Unfortunately, Eve's bright pulses have a side effect of causing a high level of afterpulsing in Bob's single-photon detectors, resulting in a large quantum bit error rate that effectively protects this system from our attack. However, in a Clavis2-like system equipped with detectors with less-noisy but realistic characteristics, an attack strategy with positive leakage of the key would exist. We confirm this by a numerical simulation. Both the eavesdropping setup and strategy can be generalized to attack most of the current QKD systems, especially if they lack proper safeguards. We also propose countermeasures to prevent such attacks.

Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams

Thomas Bauer, Sergej Orlov, Ulf Peschel, Peter Banzer, Gerd Leuchs

Highly confined vectorial electromagnetic field distributions are an excellent tool for detailed studies in nano-optics, such as nonlinear microscopy(1), advanced fluorescence imaging(2,3) or nanoplasmonics(4,5). Such field distributions can be generated, for instance, by tight focusing of polarized light beams(6-9). To guarantee high resolution in the investigation of objects with subwavelength dimensions, precise knowledge of the spatial distribution of the exciting vectorial field is of utmost importance. The full-field reconstruction methods presented to date involve, for example, complex near-field techniques(10-13). Here, we demonstrate a simple and straightforward-to-implement measurement scheme and reconstruction algorithm based on the scattering signal of a single spherical nanoparticle as a field probe. We are able to reconstruct the amplitudes and relative phases of the individual focal field components with subwavelength resolution from a single scan measurement without the need for polarization analysis of the scattered light. This scheme has the potential to improve microscopy and nanoscopy techniques.

Taking detection to the limit with optical microcavities: Recent advances presented at the 560. WE Heraeus Seminar

Frank Vollmer, Harald G. L. Schwefel

We provide a review on the applications of whispering gallery mode resonators in sensing, and biosensing in particular. We highlight the most recent developments in this area, which were presented at the 560. WE Heraeus Seminar "Taking Detection to the Limit - Biosensing with Optical Microcavities".

Wave-optics description of self-healing mechanism in Bessel beams

Andrea Aiello, Girish S. Agarwal

Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring. (C) 2014 Optical Society of America

Unpolarized states and hidden polarization

P. de la Hoz, G. Bjork, A. B. Klimov, G. Leuchs, L. L. Sanchez-Soto

We capitalize on a multipolar expansion of the polarization density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order K vanish, we can properly say that the state is Kth-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized states coincide with the corresponding classical ones, whereas unpolarized to any order tally with the quantum notion of fully invariant states. In between these two extreme cases, there is a rich variety of situations that are explored here. The existence of hidden polarization emerges in a natural way in this context.

Bright squeezed-vacuum source with 1.1 spatial mode

A. M. Perez, T. Sh. Iskhakov, P. Sharapova, S. Lemieux, O. V. Tikhonova, M. V. Chekhova, G. Leuchs

Bright squeezed vacuum, a macroscopic nonclassical state of light, can be obtained at the output of a strongly pumped nonseeded traveling-wave optical parametric amplifier (OPA). By constructing the OPA of two consecutive crystals separated by a large distance, we make the squeezed vacuum spatially single-mode without a significant decrease in the brightness or squeezing. (C) 2014 Optical Society of America

Quantum mutual information of an entangled state propagating through a fast-light medium

Jeremy B. Clark, Ryan T. Glasser, Quentin Glorieux, Ulrich Vogl, Tian Li, Kevin M. Jones, Paul D. Lett

It is widely accepted that information cannot travel faster than c, the speed of light in vacuum(1-3). Here, we investigate the behaviour of quantum correlations and information in the presence of dispersion. To do so we send one half of an entangled state of light through a gain-assisted slow-or fast-light medium and detect the transmitted quantum correlations and quantum mutual information(4-6). We show that quantum correlations can be advanced by a small fraction of the correlation time, even in the presence of noise added by phase-insensitive gain. Additionally, although the peak of the quantum mutual information between the modes can be advanced, we find that the degradation of the mutual information due to added noise appears to prevent an advancement of the leading edge. In contrast, we demonstrate a significant delay of both the leading and trailing edges of the mutual information in a slow-light system.

Sub-kHz lasing of a CaF2 whispering gallery mode resonator stabilized fiber ring laser

M. C. Collodo, F. Sedlmeir, B. Sprenger, S. Svitlov, L. J. Wang, H. G. L. Schwefel

We utilize a high quality calcium fluoride whispering-gallery-mode resonator to passively stabilize a simple erbium doped fiber ring laser with an emission frequency of 196 THz (wavelength 1530 nm) to an instantaneous linewidth below 650 Hz. This corresponds to a relative stability of 3.3 x 10(-12) over 16 mu s. In order to characterize the linewidth we use two identical self-built lasers and a commercial laser to determine the individual lasing linewidth via the three-cornered-hat method. We further show that the lasers are finely tunable throughout the erbium gain region. (C) 2014 Optical Society of America

Near field of an oscillating electric dipole and cross-polarization of a collimated beam of light: Two sides of the same coin

Andrea Aiello, Marco Ornigotti

We address the question of whether there exists a hidden relationship between the near-field distribution generated by an oscillating electric dipole and the so-called cross-polarization of a collimated beam of light. We find that the answer is affirmative by showing that the complex field distributions occurring in both cases have a common physical origin: the requirement that the electromagnetic fields must be transverse. (C) 2014 American Association of Physics Teachers.

Three-dimensional photograph of electron tracks through a plastic scintillator

Mykhaylo Filipenko, Timur Iskhakov, Patrick Hufschmidt, Gisela Anton, Michael Campbell, Thomas Gleixner, Gerd Leuchs, Timo Tick, John Vallerga, et al.

The reconstruction of particle trajectories makes it possible to distinguish between different types of charged particles. In high-energy physics, where trajectories are rather long (several meters), large size trackers must be used to achieve sufficient position resolution. However, in low-background experiments like the search for neutrinoless double beta decay, tracks are rather short (some mm to several cm, depending on the detector in use) and three-dimensional trajectories could only be resolved in gaseous time-projection chambers so far. For detectors of a large volume of around one cubic meter (large in the scope of neutrinoless double beta search) and therefore large drift distances (several decimeters to 1 m), this technique is limited by diffusion and repulsion of charge carriers. In this work we present a "proof-of-principle" experiment for a new method of the three-dimensional tracking of charged particles by scintillation light: we used a setup consisting of a scintillator, mirrors, lenses, and a novel imaging device (the hybrid photon detector) in order to image two projections of electron tracks through the scintillator. We took data at the T-22 beamline at DESY with relativistic electrons with a kinetic energy of 5GeV and from this data successfully reconstructed their three-dimensional propagation path in the scintillator. With our setup we achieved a position resolution in the range of 170-248 mu m.

All-optical phase-preserving multilevel amplitude regeneration

Tobias Roethlingshoefer, Thomas Richter, Colja Schubert, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

The possibility of all-optical phase-preserving amplitude regeneration for star-8QAM is demonstrated using a modified nonlinear optical loop mirror. Experiments show a reduction in amplitude noise on both amplitude levels simultaneously, considering two different types of signal distortions: deterministic low-frequency amplitude modulation and broadband amplitude noise. Furthermore, using this amplitude regeneration, the robustness against nonlinear phase noise from fiber nonlinearity in a transmission line is increased. The scheme suppresses the conversion of amplitude noise to nonlinear phase noise. This is shown for simultaneous amplitude regeneration of the two amplitude states as well as for amplitude regeneration of the high-power states only. If the transmission is limited by nonlinear phase noise, single-level operation at the more critical higher-power state will benefit because of the wider plateau region. Numerical simulations confirm the experimental results. (C) 2014 Optical Society of America.

Incoherent averaging of phase singularities in speckle-shearing interferometry

Klaus Mantel, Vanusch Nercissian, Norbert Lindlein

Interferometric speckle techniques are plagued by the omnipresence of phase singularities, impairing the phase unwrapping process. To reduce the number of phase singularities by physical means, an incoherent averaging of multiple speckle fields may be applied. It turns out, however, that the results may strongly deviate from the expected root N behavior. Using speckle-shearing interferometry as an example, we investigate the mechanism behind the reduction of phase singularities, both by calculations and by computer simulations. Key to an understanding of the reduction mechanism during incoherent averaging is the representation of the physical averaging process in terms of certain vector fields associated with each speckle field. (C) 2014 Optical Society of America

Advanced quantum noise correlations

Ulrich Vogl, Ryan T. Glasser, Jeremy B. Clark, Quentin Glorieux, Tian Li, Neil V. Corzo, Paul D. Lett

We use the quantum correlations of twin beams of light to investigate the fundamental addition of noise when one of the beams propagates through a fastlight medium based on phase-insensitive gain. The experiment is based on two successive four-wave mixing processes in rubidium vapor, which allow for the generation of bright two-mode-squeezed twin beams followed by a controlled advancement while maintaining the shared quantum correlations between the beams. The demonstrated effect allows the study of irreversible decoherence in a medium exhibiting anomalous dispersion, and for the first time shows the advancement of a bright nonclassical state of light. The advancement and corresponding degradation of the quantum correlations are found to be operating near the fundamental quantum limit imposed by using a phase-insensitive amplifier.

Crystalline MgF2 whispering gallery mode resonators for enhanced bulk index sensitivity

R. Zeltner, F. Sedlmeir, G. Leuchs, H. G. L. Schwefel

We report on experiments on refractrometric sensing with crystalline Whispering Gallery Mode (WGM) resonators made of magnesium fluoride, which has a refractive index that is only slightly larger than that of water (Delta n approximate to 0.05). The resulting evanescent field of a WGM resonator placed in an aqueous environment penetrates therefore deep into the surrounding medium, which makes it a promising candidate for sensing applications. We measured a bulk index sensitivity of 1.09 nm/RIU (refractive index unit) in a resonator with a radius of R = 2.91mm and intrinsic Q-factors of more than 10(8) in aqueous environments. Furthermore, we describe the fabrication process of crystalline WGM resonators.

Generalized Bessel beams with two indices

Marco Ornigotti, Andrea Aiello

We report on a new class of exact solutions of the scalar Helmholtz equation obtained by carefully engineering the form of the angular spectrum of a Bessel beam. We consider in particular the case in which the angular spectrum of such generalized beams has, in the paraxial zone, the same radial structure as Laguerre-Gaussian beams. We investigate the form of these new beams as well as their peculiar propagation properties. (C) 2014 Optical Society of America

Photon correlations for colloidal nanocrystals and their clusters

A. Shcherbina, G. A. Shcherbina, M. Manceau, S. Vezzoli, L. Carbone, M. De Vittorio, A. Bramati, E. Giacobino, M. V. Chekhova, et al.

of semiconductor "dot-in-rods" and their small clusters are studied by measuring the second-order correlation function with a spatially resolving intensified CCD camera. This measurement allows one to distinguish between a single dot and a cluster and, to a certain extent, to estimate the number of dots in a cluster. A more advanced measurement is proposed, based on higher-order correlations, enabling more accurate determination of the number of dots in a small cluster. Nonclassical features of the light emitted by such a cluster are analyzed. (C) 2014 Optical Society of America

In optical pumping, less can be more

Harald G. L. Schwefel

Cascaded phase-preserving multilevel amplitude regeneration

Tobias Roethlingshoefer, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

The performance of cascaded in-line phase-preserving amplitude regeneration using nonlinear amplifying loop mirrors has been studied in numerical simulations. As an example of a spectrally efficient modulation format with two amplitude states and multiple phase states, the regeneration performance of a star-16QAM format, basically an 8PSK format with two amplitude levels, was evaluated. An increased robustness against amplified spontaneous emission and nonlinear phase noise was observed resulting in a significantly increased transmission distance. (C) 2014 Optical Society of America

Polarization Tailored Light Driven Directional Optical Nanobeacon

Martin Neugebauer, Thomas Bauer, Peter Banzer, Gerd Leuchs

We experimentally demonstrate all-optical control of the emission directivity of a dipole-like nanoparticle with spinning dipole moment sitting on the interface to an optical denser medium. The particle itself is excited by a tightly focused polarization tailored light beam under normal incidence. The position dependent local polarization of the focal field allows for tuning the dipole moment via careful positioning of the particle relative to the beam axis. As an application of this scheme, we investigate the polarization dependent coupling to a planar two-dimensional dielectric waveguide.

Simultaneous measurement of phase and local orientation of linearly polarized light: implementation and measurement results

Sergej Rothau, Christine Kellermann, Vanusch Nercissian, Andreas Berger, Klaus Mantel, Norbert Lindlein

Optical components manipulating both polarization and phase of wave fields find many applications in today's optical systems. With modern lithography methods it is possible to fabricate optical elements with nanostructured surfaces from different materials capable of generating spatially varying, locally linearly polarized-light distributions, tailored to the application in question. Since such elements in general also affect the phase of the light field, the characterization of the function of such elements consists in measuring the phase and the polarization of the generated light, preferably at the same time. Here, we will present first results of an interferometric approach for a simultaneous and spatially resolved measurement of both phase and polarization, as long as the local polarization at any point is linear (e.g., for radially or azimuthally polarized light). (C) 2014 Optical Society of America

Compensation of anisotropy effects in the generation of two-photon light

Andrea Cavanna, Angela M. Perez, Felix Just, Maria V. Chekhova, Gerd Leuchs

We analyse a method to compensate for anisotropy effects in the spatial distribution of parametric down-conversion (PDC) radiation in bulk crystals. In this method, a single nonlinear crystal is replaced by two consecutive crystals with opposite transverse walk-off directions. We implement a simple numerical model to calculate the spatial distribution of intensity and correlations, as well as the Schmidt mode structure, with an account for the anisotropy. Experimental results are presented which prove the validity of both the model and the method. (C) 2014 Optical Society of America

Structure of the sets of mutually unbiased bases with cyclic symmetry

U. Seyfarth, L. L. Sanchez-Soto, G. Leuchs

Mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest, for they can be readily implemented in practice. We show that, for a system of qubits, finding such a generator can be cast as the problem of finding a symmetric matrix over the field. 2 equipped with an irreducible characteristic polynomial of a given Fibonacci index. The entanglement structure of the resulting complete sets is determined by two additive matrices of the same size.

Generation of entangled matter qubits in two opposing parabolic mirrors

N. Trautmann, J. Z. Bernad, M. Sondermann, G. Alber, L. L. Sanchez-Soto, G. Leuchs

We propose a scheme for the remote preparation of entangled matter qubits in free space. For this purpose, a setup of two opposing parabolic mirrors is considered, each one with a single ion trapped at its focus. To get the required entanglement in this extreme multimode scenario, we take advantage of the spontaneous decay, which is usually considered as an apparent nuisance. Using semiclassical methods, we derive an efficient photon-path representation to deal with this problem. We also present a thorough examination of the experimental feasibility of the scheme. The vulnerabilities arising in realistic implementations reduce the success probability, but leave the fidelity of the generated state unaltered. Our proposal thus allows for the generation of high- fidelity entangled matter qubits with high rate.

Radial quantum number of Laguerre-Gauss modes

E. Karimi, R. W. Boyd, P. de la Hoz, H. de Guise, J. Rehacek, Z. Hradil, A. Aiello, G. Leuchs, L. L. Sanchez-Soto

We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes.

Observation of the Geometric Spin Hall Effect of Light

Jan Korger, Andrea Aiello, Vanessa Chille, Peter Banzer, Christoffer Wittmann, Norbert Lindlein, Christoph Marquardt, Gerd Leuchs

The spin Hall effect of light (SHEL) is the photonic analogue of the spin Hall effect occurring for charge carriers in solid-state systems. This intriguing phenomenon manifests itself when a light beam refracts at an air-glass interface (conventional SHEL) or when it is projected onto an oblique plane, the latter effect being known as the geometric SHEL. It amounts to a polarization-dependent displacement perpendicular to the plane of incidence. In this work, we experimentally investigate the geometric SHEL for a light beam transmitted across an oblique polarizer. We find that the spatial intensity distribution of the transmitted beam depends on the incident state of polarization and its centroid undergoes a positional displacement exceeding one wavelength. This novel phenomenon is virtually independent from the material properties of the polarizer and, thus, reveals universal features of spin-orbit coupling.

Phase regeneration of a star-8QAM signal in a phase-sensitive amplifier with conjugated pumps

B. Stiller, G. Onishchukov, B. Schmauss, G. Leuchs

We demonstrate numerically phase regeneration of a star8QAM signal with two amplitude and four phase states in a phase-sensitive amplifier. In a dual-stage setup, two phase-conjugated idlers are generated in a first stage consisting of two fiber-optic parametric phase-insensitive amplifiers operated in highly nonlinear gain regime. These are used as pumps in the second, phase-sensitive amplification stage which enables efficient phase regeneration via a degenerate four-wave-mixing process. The latter can be operated in two different operation modes: without format conversion or with phase-shifted amplitude levels. In both regimes, we observe high phase-regeneration efficiency for all amplitude levels: the initial phase noise with 0.2 rad standard deviation is reduced by a factor of 5. (C) 2014 Optical Society of America

All-Optical Simultaneous Multilevel Amplitude and Phase Regeneration

Tobias Roethlingshoefer, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

Simultaneous amplitude and phase noise reduction of multiple signal states using a nonlinear amplifying loop mirror with integrated directional phase-sensitive amplifier are presented for the star-eight quadrature amplitude modulation transmission format as an example. The performance of this combined regenerator scheme is compared with that of a cascade of separate phase and amplitude regenerators. It could be shown that an improvement in the error vector magnitude of 4 dB for the high-power states with simultaneous improvement of 5 dB for the low-power states is possible in both cases. Transmission improvement by regeneration is considered for two noise types: 1) amplified spontaneous emission and 2) nonlinear phase noise. Both schemes can either improve the bit error rate by an order of magnitude or enable an increase of the fiber launch power by 3 dB.

Fair sampling perspective on an apparent violation of duality

Eliot Bolduc, Jonathan Leach, Filippo M. Miatto, Gerd Leuchs, Robert W. Boyd

In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that "the simultaneous observation of wave and particle behavior is prohibited" [Scully MO, Englert B-G, Walther H ( 1991) Nature 351: 111-116]. Whereas wave behavior is associated with the observation of interference fringes, particle behavior generally corresponds to the acquisition of which-path information by means of coupling the paths to a measuring device or part of their environment. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, post-selected measurements on specific degrees of freedom of the environment of the two-path state. Our work gives insight into a possible mechanism for obtaining simultaneous high which-path information and high-visibility fringes in a single experiment. Further, our results introduce previously unidentified avenues for experimental tests of duality.

Efficient saturation of an ion in free space

Martin Fischer, Marianne Bader, Robert Maiwald, Andrea Golla, Markus Sondermann, Gerd Leuchs

We report on the demonstration of a lightmatter interface coupling light to a single Yb-174(+) ion in free space. The interface is realized through a parabolic mirror partially surrounding the ion. It transforms a La-guerre- Gaussian beam into a linear dipole wave converging at the mirror's focus. By measuring the non-linear response of the atomic transition, we deduce the power required for reaching an upper-level population of 1/4 to be 692 +/- 20pW at half linewidth detuning from the atomic resonance. Performing this measurement while scanning the ion through the focus provides a map of the focal intensity distribution. From the measured power, we infer a coupling efficiency of 7.2 +/- 0.2% on the linear dipole transition when illuminating from half solid angle, being among the best coupling efficiencies reported for a single atom in free space.

Towards loophole-free Bell inequality test with preselected unsymmetrical singlet states of light

Magdalena Stobinska, Falk Toeppel, Pavel Sekatski, Adam Buraczewski

Can a Bell test with no detection loophole be demonstrated for multiphoton entangled states of light within the current technology? We examine the possibility of a postselection-free Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality test with an unsymmetrical polarization singlet. To that end we employ a preselection procedure which is performed prior to the test. It allows using imperfect (coarse-grained) binary photodetection in the test. We show an example of a preselection scheme which improves violation of the CHSH inequality with the micro-macro polarization singlet produced by the optimal quantum cloning. The preselection is realized by a quantum filter which is believed not to be useful for this purpose.

High-Q MgF2 whispering gallery mode resonators for refractometric sensing in aqueous environment

Florian Sedlmeir, Richard Zeltner, Gerd Leuchs, Harald G. L. Schwefel

We present our experiments on refractometric sensing with ultrahigh-Q, crystalline, birefringent magnesium fluoride (MgF2) whispering gallery mode resonators. The difference to fused silica which is most commonly used for sensing experiments is the small refractive index of MgF2 which is very close to that of water. Compared to fused silica this leads to more than 50% longer evanescent fields and a 4:25 times larger sensitivity. Moreover the birefringence amplifies the sensitivity difference between TM and TE type modes which will enhance sensing experiments based on difference frequency measurements. We estimate the performance of our resonators and compare them with fused silica theoretically and present experimental data showing the interferometrically measured evanescent field decay and the sensitivity of mm-sized MgF2 whispering gallery mode resonators immersed in water. These data show reasonable agreement with the developed theory. Furthermore, we observe stable Q factors in water well above 1 x 10(8). (C) 2014 Optical Society of America

Interference of macroscopic beams on a beam splitter: phase uncertainty converted into photon-number uncertainty

K. Yu Spasibko, F. Toeppel, T. Sh Iskhakov, M. Stobinska, M. V. Chekhova, G. Leuchs

Squeezed-vacuum twin beams, commonly generated through parametric downconversion, are known to have perfect photon-number correlations. According to the Heisenberg principle, this is accompanied by a huge uncertainty in their relative phase. By overlapping bright twin beams on a beam splitter, we convert phase fluctuations into photon-number fluctuations and observe this uncertainty as a typical 'U-shape' of the output photon-number distribution. This effect, although reported for atomic ensembles and giving hope for phase super-resolution, has never been observed for light beams. The shape of the normalized photon-number difference distribution is similar to the one that would be observed for high-order Fock states. It can be also mimicked by classical beams with artificially mixed phase, but without any perspective for phase super-resolution. The probability distribution at the beam splitter output can be used for filtering macroscopic superpositions at the input.

Generation and subwavelength focusing of longitudinal magnetic fields in a metallized fiber tip

Daniel Ploss, Arian Kriesch, Hannes Pfeifer, Peter Banzer, Ulf Peschel

We demonstrate experimentally and numerically that in fiber tips as they are used in NSOMs azimuthally polarized electrical fields (broken vertical bar E-azi broken vertical bar(2) / broken vertical bar E-tot broken vertical bar(2) approximate to 55% +/- 5% for lambda(0) = 1550 nm), respectively subwavelength confined (FWHM approximate to 450 nm approximate to lambda(0)/3.5) magnetic fields, are generated for a certain tip aperture diameter (d = 1.4 mu m). We attribute the generation of this field distribution in metal-coated fiber tips to symmetry breaking in the bend and subsequent plasmonic mode filtering in the truncated conical taper. (C) 2014 Optical Society of America

Atmospheric continuous-variable quantum communication

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, Ch Marquardt, G. Leuchs

We present a quantum communication experiment conducted over a point-topoint free-space link of 1.6 km in urban conditions. We study atmospheric influences on the capability of the link to act as a continuous-variable (CV) quantum channel. Continuous polarization states (that contain the signal encoding as well as a local oscillator (LO) in the same spatial mode) are prepared and sent over the link in a polarization multiplexed setting. Both signal and LO undergo the same atmospheric fluctuations. These are intrinsically auto-compensated which removes detrimental influences on the interferometric visibility. At the receiver, we measure the Q-function and interpret the data using the framework of effective entanglement (EE). We compare different state amplitudes and alphabets (two-state and four-state) and determine their optimal working points with respect to the distributed EE. Based on the high entanglement transmission rates achieved, our system indicates the high potential of atmospheric links in the field of CV quantum key distribution.

Atomic mercury vapor inside a hollow-core photonic crystal fiber

Ulrich Vogl, Christian Peuntinger, Nicolas Y. Joly, Philip St. J. Russell, Christoph Marquardt, Gerd Leuchs

We demonstrate high atomic mercury vapor pressure in a kagome-style hollow-core photonic crystal fiber at room temperature. After a few days of exposure to mercury vapor the fiber is homogeneously filled and the optical depth achieved remains constant. With incoherent optical pumping from the ground state we achieve an optical depth of 114 at the 6(3)P(2) - 6(3)D(3) transition, corresponding to an atomic mercury number density of 6 x 10(10) cm(-3). The use of mercury vapor in quasi one-dimensional confinement may be advantageous compared to chemically more active alkali vapor, while offering strong optical nonlinearities in the ultraviolet region of the optical spectrum. (C) 2014 Optical Society of America

Surface angular momentum of light beams

Marco Ornigotti, Andrea Aiello

Traditionally, the angular momentum of light is calculated for "bullet-like" electromagnetic wave packets, although in actual optical experiments "pencil-like" beams of light are more commonly used. The fact that a wave packet is bounded transversely and longitudinally while a beam has, in principle, an infinite extent along the direction of propagation, renders incomplete the textbook calculation of the spin/orbital separation of the angular momentum of a light beam. In this work we demonstrate that a novel, extra surface part must be added in order to preserve the gauge invariance of the optical angular momentum per unit length. The impact of this extra term is quantified by means of two examples: a Laguerre-Gaussian and a Bessel beam, both circularly polarized. (C) 2014 Optical Society of America

Microlocal approach towards construction of nonreflecting boundary conditions

V. Vaibhav

This paper addresses the problem of construction of non-reflecting boundary condition for certain second-order nonlinear dispersive equations. It is shown that using the concept of microlocality it is possible to relax the requirement of compact support of the initial data. The method is demonstrated for a class of initial data such that outside the computational domain it behaves like a continuous-wave. The generalization is detailed for two existing schemes in the framework of pseudo-differential calculus, namely, Szeftel's method (Szeftel (2006) [1]) and gauge transformation strategy (Antoine et al. (2006) [2]). Efficient numerical implementation is discussed and a comparative performance analysis is presented. The paper also briefly surveys the possibility of extension of the method to higher-dimensional PDEs. (C) 2014 Elsevier Inc. All rights reserved.

Separable Schmidt modes of a nonseparable state

A. Avella, M. Gramegna, A. Shurupov, G. Brida, M. Chekhova, M. Genovese

Two-photon states entangled in continuous variables such as wave vector or frequency represent a powerful resource for quantum-information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several nonoverlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comblike spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely, passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of nonoverlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range, and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.

Distribution of Squeezed States through an Atmospheric Channel

Christian Peuntinger, Bettina Heim, Christian R. Mueller, Christian Gabriel, Christoph Marquardt, Gerd Leuchs

Continuous variable quantum states of light are used in quantum information protocols and quantum metrology and known to degrade with loss and added noise. We were able to show the distribution of bright polarization squeezed quantum states of light through an urban free-space channel of 1.6 km length. To measure the squeezed states in this extreme environment, we utilize polarization encoding and a postselection protocol that is taking into account classical side information stemming from the distribution of transmission values. The successful distribution of continuous variable squeezed states is accentuated by a quantum state tomography, allowing for determining the purity of the state.

Vectorial complex-source vortex beams

S. Orlov, P. Banzer

The scalar complex source vortex model is an accurate description of highly focused scalar vortices. We use it to construct a variety of vectorial solutions of Maxwell's equations describing highly focused and variously polarized vector vortex beams accurately. Three different families of optical vector vortex beams are presented and studied in detail. In this model, optical vortices derived within Cartesian symmetry correspond to circularly and linearly polarized highly focused vortex beams in the focus of a high numerical aperture focusing system. In addition, we report on vortical complex-source beams derived within cylindrical and spherical symmetries which exhibit very special and intriguing properties.

Geometric spin Hall effect of light in tightly focused polarization-tailored light beams

Martin Neugebauer, Peter Banzer, Thomas Bauer, Sergej Orlov, Norbert Lindlein, Andrea Aiello, Gerd Leuchs

Recently, it was shown that a nonzero transverse angular momentum manifests itself in a polarization-dependent intensity shift of the barycenter of a paraxial light beam [Aiello et al., Phys. Rev. Lett. 103, 100401 (2009)]. The underlying effect is phenomenologically similar to the spin Hall effect of light but does not depend on the specific light-matter interaction and can be interpreted as a purely geometric effect. Thus, it was named the geometric spin Hall effect of light. Here, we experimentally investigate the appearance of this effect in tightly focused vector beams. We use an experimental nanoprobing technique in combination with a reconstruction algorithm to verify the relative shifts of the components of the electric energy density and the shift of the intensity in the focal plane. By that, we experimentally demonstrate the geometric spin Hall effect of light in a highly nonparaxial beam.

Interaction of Relativistic Electron-Vortex Beams with Few-Cycle Laser Pulses

Armen G. Hayrapetyan, Oliver Matula, Andrea Aiello, Andrey Surzhykov, Stephan Fritzsche

We study the interaction of relativistic electron-vortex beams (EVBs) with laser light. Exact analytical solutions for this problem are obtained by employing the Dirac-Volkov wave functions to describe the (monoenergetic) distribution of the electrons in vortex beams with well-defined orbital angular momentum. Our new solutions explicitly show that the orbital angular momentum components of the laser field couple to the total angular momentum of the electrons. When the field is switched off, it is shown that the laser-driven EVB coincides with the field-free EVB as reported by Bliokh et al. [Phys. Rev. Lett. 107, 174802 (2011)]. Moreover, we calculate the probability density for finding an electron in the beam profile and demonstrate that the center of the beam is shifted with respect to the center of the field-free EVB.

Transverse entanglement of biphotons

F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs

We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric down-conversion (SPDC). The Fedorov ratio, depending on the widths of conditional and unconditional intensity measurements, is shown to be only able to characterize entanglement in the near and far field zones of the source. Therefore we also follow a different approach. By evaluating the first-order coherence of a subsystem of the state we can quantify its entanglement. Unlike previous measurements, which determine the Fedorov ratio via intensity correlations, our setup is sensitive to both phase and modulus of the biphoton state and thus always grants experimental access to the full transverse entanglement of the SPDC state. It is shown theoretically that this scheme represents a direct measurement of the Schmidt number.

Nonlinear cross-Kerr quasiclassical dynamics

I. Rigas, A. B. Klimov, L. L. Sanchez-Soto, G. Leuchs

We study the quasiclassical dynamics of the cross-Kerr effect. In this approximation, the typical periodical revivals of the decorrelation between the two polarization modes disappear and remain entangled. By mapping the dynamics onto the Poincare space, we find simple conditions for polarization squeezing. When dissipation is taken into account, the shape of the states in such a space is not considerably modified, but their size is reduced.

SCATTERING OF AN EXPONENTIAL PULSE BY A SINGLE ATOM

Markus Sondermann, Gerd Leuchs

We discuss the scattering of a light pulse by a single atom in free space using a purely semi-classical framework. The atom is treated as a linear elastic scatterer allowing to treat each spectral component of the incident pulse separately. For an increasing exponential pulse with a dipole radiation pattern incident from full solid angle the spectrum resulting from interference of incident and scattered components is a decreasing exponential pulse.*

Observation of acoustically induced modulation instability in a Brillouin photonic crystal fiber laser

Birgit Stiller, Thibaut Sylvestre

We report the experimental observation of self-induced modulation instability (MI) in a Brillouin fiber laser made with a solid-core photonic crystal fiber (PCF) with strong anomalous dispersion. We identify this MI as the result of parametric amplification of optical sidebands generated by guided acoustic modes within the core of the PCF. It is further shown that MI leads to passive harmonic mode locking and to the generation of a picosecond pulse train at a repetition rate of 1.15 GHz which matches the acoustic frequency of the fundamental acoustic mode of the PCF. (C) 2013 Optical Society of America

Quantum versus classical polarization states: when multipoles count

L. L. Sanchez-Soto, A. B. Klimov, P. de la Hoz, G. Leuchs

We advocate a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables, the first one corresponding to the classical picture on the Poincare sphere. We employ the particular case of the Q function to formulate a whole hierarchy of measures that properly assess higher-order polarization correlations.

Radially and azimuthally polarized nonparaxial Bessel beams made simple

Marco Ornigotti, Andrea Aiello

We present a method for the realization of radially and azimuthally polarized nonparaxial Bessel beams in a rigorous but simple manner. This result is achieved by using the concept of Hertz vector potential to generate exact vector solutions of Maxwell's equations from scalar Bessel beams. The scalar part of the Hertz potential is built by analogy with the paraxial case as a linear combination of Bessel beams carrying a unit of orbital angular momentum. In this way we are able to obtain spatial and polarization patterns analogous to the ones exhibited by the standard cylindrically polarized paraxial beams. Applications of these beams are discussed. (C) 2013 Optical Society of America

The phase shift induced by a single atom in free space

M. Sondermann, G. Leuchs

In this article we theoretically study the phase shift a single atom imprints onto a coherent state light beam in free space. The calculations are performed in a semiclassical framework. The key parameters governing the interaction and thus the measurable phase shift are the solid angle from which the light is focused onto the atom and the overlap of the incident radiation with the atomic dipole radiation pattern. The analysis includes saturation effects and discusses the associated Kerr-type non-linearity of a single atom.

Functional Plasmonic Nanocircuits with Low Insertion and Propagation Losses

Arian Kriesch, Stanley P. Burgos, Daniel Ploss, Hannes Pfeifer, Harry A. Atwater, Ulf Peschel

We experimentally demonstrate plasmonic nanocircuits operating as subdiffraction directional couplers optically excited with high efficiency from free-space using optical Yagi-Uda style antennas at lambda(0) = 1550 nm. The optical Yagi-Uda style antennas are designed to feed channel plasmon waveguides with high efficiency (45% in coupling, 60% total emission), narrow angular directivity (<40 degrees), and low insertion loss. SPP channel waveguides exhibit propagation lengths as large as 34 mu m with adiabatically tuned confinement and are integrated with ultracompact (5 x 10 mu m(2)), highly dispersive directional couplers, which enable 30 dB discrimination over Delta lambda = 200 nm with only 0.3 dB device loss.

Goos-Hanchen and Imbert-Fedorov shifts for bounded wavepackets of light

Marco Ornigotti, Andrea Aiello

We present precise expressions for the spatial and angular Goos-Hanchen and Imbert-Fedorov shifts experienced by a longitudinally and transversally limited beam of light (wavepacket) upon reflection from a dielectric interface, as opposed to the well-known case of a monochromatic beam which is bounded in transverse directions but infinitely extended along the direction of propagation. This is done under the assumption that the detector time is longer than the temporal length of the wavepacket (wavepacket regime). Our results will be applied to the case of a Gaussian wavepacket and show that, at the leading order in the Taylor expansion of reflected field amplitudes, the results are the same as in the monochromatic case.

Goos-Hanchen and Imbert-Fedorov beam shifts: an overview

K. Y. Bliokh, A. Aiello

We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the plane-wave representation and geometric rotations. Using geometrical-optics coordinate frames accompanying the beams, we construct an effective Jones matrix characterizing spatial-dispersion properties of the interface. This results in a unified self-consistent description of the Goos-Hanchen and Imbert-Fedorov shifts (the latter being also known as the spin Hall effect of light). Our description reveals the intimate relation of the transverse Imbert-Fedorov shift to the geometric phases between constituent waves in the beam spectrum and to the angular momentum conservation for the whole beam. Both spatial and angular shifts are considered as well as their analogues for higher-order vortex beams carrying intrinsic orbital angular momentum. We also give a brief overview of various extensions and generalizations of the basic beam-shift phenomena and related effects.

Whispering gallery modes at the rim of an axisymmetric optical resonator: Analytical versus numerical description and comparison with experiment

I. Breunig, B. Sturman, F. Sedlmeir, H. G. L. Schwefel, K. Buse

Optical whispering gallery modes (WGMs) of mm-sized axisymmetric resonators are well localized at the equator. Employing this distinctive feature, we obtain simple analytical relations for the frequencies and eigenfunctions of WGMs which include the major radius of the resonator and the curvature radius of the rim. Being compared with results of finite-element simulations, these relations show a high accuracy and practicability. High-precision free-spectral-range measurements with a millimeter-sized disc resonator made of MgF2 allow us to identify the WGMs and confirm the applicability of our analytical description. (C) 2013 Optical Society of America

Interferometric homogeneity test using adaptive frequency comb illumination

Klaus Mantel, Johannes Schwider

The homogeneity test of glass plates in a Fizeau interferometer requires the measurement of the glass sample in reflected as well as in transmitted light. For the measurement in transmitted light, the sample has to be inserted into the ray path of a Fizeau or Twyman-Green interferometer, which leads to a nested cavity setup. To separate the interference signals from the different cavities, we illuminate a Fizeau interferometer with an adaptive frequency comb. In this way, rigid glass plates can be measured, and linear variations in the homogeneity can also be detected. The adaptive frequency comb is provided by a variable Fabry-Perot filter under broadband illumination from a superluminescence diode. Compared to approaches using a two-beam interferometer as a filter for the broadband light source, the visibility of the fringe system is considerably higher. (C) 2013 Optical Society of America

Identical classical particles: Half fermions and half bosons

Falk Toeppel, Andrea Aiello

We study the problem of particle indistinguishability for the three cases known in nature: identical classical particles, identical bosons, and identical fermions. By exploiting the fact that different types of particles are associated with Hilbert space vectors with different symmetries, we establish some relations between the expectation value of several different operators, as the particle number one and the interparticle correlation one, evaluated for states of a pair of identical classical particles, bosons, and fermions. We find that the quantum behavior of a pair of identical classical particles has exactly half fermionic and half bosonic characteristics.

Multiphoton nonclassical correlations in entangled squeezed vacuum states

Bhaskar Kanseri, Timur Iskhakov, Georgy Rytikov, Maria Chekhova, Gerd Leuchs

Photon-number correlation measurements are performed on bright squeezed vacuum states using a standard Bell-test setup, and quantum correlations are observed for conjugate polarization-frequency modes. We further test the entanglement witnesses for these states and demonstrate the violation of the separability criteria, which infers that all of the macroscopic Bell states, containing typically 10(6) photons per pulse, are polarization entangled. The study also reveals the symmetry of macroscopic Bell states with respect to local polarization transformations. DOI: 10.1103/PhysRevA.87.032110

Experimental characterization of an uniaxial angle cut whispering gallery mode resonator

Florian Sedlmeir, Martin Hauer, Josef U. Fuerst, Gerd Leuchs, Harald G. L. Schwefel

The usual configuration of uniaxial whispering gallery mode resonators is a disk shaped geometry where the optic axis points along the symmetry axis, a so called z-cut resonator. Recently x-cut resonators, where the optic axis lies in the equatorial plane, became of interest as they enable extremely broadband second harmonic generation. In this paper we report on the properties of a more generalized system, the so called angle-cut resonator, where the optic axis exhibits an arbitrary angle against the symmetry axis. We show experimentally that the modal structure and quality factors are similar to common resonators but that the polarization properties differ quite significantly: due to the asymmetry the polarization depends on the equatorial position and is, in general, elliptical. (C) 2013 Optical Society of America

The Schmidt modes of biphoton qutrits: Poincare-sphere representation

M. V. Chekhova, M. V. Fedorov

For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for factorizing the state vector and the explicit expressions for the factorizing photon creation operators are found. The degrees of entanglement and polarization of a qutrit are shown to depend directly on the commutation features of the factorizing operators. Clear graphic representations for the Stokes vectors of the qutrit state as a whole, its Schmidt modes and factorizing single-photon creation operators are given based on the Poincare sphere. An experimental scheme is proposed for measuring the parameters of the Schmidt decomposition as well as for demonstrating the operational meaning of qutrit entanglement.

Goos-Hanchen and Imbert-Fedorov shifts from a quantum-mechanical perspective

Falk Toeppel, Marco Ornigotti, Andrea Aiello

We study the classical optics effects known as Goos-Hanchen and Imbert-Fedorov shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-versus-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transverse components of the wave vector. Moreover, we extend our treatment to the enhancement of beam shifts via weak measurements and relate our results to the recent experiments.

A sum rule for charged elementary particles

Gerd Leuchs, Luis L. Sanchez-Soto

There may be a link between the quantum properties of the vacuum and the parameters describing the properties of light propagation, culminating in a sum over all types of elementary particles existing in Nature weighted only by their squared charges and independent of their masses. The estimate for that sum is of the order of 100.

QED with a parabolic mirror

G. Alber, J. Z. Bernad, M. Stobinska, L. L. Sanchez-Soto, G. Leuchs

We investigate the quantum electrodynamics of a single two-level atom located at the focus of a parabolic cavity. We first work out the modifications of the spontaneous emission induced by the presence of this boundary in the optical regime, where the dipole and the rotating-wave approximations apply. Furthermore, the single-photon state that leaves the cavity asymptotically is determined. The corresponding time-reversed single-photon quantum state is capable of exciting the atom in this extreme multimode scenario with near-unit probability. Using semiclassical methods, we derive a photon-path representation for the relevant transition amplitudes and show that it constitutes a satisfactory approximation for a wide range of wavelengths.

A versatile source of single photons for quantum information processing

Michael Foertsch, Josef U. Fuerst, Christoffer Wittmann, Dmitry Strekalov, Andrea Aiello, Maria V. Chekhova, Christine Silberhorn, Gerd Leuchs, Christoph Marquardt

The generation of high-quality single-photon states with controllable narrow spectral bandwidths and central frequencies is key to facilitate efficient coupling of any atomic system to non-classical light fields. Such an interaction is essential in numerous experiments for fundamental science and applications in quantum communication and information processing, as well as in quantum metrology. Here we implement a fully tunable, narrow-band and efficient single-photon source based on a whispering gallery mode resonator. Our disk-shaped, monolithic and intrinsically stable resonator is made of lithium niobate and supports a cavity-assisted spontaneous parametric down-conversion process. The generated photon pairs are emitted into two highly tunable resonator modes. We verify wavelength tuning over 100 nm of both modes with controllable bandwidth between 7.2 and 13 MHz. Heralding of single photons yields anti-bunching with g((2))(0) < 0.2.

Polarization assisted fast data encoding and transmission using coherence based spectral anomalies

Bhaskar Kanseri

Two methods for fast information encoding and free space communication are proposed, which are based on the rapid transitions in coherence-based (spatial and temporal) spectral anomalies called 'spectral switches'. The information (data bits) could be encoded in terms of red and blue shifts in the source spectrum. The encoding process itself could be made fast by polarization assisted switching of spectral anomalies using a polarization selective device such as an electro-optic modulator. The advantages and limitations of this polarization based data processing mechanism are also discussed.

Amplification of realistic Schrodinger-cat-state-like states by homodyne heralding

Amine Laghaout, Jonas S. Neergaard-Nielsen, Ioannes Rigas, Christian Kragh, Anders Tipsmark, Ulrik L. Andersen

We present a scheme for the amplification of Schrodinger cat states that collapses two smaller states onto their constructive interference via a homodyne projection. We analyze the performance of the amplification in terms of fidelity and success rate when the input consists of either exact coherent state superpositions or of photon-subtracted squeezed vacua. The impact of imprecise homodyne detection and of impure squeezing is quantified. We also assess the scalability of iterated amplifications. DOI: 10.1103/PhysRevA.87.043826

Total internal reflection of orbital angular momentum beams

W. Loffler, N. Hermosa, Andrea Aiello, J. P. Woerdman

We investigate how beams with orbital angular momentum (OAM) behave under total internal reflection. This is studied in two complementary experiments: in the first experiment, we study geometric shifts of OAM beams upon total internal reflection (Goos-Hanchen and Imbert-Fedorov shifts, for each the spatial and angular variant), and in the second experiment we determine changes in the OAM mode spectrum of a beam, again upon total internal reflection. As a result we find that, in the first case, the shifts are independent of OAM and beam focusing, while in the second case, modifications in the OAM spectrum occur which depend on the input OAM mode as well as on the beam focusing. This is investigated by experiment and theory. We also show how the two methods, beam shifts on the one hand, and OAM spectrum changes on the other, are related theoretically.

Corrections to the knife-edge based reconstruction scheme of tightly focused light beams

C. Huber, S. Orlov, P. Banzer, G. Leuchs

The knife-edge method is an established technique for profiling light beams. It was shown, that this technique even works for tightly focused beams, if the material and geometry of the probing knife-edges are chosen carefully. Furthermore, it was also reported recently that this method fails, when the knife-edges are made from pure materials. The artifacts introduced in the reconstructed beam shape and position depend strongly on the edge and input beam parameters, because the knife-edge is excited by the incoming beam. Here we show, that the actual beam shape and spot size of tightly focused beams can still be derived from knife-edge measurements for pure edge materials and different edge thicknesses by adapting the analysis method of the experimental data taking into account the interaction of the beam with the edge. (C) 2013 Optical Society of America

Finite element simulation of a perturbed axial-symmetric whispering-gallery mode and its use for intensity enhancement with a nanoparticle coupled to a microtoroid

Alex Kaplan, Matthew Tomes, Tal Carmon, Maxim Kozlov, Oren Cohen, Guy Bartal, Harald G. L. Schwefel

We present an optical mode solver for a whispering gallery resonator coupled to an adjacent arbitrary shaped nano-particle that breaks the axial symmetry of the resonator. Such a hybrid resonator-nanoparticle is similar to what was recently used for bio-detection and for field enhancement. We demonstrate our solver by parametrically studying a toroid-nanoplasmonic device and get the optimal nano-plasmonic size for maximal enhancement. We investigate cases near a plasmonic resonance as well as far from a plasmonic resonance. Unlike common plasmons that typically benefit from working near their resonance, here working far from plasmonic resonance provides comparable performance. This is because the plasmonic resonance enhancement is accompanied by cavity quality degradation through plasmonic absorption. (C) 2013 Optical Society of America

Enhanced Raman Scattering of Graphene using Arrays of Split Ring Resonators

George Sarau, Basudev Lahiri, Peter Banzer, Priti Gupta, Arnab Bhattacharya, Frank Vollmer, Silke Christiansen

Combining graphene with plasmonic nanostructures is currently being explored for high sensitivity biochemical detection based on the surface-enhanced Raman scattering (SERS) effect. Here, a novel and tunable platform for understanding SERS based on graphene monolayers transferred on arrays of split ring resonators (SRRs) exhibiting resonances in the visible range is introduced. Raman enhancement factors per area of graphene of up to 75 are measured, demonstrating the strong plasmonic coupling between graphene and the metamaterial resonances. Apart from the incident laser light, both the photoluminescence signal emitted by the SRRs and the Raman scattered light from graphene contribute to the excitation of distinct resonances, resulting in different SERS. This new perspective allows control of SERS in the case of graphene on plasmonic metamaterials or nanostructures and potentially paves the way towards an advanced SERS substrate that could lead to the detection of single molecules attached to graphene in future biochemical sensing devices.

Optical diametric drive acceleration through action-reaction symmetry breaking

Martin Wimmer, Alois Regensburger, Christoph Bersch, Mohammad-Ali Miri, Sascha Batz, Georgy Onishchukov, Demetrios N. Christodoulides, Ulf Peschel

Newton's third law of motion is one of the pillars of classical physics. This fundamental principle states that the forces two bodies exert on each other are equal and opposite. Had the resulting accelerations been oriented in the same direction, this would have instead led to a counterintuitive phenomenon, that of diametric drive(1). In such a hypothetical arrangement, two interacting particles constantly accelerate each other in the same direction through a violation of the action-reaction symmetry. Although in classical mechanics any realization of this process requires one of the two particles to have a negative mass and hence is strictly forbidden, it could nevertheless be feasible in periodic structures where the effective mass can also attain a negative sign(2-7). Here we report the first experimental observation of such diametric drive acceleration for pulses propagating in a nonlinear optical mesh lattice(8-14). The demonstrated reversal of action-reaction symmetry could enable altogether new possibilities for frequency conversion and pulse-steering applications.

Optimal working points for continuous-variable quantum channels

Imran Khan, Christoffer Wittmann, Nitin Jain, Nathan Killoran, Norbert Luetkenhaus, Christoph Marquardt, Gerd Leuchs

The most important ability of a quantum channel is to preserve the quantum properties of transmitted quantum states. We experimentally demonstrate a continuous-variable system for efficient benchmarking of quantum channels. We probe the tested quantum channels for a wide range of experimental parameters such as amplitude, phase noise, and channel lengths up to 40 km. The data is analyzed using the framework of effective entanglement. We subsequently are able to deduce an optimal point of operation for each quantum channel with respect to the rate of distributed entanglement. This procedure is a promising candidate for benchmarking quantum nodes and individual links in large quantum networks of different physical implementations.

Sizing up entanglement in mutually unbiased bases with Fisher information

J. Rehacek, Z. Hradil, A. B. Klimov, G. Leuchs, L. L. Sanchez-Soto

An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of different sets of mutually unbiased bases are the same, differences appear when particular aspects of the measured system are contemplated. This point is illustrated by estimating the fidelities of genuinely tripartite entangled states.

An optimized photon pair source for quantum circuits

Georg Harder, Vahid Ansari, Benjamin Brecht, Thomas Dirmeier, Christoph Marquardt, Christine Silberhorn

We implement an ultrafast pulsed type-II parametric down conversion source in a periodically poled KTP waveguide at telecommunication wavelengths with almost identical properties between signal and idler. As such, our source resembles closely a pure, genuine single mode photon pair source with indistinguishable modes. We measure the joint spectral intensity distribution and second order correlation functions of the marginal beams and find with both methods very low effective mode numbers corresponding to a Schmidt number below 1.16. We further demonstrate the indistinguishability as well as the purity of signal and idler photons by Hong-Ou-Mandel interferences between signal and idler and between signal/idler and a coherent field, respectively. Without using narrowband spectral filtering, we achieve a visibility for the interference between signal and idler of 94.8% and determine a purity of more than 80% for the heralded single photon states. Moreover, we measure raw heralding efficiencies of 20.5% and 15.5% for the signal and idler beams corresponding to detector-loss corrected values of 80% and 70%. (C) 2013 Optical Society of America

Classical optics representation of the quantum mechanical translation operator via ABCD matrices

Marco Ornigotti, Andrea Aiello

The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established.

Orbital angular momentum from marginals of quadrature distributions

L. L. Sanchez-Soto, A. B. Klimov, P. de la Hoz, I. Rigas, J. Rehacek, Z. Hradil, G. Leuchs

We set forth a method to analyze the orbital angular momentum of a light field. Instead of using the canonical formalism for the conjugate pair angle-angular momentum, we model this latter variable by the superposition of two independent harmonic oscillators along two orthogonal axes. By describing each oscillator by a standard Wigner function, we derive, via a consistent change of variables, a comprehensive picture of the orbital angular momentum. We compare this with previous approaches and show how this method works in some relevant examples.

Nonclassical features of the polarization quasiprobability distribution

M. V. Chekhova, F. Ya. Khalili

Polarization quasiprobability distribution is defined in the space of the Stokes observables. It can be reconstructed with the help of polarization quantum tomography and provides a full description of the so-called polarization sector of quantum states of light. We show here that due to its definition in terms of the discrete-valued Stokes operators, polarization quasiprobability distribution has singularities at integer values of the Stokes observables and takes negative values even for the quantum states typically considered as "classical" ones. In experiments with "bright" multiphoton states, the photon-number resolution is smeared due to the photodetectors' technical limitations. In this case, nonclassical features of the explored quantum states can be revealed by adding a strong coherent beam into the orthogonal polarization.

Total absorption of light by a nanoparticle: an electromagnetic sink in the optical regime

A. Sentenac, P. C. Chaumet, G. Leuchs

In this Letter, we give a general description of the illumination and object properties for obtaining total absorption. We show theoretically and numerically that properly designed sub-100 nm metallic particles are able to absorb all the energy of an incident beam if the latter is adequately shaped. In addition to their interest as absorbers, these particles act as efficient near-field probes as they convert the incident propagating beam into a localized nonradiative field. (C) 2013 Optical Society of America

Macroscopic Hong-Ou-Mandel interference

T. Sh Iskhakov, K. Yu Spasibko, M. V. Chekhova, G. Leuchs

We report on a Hong-Ou-Mandel interference experiment for twin beams with photon numbers per mode as large as 10(6) generated via high-gain parametric down conversion (PDC). The standard technique of coincidence counting leads in this case to a dip with a very low visibility. By measuring, instead of coincidence counting rate, the variance of the photon-number difference, we observe an extremely well-pronounced peak. From the shape of the peak, one can infer information about the spectral properties of the PDC radiation, including the number of frequency/temporal modes.

Observation of Defect States in PT-Symmetric Optical Lattices

Alois Regensburger, Mohammad-Ali Miri, Christoph Bersch, Jakob Naeger, Georgy Onishchukov, Demetrios N. Christodoulides, Ulf Peschel

We provide the first experimental demonstration of defect states in parity-time (PT) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they remain localized in a PT-symmetric periodic environment. Even more intriguing is the possibility of observing a linearly growing radiation emission from such defects provided their eigenvalue is associated with an exceptional point that resides within the continuum part of the spectrum. Localized complex modes existing outside the band-gap regions are also reported along with their evolution dynamics.

The polarization properties of a tilted polarizer

Jan Korger, Tobias Kolb, Peter Banzer, Andrea Aiello, Christoffer Wittmann, Christoph Marquardt, Gerd Leuchs

Polarizers are key components in optical science and technology. Thus, understanding the action of a polarizer beyond oversimplifying approximations is crucial. In this work, we study the interaction of a polarizing interface with an obliquely incident wave experimentally. To this end, a set of Mueller matrices is acquired employing a novel procedure robust against experimental imperfections. We connect our observation to a geometric model, useful to predict the effect of polarizers on complex light fields. (C) 2013 Optical Society of America

Efficient coupling to an optical resonator by exploiting time-reversal symmetry

M. Bader, S. Heugel, A. L. Chekhov, M. Sondermann, G. Leuchs

The interaction of a cavity with an external field is symmetric under time reversal. Thus, coupling to a resonator is most efficient when the incident light is the time reversed version of a free cavity decay, i.e. when it has a rising exponential shape matching the cavity lifetime. For light entering the cavity from only one side, the maximally achievable coupling efficiency is limited by the choice of the cavity mirrors' reflectivities. Such an empty-cavity experiment serves also as a model system for single-photon single-atom absorption dynamics. We present experiments coupling exponentially rising pulses to a cavity system which allows for high coupling efficiencies. The influence of the time constant of the rising exponential is investigated as well as the effect of a finite pulse duration. We demonstrate coupling 94% of the incident TEM00 mode into the resonator.

Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation

A. M. Perez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs

Squeezed vacuum can be obtained by an optical parametric amplifier (OPA) with the quantum vacuum state at the input. We are interested in a degenerate type-I OPA based on parametric down-conversion (PDC) where, due to phase matching requirements, an extraordinary polarized pump must impinge onto a birefringent crystal with a large chi((2)) nonlinearity. As a consequence of the optical anisotropy of the medium, the spatial spectrum of the generated radiation is affected by the transverse walk-off. In this work we describe a method that reduces the spatial distortions, by using two consecutive crystals instead of one. We show that after anisotropy compensation the two-photon amplitude becomes symmetric, allowing for a simple Schmidt expansion, a procedure that in practice requires states that come from experimental systems free of anisotropy effects. Qualitative experimental observations are made for the case of high-gain PDC.

Multipolar hierarchy of efficient quantum polarization measures

P. de la Hoz, A. B. Klimov, G. Bjork, Y. -H. Kim, C. Mueller, Ch. Marquardt, G. Leuchs, L. L. Sanchez-Soto

We advocate a simple multipole expansion of the polarization density matrix. The resulting multipoles appear as successive moments of the Stokes variables and can be obtained from feasible measurements. In terms of these multipoles we construct a whole hierarchy of measures that accurately assess higher-order polarization fluctuations.

Distributing Entanglement with Separable States

Christian Peuntinger, Vanessa Chille, Ladislav Mista Jr., Natalia Korolkova, Michael Foertsch, Jan Korger, Christoph Marquardt, Gerd Leuchs

We experimentally demonstrate a protocol for entanglement distribution by a separable quantum system. In our experiment, two spatially separated modes of an electromagnetic field get entangled by local operations, classical communication, and transmission of a correlated but separable mode between them. This highlights the utility of quantum correlations beyond entanglement for the establishment of a fundamental quantum information resource and verifies that its distribution by a dual classical and separable quantum communication is possible.

Causal signal transmission by quantum fields. VI: The Lorentz condition and Maxwell's equations for fluctuations of the electromagnetic field

L. I. Plimak, S. Stenholm

The general structure of electromagnetic interactions in the so-called response representation of quantum electrodynamics (QED) is analysed. A formal solution to the general quantum problem of the electromagnetic field interacting with matter is found. Independently, a formal solution to the corresponding problem in classical stochastic electrodynamics (CSED) is constructed. CSED and QED differ only in the replacement of stochastic averages of c-number fields and currents by time-normal averages of the corresponding Heisenberg operators. All relations of QED connecting quantum field to quantum current lack Planck's constant, and thus coincide with their counterparts in CSED. In Feynman's terms, one encounters complete disentanglement of the potential and current operators in response picture. Based on this parallelism between QED and CSED, it is natural to expect validity of the Lorentz condition and Maxwell's equations for the time-normal averages of the potential and current. Things however turn out to be more complicated. Maxwell's equations under the time-normal ordering can only be demonstrated subject to cancellation of the so-called Schwinger terms by gauge-invariant regularisations. We presume this pattern to be general, formulating this as "commutativity conjecture". Consistency of the latter with the Heisenberg uncertainty principle is discussed. (C) 2013 Elsevier Inc. All rights reserved.

Measurement-induced optical Kerr interaction

Seckin Sefi, Vishal Vaibhav, Peter van Loock

We present a method for implementing a weak optical Kerr interaction (single-mode Kerr Hamiltonian) in a measurement-based fashion using the common set of universal elementary interactions for continuous-variable quantum computation. Our scheme is a conceptually distinct alternative to the use of naturally occurring, weak Kerr nonlinearities or specially designed nonlinear media. Instead, we propose to exploit suitable off-line prepared quartic ancilla states together with beam splitters, squeezers, and homodyne detectors. For perfect ancilla states and ideal operations, our decompositions for obtaining the measurement-based Kerr Hamiltonian lead to a realization with near-unit fidelity. Nonetheless, even by using only approximate ancilla states in the form of superposition states of up to four photons, high fidelities are still attainable. Our scheme requires four elementary operations and its deterministic implementation corresponds to about 10 ancilla-based gate teleportations. We test our measurement-based Kerr interaction against an ideal Kerr Hamiltonian by applying them both to weak coherent states and single-photon superposition states.

The photonic wheel - demonstration of a state of light with purely transverse angular momentum

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, G. Leuchs

In classical mechanics, a system may possess angular momentum which can be either transverse (e.g. in a spinning wheel) or longitudinal (e.g. for a spiraling seed falling from a tree) with respect to the direction of motion. However, for light, a typical massless wave system, the situation is less versatile. Photons are well-known to exhibit intrinsic angular momentum which is longitudinal only: the spin angular momentum defining the polarization and the orbital angular momentum associated with a spiraling phase front. Here we show that it is possible to generate a novel state of the light field that contains purely transverse angular momentum, the analogue of a spinning mechanical wheel. We realize this state by tight focusing of a polarization tailored light beam and measure it using an optical nano-probing technique. Such a novel state of the light field can find applications in optical tweezers and spanners where it allows for additional rotational degree of freedom not achievable in single-beam configurations so far.

Directional emission of dielectric disks with a finite scatterer in the THz regime

S. Preu, S. I. Schmid, F. Sedlmeir, J. Evers, H. G. L. Schwefel

In the Terahertz (THz) domain, we investigate both numerically and experimentally the directional emission of whispering gallery mode resonators that are perturbed by a small scatterer in the vicinity of the resonators rim. We determine quality factor degradation, the modal structure and the emission direction for various geometries. We find that scatterers do allow for directional emission without destroying the resonator's quality factor. This finding allows for new geometries and outcoupling scenarios for active whispering gallery mode structures such as quantum cascade lasers and passive resonators such as evanescent sensors. The experimental results agree well with finite difference time domain simulations. (C) 2013 Optical Society of America

Lightmatter interaction in free space

Gerd Leuchs, Markus Sondermann

We review recent experimental advances in the field of efficient coupling of single atoms and light in free space. Furthermore, a comparison of efficient free space coupling and strong coupling in cavity quantum electrodynamics (QED) is given. Free space coupling does not allow for observing oscillatory exchange between the light field and the atom which is the characteristic feature of strong coupling in cavity QED. Like cavity QED, free space QED does, however, offer full switching of the light field, a 180 degrees phase shift conditional on the presence of a single atom as well as 100% absorption probability of a single photon by a single atom. Furthermore, free space cavity QED comprises the interaction with a continuum of modes.

Entanglement of Gaussian states and the applicability to quantum key distribution over fading channels

Vladyslav C. Usenko, Bettina Heim, Christian Peuntinger, Christoffer Wittmann, Christoph Marquardt, Gerd Leuchs, Radim Filip

Entanglement properties of Gaussian states of light as well as the security of continuous variable quantum key distribution with Gaussian states in free-space fading channels are studied. These qualities are shown to be sensitive to the statistical properties of the transmittance distribution in the cases when entanglement is strong or when channel excess noise is present. Fading, i.e. transmission fluctuations, caused by beam wandering due to atmospheric turbulence, is a frequent challenge in free-space communication. We introduce a method of fading discrimination and subsequent post-selection of the corresponding sub-states and show that it can improve the entanglement resource and restore the security of the key distribution over a realistic fading link. Furthermore, the optimal post-selection strategy in combination with an optimized entangled resource is shown to drastically increase the protocol's robustness to excess noise, which is confirmed for experimentally measured fading channel characteristics. The stability of the result against finite data ensemble size and imperfect channel estimation is also addressed.

Entanglement witnesses and measures for bright squeezed vacuum

Magdalena Stobinska, Falk Toeppel, Pavel Sekatski, Maria V. Chekhova

Quantum entanglement is a fascinating phenomenon, especially if it is observed at the macroscopic scale. Importantly, macroscopic quantum correlations can be revealed only by accurate measurement outcomes and strategies. Here, we formulate feasible entanglement witnesses for bright squeezed vacuum in the form of the macroscopically populated polarization triplet Bell states. Their testing involves efficient photodetection and the measurement of the Stokes operators' variances. We also calculate the measures of entanglement for these states such as the Schmidt number and the logarithmic negativity. Our results show that the bright squeezed vacuum degree of polarization entanglement scales as the mean photon number squared. We analyze the applicability of an operational analog of the Schmidt number.

Probing guided modes in a monolayer colloidal crystal on a flat metal film

Sergei G. Romanov, Nicolas Vogel, Karina Bley, Katharina Landfester, Clemens K. Weiss, Sergej Orlov, Alexander V. Korovin, Gennady P. Chuiko, Alois Regensburger, et al.

Two-dimensional slab hybrid metal-dielectric photonic crystals, which are prepared by assembling polymer colloidal spheres into closely packed monolayers of hexagonal symmetry on a gold-coated glass substrate, show an improved confinement of light compared with a colloidal monolayer on a glass substrate. We demonstrated that the optical response of such hybrid crystals consists of diffractively coupled waveguiding modes, Fabry-Perot resonances, and Mie resonances. Correspondingly, two major mechanisms, namely, band transport and hopping of localized excitations, participate in the in-plane light transport in such hybrid crystals.

Compensation of Nonlinear Phase Noise Using the Effective Negative Nonlinearity of a Nonlinear Amplifying Loop Mirror

Klaus Sponsel, Christian Stephan, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

The nonlinear amplifying loop mirror (NALM) has been explored for use as a nonlinear phase-shift compensator (NPSC). Operation conditions for a tunable effective negative nonlinearity are considered and the NALM parameter optimization is discussed for direct bit-error-ratio (BER) improvement by post-compensation after a nonlinear transmission line. In this configuration, the fundamental limits for NPSC are estimated for differential quadrature phase-shift keying (DQPSK) using a simplified model. Numerical simulations of a 20 Gb/s RZ-DQPSK transmission system confirmed the applicability of this model and showed a significant BER improvement in a realistic transmission line. Alternatively, the fiber launch power per span could be increased by 2 dB for the same BER.

Electrical circuit model of arrays of resonant elements

V. Lomanets, O. Zhuromskyy, G. Onishchukov, U. Peschel

We present an effective electrical circuit model that can be used for a quasianalytic analysis of electromagnetic oscillations in arrays of coupled elements, resonant in the microwave domain. The model accounts for electric and magnetic interactions between charges and currents excited in individual resonators. Respective coupling coefficients can be calculated from the field and current distributions in a subsystem of just one or two elements, provided by a finite-difference electromagnetic solver. The model was used to investigate current distributions and dispersion relations of wave propagation on chains of coupled split-ring resonators. The change of the dispersion characteristics from forward to backward propagating wave type observed experimentally is readily reproduced by the model.

Collecting more than half the fluorescence photons from a single ion

Robert Maiwald, Andrea Golla, Martin Fischer, Marianne Bader, Simon Heugel, Benoit Chalopin, Markus Sondermann, Gerd Leuchs

We demonstrate the trapping of a single ion in the focus of a deep parabolic mirror that covers 81% of the solid angle surrounding the ion. Accounting for the reflectivity of the mirror we infer a photon collection efficiency of 54.8% for our setup. The underlying experimentally detected maximum fluorescence rate is 1.91 x 10(6) s(-1) from a single Yb-174(+) ion, mainly limited by the quantum efficiency of our photon detector. Besides the high collection efficiency, the integration of an ion trap into a parabolic mirror is a key ingredient for efficient coupling of light to a single ion in free space.

Time-reversal symmetry in optics

G. Leuchs, M. Sondermann

The utilization of time-reversal symmetry in designing and implementing (quantum) optical experiments has become more and more frequent over the last few years. We review the basic idea underlying time-reversal methods, illustrate it with several examples and discuss a number of implications.

Plasmonic dimer antennas for surface enhanced Raman scattering

Katja Hoeflich, Michael Becker, Gerd Leuchs, Silke Christiansen

Electron beam induced deposition (EBID) has recently been developed into a method to directly write optically active three-dimensional nanostructures. For this purpose a metal-organic precursor gas (here dimethyl-gold(III)-acetylacetonate) is introduced into the vacuum chamber of a scanning electron microscope where it is cracked by the focused electron beam. Upon cracking the aforementioned precursor gas, 3D deposits are realized, consisting of gold nanocrystals embedded in a carbonaceous matrix. The carbon content in the deposits hinders direct plasmonic applications. However, it is possible to activate the deposited nanostructures for plasmonics by coating the EBID structures with a continuous silver layer of a few nanometers thickness. Within this silver layer collective motions of the free electron gas can be excited. In this way, EBID structures with their intriguing precision at the nanoscale have been arranged in arrays of free-standing dimer antenna structures with nanometer sized gaps between the antennas that face each other with an angle of 90 degrees. These dimer antenna ensembles can constitute a reproducibly manufacturable substrate for exploiting the surface enhanced Raman effect (SERS). The achieved SERS enhancement factors are of the order of 10(4) for the incident laser light polarized along the dimer axes. To prove the signal enhancement in a Raman experiment we used the dye methyl violet as a robust test molecule. In future applications the thickness of such a silver layer on the dimer antennas can easily be varied for tuning the plasmonic resonances of the SERS substrate to match the resonance structure of the analytes to be detected.

Filtering of the absolute value of photon-number difference for two-mode macroscopic quantum superpositions

M. Stobinska, F. Toeppel, P. Sekatski, A. Buraczewski, M. Zukowski, M. V. Chekhova, G. Leuchs, N. Gisin

We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of macroscopic quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of "macroscopic" qubits. We propose an optical scheme, which is a relatively simple, albeit nonideal, operational implementation of such a filter. It uses tapping of the original polarization two-mode field, with a polarization-neutral beam splitter of low reflectivity. Next, the reflected beams are suitably interfered on a polarizing beam splitter. It is oriented such that it selects unbiased polarization modes with respect to the original ones. The more an incoming two-mode Fock state is unequally populated, the more the polarizing beam-splitter output modes are equally populated. This effect is especially pronounced for highly populated states. Additionally, for such states we expect strong population correlations between the original fields and the tapped one. Thus, after a photon-number measurement of the polarizing beam-splitter outputs, a feed-forward loop can be used to let through a shutter the field, which was transmitted by the tapping beam splitter. This happens only if the counts at the outputs are roughly equal. In such a case, the transmitted field differs strongly in occupation number of the two modes, while information on which mode is more populated is nonexistent (a necessary condition for preserving superpositions).

Optical mesh lattices with PT symmetry

Mohammad-Ali Miri, Alois Regensburger, Ulf Peschel, Demetrios N. Christodoulides

We investigate a class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled, while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response are studied in both the passive and parity-time (PT)-symmetric regime. The possibility of band merging and the emergence of exceptional points, along with the associated optical dynamics, are considered in detail both above and below the PT-symmetry breaking point. Finally, unidirectional invisibility in PT-synthetic mesh lattices is also examined, along with possible superluminal light transport dynamics.

Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes

C. Gabriel, A. Aiello, S. Berg-Johansen, Ch Marquardt, G. Leuchs

Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [C. Gabriel et al., Phys. Rev. Lett. 106, 060502 (2011)]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, -1.2dB +/- 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations are, depending on the measurement scheme.

Radial mode dependence of optical beam shifts

N. Hermosa, Andrea Aiello, J. P. Woerdman

It is known that orbital angular momentum (OAM) couples the Goos-Hanchen and Imbert-Fedorov shifts. Here, we present the first study of these shifts when the OAM-endowed LG(l,p) beams have higher-order radial mode index (p > 0). We show theoretically and experimentally that the angular shifts are enhanced by p while the positional shifts are not. (C) 2012 Optical Society of America

Spectral properties of high-gain parametric down-conversion

K. Yu Spasibko, T. Sh Iskhakov, M. V. Chekhova

High-gain parametric down-conversion (PDC) is a source of bright squeezed vacuum, which is a macroscopic nonclassical state of light and a promising candidate for quantum information applications. Here we study its properties, such as the intensity spectral width and the spectral width of pairwise correlations. In agreement with the theory, we observe an increase in the spectral width by 27% compared with the low-gain PDC. Frequency cross- and auto-correlations are registered by measuring the reduction of noise in the difference of PDC intensities at various pairs of wavelengths. The noise reduction plots also demonstrate super-bunching typical for collinear frequency-degenerate PDC. (C) 2012 Optical Society of America

On the use of a Continuous Wave Nd:YAG Laser in the Generation of Random Numbers

M. Sabuncu

The Nd:YAG laser is a solid state laser that has many applications in the industry, science and medicine. We in this paper use a continuous wave (CW) Nd:YAG laser emitting light at 1064 nm to generate random numbers. We first give a recipe of an experimental setup that is capable of measuring and recording the vacuum fluctuations with the help of our cw Nd:YAG laser. The basic scheme simply involves the Nd:YAG laser, detectors and some radio frequency electronic components. The laser source used in the demonstration provides us with a quantum noise limited CW at a radio frequency sideband of 14 MHz. The final data obtained after appropriate electronic signal processing are digitized voltage fluctuations that correspond to the vacuum fluctuations in the optical domain. The data randomly lies above or below zero due to its quantum mechanical probabilistic nature. We assign a '1' to the data that is positive and a '0' to the data that is negative, hence we are able to generate a random bit sequence by using a cw Nd:YAG laser. This result adds yet another interesting application to the many number of broad applications of the Nd:YAG laser system.

Quadrature phase shift keying coherent state discrimination via a hybrid receiver

C. R. Mueller, M. A. Usuga, C. Wittmann, M. Takeoka, Ch Marquardt, U. L. Andersen, G. Leuchs

We propose and experimentally demonstrate a near-optimal discrimination scheme for the quadrature phase shift keying (QPSK) protocol. We show in theory that the performance of our hybrid scheme is superior to the standard scheme-heterodyne detection-for all signal amplitudes and underpin the predictions with our experimental results. Furthermore, our scheme provides hitherto the best performance in the domain of highly attenuated signals. The discrimination is composed of a quadrature measurement, a conditional displacement and a threshold detector.

Informational completeness of continuous-variable measurements

D. Sych, J. Rehacek, Z. Hradil, G. Leuchs, L. L. Sanchez-Soto

We justify that homodyne tomography turns out to be informationally complete when the number of independent quadrature measurements is equal to the dimension of the density matrix in the Fock representation. Using this as our thread, we examine the completeness of other schemes when continuous-variable observations are truncated to discrete finite-dimensional subspaces.

Evaluation algorithms for multistep measurement of spatially varying linear polarization and phase

Andreas Berger, Vanusch Nercissian, Klaus Mantel, Irina Harder

Optical components manipulating both polarization and phase of wave fields find more and more applications in today's optical systems. In particular, the polarization orientation may vary across the aperture. New measurement techniques and evaluation algorithms are needed to simultaneously characterize the properties of such elements. In this Letter, a general measurement algorithm for locally linear polarization distributions is presented, extending the methods of phase shifting interferometry to the simultaneous determination of polarization and phase. A class of evaluation algorithms is derived, and some example algorithms are described and tested for their resilience against systematic and stochastic stepping errors. (C) 2012 Optical Society of America

Generation of a wave packet tailored to efficient free space excitation of a single atom

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, G. Leuchs

We demonstrate the generation of an optical dipole wave suitable for the process of efficiently coupling single quanta of light and matter in free space. We employ a parabolic mirror for the conversion of a transverse beam mode to a focused dipole wave and show the required spatial and temporal shaping of the mode incident onto the mirror. The results include a proof of principle correction of the parabolic mirror's aberrations. For the application of exciting an atom with a single photon pulse, we demonstrate the creation of a suitable temporal pulse envelope. We infer coupling strengths of 89% and success probabilities of up to 87% for the application of exciting a single atom for the current experimental parameters.

Far field spectrum in surface plasmon-assisted Young's double-slit interferometer

Bhaskar Kanseri, Hem Chandra Kandpal, Ramesh Chandra Budhani

We derive an expression for the resultant spectral density (spectrum) at a point in the far zone for the surface plasmons modulated Young's double-slit interference setup. The resultant spectral interference law has the same form as the standard spectral interference law for the scalar fields. This resemblance in turn provides a means for determination of the modified spectral degree of coherence at the two slits. The mathematical results also show that in an interesting situation when the field is incident at one slit only, the interference can still be observed at the observation plane. These findings are verified theoretically using a wide-band source, i.e. a black-body, having a spectrum following Planck's radiation law. (C) 2012 Elsevier B.V. All rights reserved.

Parity-time synthetic photonic lattices

Alois Regensburger, Christoph Bersch, Mohammad-Ali Miri, Georgy Onishchukov, Demetrios N. Christodoulides, Ulf Peschel

The development of new artificial structures and materials is today one of the major research challenges in optics. In most studies so far, the design of such structures has been based on the judicious manipulation of their refractive index properties. Recently, the prospect of simultaneously using gain and loss was suggested as a new way of achieving optical behaviour that is at present unattainable with standard arrangements. What facilitated these quests is the recently developed notion of 'parity-time symmetry' in optical systems, which allows a controlled interplay between gain and loss. Here we report the experimental observation of light transport in large-scale temporal lattices that are parity-time symmetric. In addition, we demonstrate that periodic structures respecting this symmetry can act as unidirectional invisible media when operated near their exceptional points. Our experimental results represent a step in the application of concepts from parity-time symmetry to a new generation of multifunctional optical devices and networks.

Role of spatial coherence in Goos-Hanchen and Imbert-Fedorov shifts: reply to comment

Andrea Aiello, J. P. Woerdman

Wang and Liu [Opt. Lett. 37, 1056 (2012)] comment on our previous Letter [Opt. Lett. 36, 3151 (2011)] regarding the validity of the theory we presented. We reply to their comment here. (C) 2012 Optical Society of America

Generation and Characterization of Multimode Quantum Frequency Combs

Olivier Pinel, Pu Jian, Renne Medeiros de Araujo, Jinxia Feng, Benoit Chalopin, Claude Fabre, Nicolas Treps

Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables, for example, in cluster state computation. We report in this Letter the first experimental evidence of a multimode nonclassical frequency comb in a femtosecond synchronously pumped optical parametric oscillator. In addition to a global reduction of its quantum intensity fluctuations, the system features quantum correlations between different parts of its frequency spectrum. This allows us to show that the frequency comb is composed of several uncorrelated eigenmodes having specific spectral shapes, two of them at least being squeezed, and to characterize their spectral shapes.

Superbunched bright squeezed vacuum state

T. Sh. Iskhakov, A. M. Perez, K. Yu. Spasibko, M. V. Chekhova, G. Leuchs

In this Letter, we experimentally study the statistical properties of a bright squeezed vacuum state containing up to 10(13) photons per mode (10 mu J per pulse), produced via high-gain parametric down conversion (PDC). The effects of bunching and superbunching of photons were observed for a single-mode PDC radiation by second-order intensity correlation function measurements with analog detectors. (C) 2012 Optical Society of America

Polarization-Entangled Light Pulses of 10(5) Photons

Timur Sh. Iskhakov, Ivan N. Agafonov, Maria V. Chekhova, Gerd Leuchs

We experimentally demonstrate polarization entanglement for squeezed vacuum pulses containing more than 105 photons. We also study photon-number entanglement by calculating the Schmidt number and measuring its operational counterpart. Theoretically, our pulses are the more entangled the brighter they are. This promises important applications in quantum technologies, especially photonic quantum gates and quantum memories.

Optical Gap solitons and Truncated Nonlinear Bloch Waves in Temporal Lattices

Christoph Bersch, Georgy Onishchukov, Ulf Peschel

We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form gap solitons and nonlinear truncated Bloch waves. Multi-pulse solitons with defects, as well as novel structures composed of a strong soliton riding on a weaker truncated nonlinear Bloch wave are shown to propagate over up to eleven coupling lengths. The nonlinear dynamics of all pulse structures is monitored over the full propagation distance which provides detailed insight into the soliton dynamics.

Visualizing the quantum interaction picture in phase space

Bahar Mehmani, Andrea Aiello

We present a graphical example of the interaction picture-time evolution. Our aim is to help students understand in a didactic manner the simplicity that this picture provides. Visualizing the interaction picture unveils its advantages, which are hidden behind the involved mathematics. Specifically, we show that the time evolution of a driven harmonic oscillator in the interaction picture corresponds to a local transformation of a phase space-reference frame into the one that is co-rotating with the Wigner function.

Spatial Coherence and Optical Beam Shifts

W. Loffler, Andrea Aiello, J. P. Woerdman

A beam of light, reflected at a planar interface, does not follow perfectly the ray optics prediction. Diffractive corrections lead to beam shifts; the reflected beam is displaced (spatial Goos-Hanchen type shifts) and/or travels in a different direction (angular Imbert-Fedorov type shifts), as compared to geometric optics. How does the degree of spatial coherence of light influence these shifts? We investigate this issue first experimentally and find that the degree of spatial coherence influences the angular beam shifts, while the spatial beam shifts are unaffected.

Probabilistic cloning of coherent states without a phase reference

Christian R. Mueller, Christoffer Wittmann, Petr Marek, Radim Filip, Christoph Marquardt, Gerd Leuchs, Ulrik L. Andersen

We present a probabilistic cloning scheme operating independently of any phase reference. The scheme is based solely on a phase-randomized displacement and photon counting, omitting the need for nonclassical resources and nonlinear materials. In an experimental implementation, we employ the scheme to clone coherent states from a phase covariant alphabet and demonstrate that the cloner is capable of outperforming the hitherto best-performing deterministic scheme. An analysis of the covariances between the output states shows that uncorrelated clones can be approached asymptotically. This simultaneously demonstrates how the effect of loss on coherent states can be compensated via noiseless preamplification.

Goos-Hanchen and Imbert-Fedorov shifts: a novel perspective

Andrea Aiello

When a beam of light is reflected by a smooth surface its behavior deviates from geometrical optics predictions. Such deviations are quantified by the so-called spatial and angular Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts of the reflected beam. These shifts depend upon the shape of the incident beam, its polarization and on the material composition of the reflecting surface. In this paper we suggest a novel approach that allows one to unambiguously isolate the beam-shape dependent aspects of GH and IF shifts. We show that this separation is possible as a result of some universal features of shifted distribution functions which are presented and discussed.

Homodyne detection for atmosphere channels

A. A. Semenov, F. Toeppel, D. Yu Vasylyev, H. V. Gomonay, W. Vogel

We give a systematic theoretical description of homodyne detection in the case where both the signal and the local oscillator pass through the turbulent atmosphere. Imperfect knowledge of the local-oscillator amplitude is effectively included in a noisy density operator, leading to postprocessing noise. Alternatively, we propose a technique with monitored transmission coefficient of the atmosphere, which is free of postprocessing noise.

Measurement of two-mode squeezing with photon number resolving multipixel detectors

Dmitry A. Kalashnikov, Si-Hui Tan, Timur Sh. Iskhakov, Maria V. Chekhova, Leonid A. Krivitsky

The measurement of the two-mode squeezed vacuum generated in an optical parametric amplifier (OPA) was performed with photon number resolving multipixel photon counters (MPPCs). Implementation of the MPPCs allows for the observation of noise reduction in a broad dynamic range of the OPA gain, which is inaccessible with standard single photon avalanche photodetectors. (c) 2012 Optical Society of America

Quantum polarization tomography of bright squeezed light

C. R. Mueller, B. Stoklasa, C. Peuntinger, C. Gabriel, J. Rehacek, Z. Hradil, A. B. Klimov, G. Leuchs, Ch Marquardt, et al.

We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2) Wigner distribution to represent states. In the limit of localized bright states, the Wigner function can be approximated by an inverse three-dimensional Radon transform. We compare this direct reconstruction with the results of a maximum likelihood estimation, thus finding excellent agreement.

Three-dimensional quantum polarization tomography of macroscopic Bell states

Bhaskar Kanseri, Timur Iskhakov, Ivan Agafonov, Maria Chekhova, Gerd Leuchs

The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional (3D) inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.

Resonant metamaterials for contrast enhancement in optical lithography

Sabine Dobmann, Dzmitry Shyroki, Peter Banzer, Andreas Erdmann, Ulf Peschel

The transmission through ultra-thin metal films is noticeable and thus limits their potential for the formation of lithographic masks. By sub-wavelength patterning of a metal film with a post structure, a resonant metamaterial is formed, which can effectively suppress the transmission. Measurements as well as calculations identify the width of the metal islands as a critical geometrical feature. Hence, the extraordinarily low transmission effect can be explained by the resonant response of single scatterers known as Localized Surface Plasmon Resonances (LSPR). A potential application of this suppressed transmission effect to thin metal masks in optical lithography is experimentally investigated. (C) 2012 Optical Society of America

Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere

C. Erven, B. Heim, E. Meyer-Scott, J. P. Bourgoin, R. Laflamme, G. Weihs, T. Jennewein

The statistical fluctuations in free-space links in the turbulent atmosphere are important for the distribution of quantum signals. To that end, we first study statistics generated by the turbulent atmosphere in an entanglement-based free-space quantum key distribution (QKD) system. Using the insights gained from this analysis, we study the effect of link fluctuations on the security and key generation rate of decoy state QKD concluding that it has minimal effect in the typical operating regimes. We then investigate the novel idea of using these turbulent fluctuations to our advantage in QKD experiments. We implement a signal-to-noise ratio filter (SNRF) in our QKD system which rejects measurements during periods of low transmission efficiency, where the measured quantum bit error rate is temporarily elevated. Using this, we increase the total secret key generated by the system from 78 009 bits to 97 678 bits, representing an increase of 25.2% in the final secure key rate, generated from the same raw signals. Lastly, we present simulations of a QKD exchange with an orbiting low earth orbit satellite and show that an SNRF will be extremely useful in such a situation, allowing many more passes to extract a secret key than would otherwise be possible.

Narrow-bandwidth high-order harmonics driven by long-duration hot spots

Maxim Kozlov, Ofer Kfir, Avner Fleischer, Alex Kaplan, Tal Carmon, Harald G. L. Schwefel, Guy Bartal, Oren Cohen

We predict and investigate the emission of high-order harmonics by atoms that cross intense laser hot spots that last for a nanosecond or longer. An atom that moves through a nanometer-scale hot spot at characteristic thermal velocity can emit high-order harmonics in a similar fashion to an atom that is irradiated by a short-duration (picosecond-scale) laser pulse. We analyze the collective emission from a thermal gas and from a jet of atoms. In both cases, the line shape of a high-order harmonic exhibits a narrow spike with spectral width that is determined by the bandwidth of the driving laser. Finally, we discuss a scheme for producing long-duration laser hot spots with intensity in the range of the intensity threshold for high-harmonic generation. In the proposed scheme, the hot spot is produced by a long laser pulse that is consecutively coupled to a high-quality micro-resonator and a metallic nano-antenna. This system may be used for generating ultra-narrow bandwidth extreme-ultraviolet radiation through frequency up-conversion of a low-cost compact pump laser.

Analytical expansion of highly focused vector beams into vector spherical harmonics and its application to Mie scattering

S. Orlov, U. Peschel, T. Bauer, P. Banzer

The analytical expansion of linearly, azimuthally, and radially polarized rigorous beam-type solutions of Maxwell's equations into vector spherical harmonics (VSHs) is presented. We report on the dominance of higher order multipoles in highly focused radially and azimuthally polarized beams compared to linearly polarized beams under similar conditions. Furthermore, we theoretically investigate a scenario in which highly focused azimuthally and radially polarized beams interact with a linear polarizer placed in the focal plane and expand the resulting fields into VSHs. The generalized Mie theory is used afterwards to investigate the scattering of the studied beams off a spherical gold nanoparticle.

The role of self-trapped excitons and defects in the formation of nanogratings in fused silica

Soeren Richter, Fei Jia, Matthias Heinrich, Sven Doering, Ulf Peschel, Andreas Tuennermann, Stefan Nolte

We investigate the role of self-trapped excitons (STEs) and defects in the formation of femtosecond laser pulse induced nanogratings (NGs) in fused silica. Our experiments reveal strongly enhanced NG formation for pulse separations up to the STE lifetime. In addition, the absorption spectra show that the weaker cumulative action of laser pulses for longer temporal separations is predominantly mediated by dangling-bond-type lattice defects that emerge from decaying STEs. (C) 2012 Optical Society of America

Observation of Orbital Angular Momentum Sidebands due to Optical Reflection

W. Loffler, Andrea Aiello, J. P. Woerdman

We investigate how the orbital angular momentum of a paraxial light beam is affected upon reflection at a planar interface. Theoretically, the unavoidable angular spread of the beam leads to orbital angular momentum sidebands, which are found to be already significant for a modest beam spread (0.05). In analogy to the polarization Fresnel coefficients, we develop an analytical theory based upon spatial Fresnel coefficients; this allows a straightforward prediction of the strength of the sidebands. We confirm this by experiment and numerical simulation.

Dipole pulse theory: Maximizing the field amplitude from 4 pi focused laser pulses

Ivan Gonoskov, Andrea Aiello, Simon Heugel, Gerd Leuchs

We present a class of exact nonstationary solutions of Maxwell equations in vacuum from dipole pulse theory: electric and magnetic dipole pulses. These solutions can provide for a very efficient focusing of electromagnetic field and can be generated by 4 pi focusing systems, such as parabolic mirrors, by using radially polarized laser pulses with a suitable amplitude profile. The particular cases of a monochromatic dipole wave and a short dipole pulse with either quasi-Gaussian or Gaussian envelopes in the far-field region are analyzed and compared in detail. As a result, we propose how to increase the maximum field amplitude in the focus by properly shaping the temporal profile of the input laser pulses with given main wavelength and peak power.

Quantum polarization characterization and tomography

J. Soederholm, G. Bjoerk, A. B. Klimov, L. L. Sanchez-Soto, G. Leuchs

We present a complete polarization characterization of any quantum state of two orthogonal polarization modes and give a systematic measurement procedure to collect the necessary data. Full characterization requires measurements of the photon number in both modes and linear optics. In the case where only the photon-number difference can be determined, a limited but useful characterization is obtained. The characteristic Stokes moment profiles are given for several common quantum states.

Polarization tomography of bright states of light

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, B. Kanseri, G. Leuchs

Polarization quantum tomography is performed on 4-mode squeezed vacuum states. Three-dimensional polarization quasiprobability functions are obtained and compared to that of an equal intensity coherent state. These distributions clearly demonstrate the difference in the polarization properties of the considered states. The reconstruction quality of the coherent state distribution is also analyzed by comparing the theoretically and experimentally obtained shapes for this state.

All photons are equal but some photons are more equal than others

Falk Toeppel, Andrea Aiello, Gerd Leuchs

Two photons are said to be identical if they are prepared in the same quantum state. Given the latter, there is a unique way to achieve this. Conversely, there are many different ways of preparing two non-identical photons: they may differ in frequency, polarization, amplitude, etc. Therefore, photon distinguishability depends upon the specific degree of freedom being varied. By means of a careful analysis of the coincidence probability distribution in a Hong-Ou-Mandel experiment, we can show that photon distinguishability can be actually quantified by the rate of distinguishability of photons, an experimentally measurable parameter that crucially depends on both the photon quantum state and the degree of freedom under control.

Interaction of highly focused vector beams with a metal knife-edge

P. Marchenko, S. Orlov, C. Huber, P. Banzer, S. Quabis, U. Peschel, G. Leuchs

We investigate the interaction of highly focused linearly polarized optical beams with a metal knife-edge both theoretically and experimentally. A high numerical aperture objective focusses beams of various wavelengths onto samples of different sub-wavelength thicknesses made of several opaque and pure materials. The standard evaluation of the experimental data shows material and sample dependent spatial shifts of the reconstructed intensity distribution, where the orientation of the electric field with respect to the edge plays an important role. A deeper understanding of the interaction between the knife-edge and the incoming highly focused beam is gained in our theoretical model by considering eigenmodes of the metal-insulator-metal structure. We achieve good qualitative agreement of our numerical simulations with the experimental findings. (C) 2011 Optical Society of America

Adaptive frequency comb illumination for interferometry in the case of nested two-beam cavities

Irina Harder, Gerd Leuchs, Klaus Mantel, Johannes Schwider

The homogeneity test of glass plates in a Fizeau interferometer is hampered by the superposition of multiple interference signals coming from the surfaces of the glass plate as well as the empty Fizeau cavity. To evaluate interferograms resulting from such nested cavities, various approaches such as the use of broadband light sources have been applied. In this paper, we propose an adaptive frequency comb interferometer to accomplish the cavity selection. An adjustable Fabry-Perot resonator is used to generate a variable frequency comb that can be matched to the length of the desired cavity. Owing to its flexibility, the number of measurements needed for the homogeneity test can be reduced to four. Furthermore, compared to approaches using a two-beam interferometer as a filter for the broadband light source, the visibility of the fringe system is considerably higher if a Fabry-Perot filter is applied. (C) 2011 Optical Society of America

Multilevel Phase-Preserving Amplitude Regeneration Using a Single Nonlinear Amplifying Loop Mirror

Martin Hierold, Tobias Roethlingshoefer, Klaus Sponsel, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

A possibility of multilevel phase-preserving amplitude regeneration using a nonlinear amplifying loop mirror (NALM) is presented for the optical star-8 quadrature amplitude modulation (QAM) transmission format as an example. Two significantly different state power ratios for the QAM signal, 1:3 and 1:7, were investigated. After the optimization of the coupler splitting ratio and the directional phase bias in the NALM, amplitude noise can be efficiently suppressed at both signal power levels simultaneously. Bit-error-ratio (BER) simulations have shown that in a system limited by nonlinear phase noise, the deployment of the NALM allows an increase of the fiber launch power by 1.9 and 2.2 dB at a BER of 10(-3) for a state power ratio of 1:3 and 1:7, respectively. The regeneration limits due to imperfections of the power transfer characteristic are also discussed.

The Direct Writing of Plasmonic Gold Nanostructures by Electron-Beam-Induced Deposition

Katja Hoeflich, Ren Bin Yang, Andreas Berger, Gerd Leuchs, Silke Christiansen

Various nanostructures are directly written by electron-beam-induced deposition using dimethyl-gold(III)-acetylacetonate as the precursor gas. After purification, their potential applications include plasmonic devices and metamaterials. Carbon contamination of the as-written structures can be completely removed by low-temperature ozone treatment, leaving polycrystalline pure gold structures (see figure). This treatment reduces the size of the nanostructures but does not substantially alter their functional shape.

Role of spatial coherence in Goos-Hanchen and Imbert-Fedorov shifts

Andrea Aiello, J. P. Woerdman

We present a theory for Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts for beams of light with arbitrary spatial coherence. By applying the well-known theory of partial spatial coherence, we can calculate explicitly spatial and angular GH and IF shifts for completely polarized beams of any shape and spatial coherence. For the specific case of a Gauss-Schell source, we find that only the angular part of GH and IF shifts is affected by the spatial coherence of the beam. A physical explanation of our results is given. (C) 2011 Optical Society of America

Spin Hall effect of light in metallic reflection

N. Hermosa, A. M. Nugrowati, Andrea Aiello, J. P. Woerdman

We report the first measurement of the spin Hall effect of light (SHEL) on an air-metal interface. The SHEL is a polarization-dependent out-of-plane shift on the reflected beam. For the case of metallic reflection with a linearly polarized incident light, both the spatial and angular variants of the shift are observed and are maximum for -45 degrees/45 degrees polarization, but zero for pure s and p polarization. For an incoming beam with circular polarization states however, only the spatial out-of-plane shift is present. (C) 2011 Optical Society of America

Diffractive simultaneous bidirectional shearing interferometry using tailored spatially coherent light

Vanusch Nercissian, Irina Harder, Klaus Mantel, Andreas Berger, Gerd Leuchs, Norbert Lindlein, Johannes Schwider

Measurements of wavefront deformations can be carried out with the help of lateral shearing interferometers. Here the focus is on a setup providing two shears along orthogonal directions simultaneously to generate the data needed for a reconstruction. We describe a diffractive solution using Ronchi phase gratings with a suppressed zeroth order for both the doubling of the wavefront under test and the bidirectional shearing unit. A series arrangement of the gratings offers an on-axis geometry, which minimizes the systematic errors of the test. For illumination, an extended incoherent monochromatic light source is used. High-contrast fringes can be obtained by tailoring the degree of coherence via a periodic intensity distribution. (c) 2011 Optical Society of America

Direct generation of a multi-transverse mode non-classical state of light

Benoit Chalopin, Francesco Scazza, Claude Fabre, Nicolas Treps

Quantum computation and communication protocols require quantum resources which are in the continuous variable regime squeezed and/or quadrature entangled optical modes. To perform more and more complex and robust protocols, one needs sources that can produce in a controlled way highly multimode quantum states of light. One possibility is to mix different single mode quantum resources. Another is to directly use a multimode device, either in the spatial or in the frequency domain. We present here the first experimental demonstration of a device capable of producing simultanuously several squeezed transverse modes of the same frequency and which is potentially scalable. We show that this device, which is an Optical Parametric Oscillator using a self-imaging cavity, produces a multimode quantum resource made of three squeezed transverse modes. (C) 2011 Optical Society of America

Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Foertsch, D. Elser, U. L. Andersen, et al.

Quantum systems such as, for example, photons, atoms, or Bose-Einstein condensates, prepared in complex states where entanglement between distinct degrees of freedom is present, may display several intriguing features. In this Letter we introduce the concept of such complex quantum states for intense beams of light by exploiting the properties of cylindrically polarized modes. We show that already in a classical picture the spatial and polarization field variables of these modes cannot be factorized. Theoretically it is proven that by quadrature squeezing cylindrically polarized modes one generates entanglement between these two different degrees of freedom. Experimentally we demonstrate amplitude squeezing of an azimuthally polarized mode by exploiting the nonlinear Kerr effect in a specially tailored photonic crystal fiber. These results display that such novel continuous-variable entangled systems can, in principle, be realized.

Birefringence and dispersion of cylindrically polarized modes in nanobore photonic crystal fiber

T. G. Euser, M. A. Schmidt, N. Y. Joly, C. Gabriel, C. Marquardt, L. Y. Zang, M. Foertsch, P. Banzer, A. Brenn, et al.

We demonstrate experimentally and theoretically that a nanoscale hollow channel placed centrally in the solid-glass core of a photonic crystal fiber strongly enhances the cylindrical birefringence (the modal index difference between radially and azimuthally polarized modes). Furthermore, it causes a large split in group velocity and group velocity dispersion. We show analytically that all three parameters can be varied over a wide range by tuning the diameters of the nanobore and the core. (C) 2010 Optical Society of America

Disentanglement in bipartite continuous-variable systems

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, M. Martinelli

Entanglement in bipartite continuous-variable systems is investigated in the presence of partial losses such as those introduced by a realistic quantum communication channel, e. g., by propagation in an optical fiber. We find that entanglement can vanish completely for partial losses, in a situation reminiscent of so-called entanglement sudden death. Even states with extreme squeezing may become separable after propagation in lossy channels. Having in mind the potential applications of such entangled light beams to optical communications, we investigate the conditions under which entanglement can survive for all partial losses. Different loss scenarios are examined, and we derive criteria to test the robustness of entangled states. These criteria are necessary and sufficient for Gaussian states. Our study provides a framework to investigate the robustness of continuous-variable entanglement in more complex multipartite systems.

Photon Propagation in a Discrete Fiber Network: An Interplay of Coherence and Losses

Alois Regensburger, Christoph Bersch, Benjamin Hinrichs, Georgy Onishchukov, Andreas Schreiber, Christine Silberhorn, Ulf Peschel

We study light propagation in a photonic system that shows stepwise evolution in a discretized environment. It resembles a discrete-time version of photonic waveguide arrays or quantum walks. By introducing controlled photon losses to our experimental setup, we observe unexpected effects like subexponential energy decay and formation of complex fractal patterns. This demonstrates that the interplay of linear losses, discreteness and energy gradients leads to genuinely new coherent phenomena in classical and quantum optical experiments. Moreover, the influence of decoherence is investigated.

Accessing photon bunching with a photon number resolving multi-pixel detector

Dmitry A. Kalashnikov, Si Hui Tan, Maria V. Chekhova, Leonid A. Krivitsky

In quantum optics and its applications, there is an urgent demand for photon-number resolving detectors. Recently, there appeared multi-pixel counters (MPPC) that are able to distinguish between 1,2,..10 photons. At the same time, strong coupling between different pixels (crosstalk) hinders their photon-number resolution. In this work, we suggest a method for 'filtering out' the crosstalk effect in the measurement of intensity correlation functions. The developed approach can be expanded to the analysis of higher-order intensity correlations by using just a single MPPC. (C) 2011 Optical Society of America

After-gate attack on a quantum cryptosystem

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, Ch Marquardt, V. Makarov, G. Leuchs

We present a method to control the detection events in quantum key distribution systems that use gated single-photon detectors. We employ bright pulses as faked states, timed to arrive at the avalanche photodiodes outside the activation time. The attack can remain unnoticed, since the faked states do not increase the error rate per se. This allows for an intercept-resend attack, where an eavesdropper transfers her detection events to the legitimate receiver without causing any errors. As a side effect, afterpulses, originating from accumulated charge carriers in the detectors, increase the error rate. We have experimentally tested detectors of the system id3110 (Clavis2) from ID Quantique. We identify the parameter regime in which the attack is feasible despite the side effect. Furthermore, we outline how simple modifications in the implementation can make the device immune to this attack.

Spectral and temporal Bloch oscillations in optical fibres

C. Bersch, G. Onishchukov, U. Peschel

Inspired by the space-time duality of paraxial beam diffraction and dispersive pulse spreading, the experimental implementation of a temporal equivalent of evanescently coupled waveguide arrays is demonstrated. Pulses interact with a time-periodic potential during their propagation through an optical fibre and the generic effect of discrete diffraction is observed in time. The presented system allows fast and high-resolving measurements of the complete signal evolution. To demonstrate the advanced capabilities, Bloch oscillations of an optical signal in both the time and frequency domains are realised.

Macroscopic Pure State of Light Free of Polarization Noise

Timur Sh. Iskhakov, Maria V. Chekhova, Georgy O. Rytikov, Gerd Leuchs

The preparation of completely nonpolarized light is seemingly easy; an everyday example is sunlight. The task is much more difficult if light has to be in a pure quantum state, as required by most quantum-technology applications. The pure quantum states of light obtained so far are either polarized or, in rare cases, manifest hidden polarization; even if their intensities are invariant to polarization transformations, higher-order moments are not. We experimentally demonstrate the preparation of the macroscopic singlet Bell state, which is pure, is completely nonpolarized, and has no polarization noise. Simultaneous fluctuation suppression in three Stokes observables below the shot-noise limit is demonstrated, opening perspectives for noiseless polarization measurements. The state is shown to be invariant to polarization transformations. This robust highly entangled isotropic state promises to fuel important applications in photonic quantum technologies.

Concentric ring metal grating for generating radially polarized light

Z. Ghadyani, I. Vartiainen, I. Harder, W. Iff, A. Berger, N. Lindlein, M. Kuittinen

A subwavelength concentric ring metal grating for visible light (lambda - 632.8 nm) is designed and fabricated by electron-beam lithography to transform circularly polarized light into radially polarized light. Experimental results are compared to theoretical predictions and the advantages and disadvantages of the element with alternative methods are discussed. (C) 2011 Optical Society of America

Modeling of Sloped Interfaces on a Yee Grid

Dzmitry M. Shyroki

To represent material boundaries in the finite-difference time-domain or frequency-domain method, effective cell permittivity epsilon(eff) can be introduced for each grid cell crossed by material interface. In this paper we revisit the derivation of tensorial epsilon(eff) for a sloped interface, and describe possible interpolation schemes for coupling of different effective electric field and induction components near the interface. We put the resulting non-symmetric and symmetrized effective permittivity matrices to numerical tests in the frequency domain. For very-high-contrast interfaces the symmetrized schemes perform worse than simple staircasing while non-symmetrized interpolation retains the second-order convergence.

Rate analysis for a hybrid quantum repeater

Nadja K. Bernardes, Ludmila Praxmeyer, Peter van Loock

We present a detailed rate analysis for a hybrid quantum repeater assuming perfect memories and using optimal probabilistic entanglement generation and deterministic swapping routines. The hybrid quantum repeater protocol is based on atomic qubit-entanglement distribution through optical coherent-state communication. An exact, analytical formula for the rates of entanglement generation in quantum repeaters is derived, including a study on the impacts of entanglement purification and multiplexing strategies. More specifically, we consider scenarios with as little purification as possible and we show that for sufficiently low local losses, such purifications are still more powerful than multiplexing. In a possible experimental scenario, our hybrid system can create near-maximally entangled (F = 0.98) pairs over a distance of 1280 km at rates of the order of 100 Hz.

Perfect imaging of hypersurfaces via transformation optics

Klaus Mantel, Dustin Bachstein, Ulf Peschel

Conventional optical imaging systems suffer from the presence of many imperfections, such as spherical aberrations, astigmatism, or coma. If the imaging system is corrected for spherical aberrations and fulfills the Abbe sine condition, perfect imaging is guaranteed between two parallel planes but only in a small neighborhood of the optical axis. It is therefore worth asking for optical systems that would allow for perfect imaging between arbitrary smooth surfaces without restrictions in shape or extension. In this Letter, we describe the application of transformation optics to design refractive index distributions that allow perfect, aberration-free imaging for various imaging configurations in R(n). A special case is the imaging between two extended parallel lines in R(2), which leads to the well-known hyperbolic secant index distribution that is used for the fabrication of gradient index lenses. (C) 2011 Optical Society of America

Quadrant detector calibration for vortex beams

N. Hermosa, A. Aiello, J. P. Woerdman

This Letter reports an experimental and theoretical study of the response of a quadrant detector (QD) to an incident vortex beam, specifically a Laguerre-Gaussian (LG) beam. We have found that the LG beam response depends on the vorticity index l. We compare LG beams with hard-ringed beams and find that at higher l values, the QD response to LG beams can be approximated by its response to hard-ringed beams. Our findings are important in view of the increasing interest in optical vortex beams. (C) 2011 Optical Society of America

Frustrated quantum phase diffusion and increased coherence of solitons due to nonlocality

Sascha Batz, Ulf Peschel

We investigate the quantum properties of solitons with nonlocal self-interaction. We find significant changes when compared to the local interaction. Quantum phase diffusion of nonlocal solitons is always reduced with respect to the local interaction and vanishes in the strongly nonlocal limit. Thus, coherence is increased in the nonlocal case. Furthermore, we compare the intrinsic quantum wave packet spreading to the recently discussed classical Gordon-Haus effect for nonlocal solitons [V. Folli and C. Conti, Phys. Rev. Lett. 104, 193901 (2010)].

Experimental cross-polarization detection of coupling far-field light to highly confined plasmonic gap modes via nanoantennas

J. Wen, P. Banzer, A. Kriesch, D. Ploss, B. Schmauss, U. Peschel

We experimentally demonstrate the coupling of far-field light to highly confined plasmonic gap modes via connected nanoantennas. The excitation of plasmonic gap modes is shown to depend on the polarization, position, and wavelength of the incident beam. Far-field measurements performed in crossed polarization allow for the detection of extremely weak signals re-emitted from gap waveguides and can increase the signal-to-noise ratio dramatically. (C) 2011 American Institute of Physics. [doi:10.1063/1.3564904]

Goos-Hanchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam

Andrea Aiello, J. P. Woerdman

Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts are diffractive corrections to geometric optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question of how the GH and IF shifts behave for a "nondiffracting" Bessel beam. (C) 2011 Optical Society of America

Generation of bright squeezed vacuum in the Karassiov states

M. V. Chekhova, T. Sh. Iskhakov, G. Leuchs, G. O. Rytikov

We suggest an experimental procedure allowing one to prepare squeezed vacuum in a special type of generalized Bell states, first introduced by V.P. Karassiov. We present the first results on the experimental generation of such states and observation of their polarization properties.

Superlinear threshold detectors in quantum cryptography

Lars Lydersen, Nitin Jain, Christoffer Wittmann, Oystein Maroy, Johannes Skaar, Christoph Marquardt, Vadim Makarov, Gerd Leuchs

We introduce the concept of a superlinear threshold detector, a detector that has a higher probability to detect multiple photons if it receives them simultaneously rather than at separate times. Highly superlinear threshold detectors in quantum key distribution systems allow eavesdropping the full secret key without being revealed. Here, we generalize the detector control attack, and analyze how it performs against quantum key distribution systems with moderately superlinear detectors. We quantify the superlinearity in superconducting single-photon detectors based on earlier published data, and gated avalanche photodiode detectors based on our own measurements. The analysis shows that quantum key distribution systems using detector(s) of either type can be vulnerable to eavesdropping. The avalanche photodiode detector becomes superlinear toward the end of the gate. For systems expecting substantial loss, or for systems not monitoring loss, this would allow eavesdropping using trigger pulses containing less than 120 photons per pulse. Such an attack would be virtually impossible to catch with an optical power meter at the receiver entrance.

Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, I. Harder

A discontinuous space variant sub-wavelength dielectric grating is designed and fabricated for generating radially polarized light in visible region (lambda = 632.8 nm). The design is based on sub-wavelength silicon nitride structures introducing a retardation of pi/2 by form birefringence, with space variant orientation of the optical axis. The pattern is divided into concentric ring segments with constant structural parameters, therefore reducing electron-beam writing time significantly. The design avoids the technological challenges encountered in the generation of a continuous space variant grating while maintaining good quality of the resulting polarization mode. [DOI: http://dx.doi.org/10.2971/jeos.2011.11041]

Device Calibration Impacts Security of Quantum Key Distribution

Nitin Jain, Christoffer Wittmann, Lars Lydersen, Carlos Wiechers, Dominique Elser, Christoph Marquardt, Vadim Makarov, Gerd Leuchs

Characterizing the physical channel and calibrating the cryptosystem hardware are prerequisites for establishing a quantum channel for quantum key distribution (QKD). Moreover, an inappropriately implemented calibration routine can open a fatal security loophole. We propose and experimentally demonstrate a method to induce a large temporal detector efficiency mismatch in a commercial QKD system by deceiving a channel length calibration routine. We then devise an optimal and realistic strategy using faked states to break the security of the cryptosystem. A fix for this loophole is also suggested.

Quick root searching method for resonances of dielectric optical microcavities with the boundary element method

Chang-Ling Zou, Harald G. L. Schwefel, Fang-Wen Sun, Zheng-Fu Han, Guang-Can Guo

In this paper, we developed an efficient method for searching the resonant eigenfrequency of dielectric optical microcavities by the boundary element method. By transforming the boundary integral equation to a general eigenvalue problem for arbitrary, symmetric, and multi-domain shaped optical microcavities, we analyzed the regular motion of the eigenvalues against the frequency. The new strategy can predict multiple resonances, increase the speed of convergence, and avoid non-physical spurious solutions. These advantages greatly reduce the computation time in the search process of the resonances. Moreover, this method is not only valuable for dielectric microcavities, but is also suitable for other photonic systems with dissipations, whose resonant eigenfrequencies are complex numbers. (C) 2011 Optical Society of America

Quantum Light from a Whispering-Gallery-Mode Disk Resonator

J. U. Fuerst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch Marquardt, G. Leuchs

Optical parametric down-conversion has proven to be a valuable source of nonclassical light. The process is inherently able to produce twin-beam correlations along with individual intensity squeezing of either parametric beam, when pumped far above threshold. Here, we present for the first time the direct observation of intensity squeezing of -1.2 dB of each of the individual parametric beams in parametric down-conversion by use of a high quality whispering-gallery-mode disk resonator. In addition, we observed twin-beam quantum correlations of -2.7 dB with this cavity. Such resonators feature strong optical confinement and offer tunable coupling to an external optical field. This work exemplifies the potential of crystalline whispering-gallery-mode resonators for the generation of quantum light. The simplicity of this device makes the application of quantum light in various fields highly feasible.

Theory of anisotropic whispering-gallery-mode resonators

Marco Ornigotti, Andrea Aiello

An analytic solution for a uniaxial spherical resonator is presented using the method of Debye potentials. This serves as a starting point for the calculation of whispering gallery modes (WGMs) in such a resonator. Suitable approximations for the radial functions are discussed in order to best characterize WGMs. The characteristic equation and its asymptotic expansion for the anisotropic case is also discussed, and an analytic formula with a precision of the order O[nu(-1)] is also given. Our careful treatment of both boundary conditions and asymptotic expansions makes the present work a particularly suitable platform for a quantum theory of whispering gallery resonators.

Polarization properties of macroscopic Bell states

Timur Sh. Iskhakov, Ivan N. Agafonov, Maria V. Chekhova, Georgy O. Rytikov, Gerd Leuchs

The four two-photon polarization Bell states are one of the main instruments in the toolbox of quantum optics and quantum information. In our experiment we produce their multiphoton counterparts, macroscopic Bell states. These are relevant to applications in quantum technologies because they provide efficient interactions with material quantum objects and with each other via nonlinear interactions. Furthermore, we study the polarization properties of these states using the concept of second-order degree of polarization and its higher-order generalization.

Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, I. Ruo Berchera

We present a complete and exhaustive theory of signal-to-noiseratio in bipartite ghost imaging with classical (thermal) and quantum (twin beams) light. The theory is compared with experiment for both twin beams and thermal light in a certain regime of interest.

Artificial boundary conditions for certain evolution PDEs with cubic nonlinearity for non-compactly supported initial data

V. Vaibhav

The paper addresses the problem of constructing non-reflecting boundary conditions for two types of one dimensional evolution equations, namely, the cubic nonlinear Schrodinger (NLS) equation, partial derivative(t)u + Lu - i chi vertical bar u vertical bar(2)u = 0 with L -i partial derivative(2)(x), and the equation obtained by letting L partial derivative(3)(x). The usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain. We adapt the pseudo-differential approach developed by Antoine et al. (2006) [5] for the NLS equation to the second type of evolution equation, and further, extend the scheme to the aforementioned class of initial data for both of the equations. In addition, we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness. (C) 2011 Elsevier Inc. All rights reserved.

COMPARATIVE TEST OF TWO METHODS OF QUANTUM EFFICIENCY ABSOLUTE MEASUREMENT BASED ON SQUEEZED VACUUM DIRECT DETECTION

I. N. Agafonov, M. V. Chekhova, A. N. Penin, G. O. Rytikov, O. A. Shumilkina, T. Sh Iskhakov

We realize and test in experiment a method recently proposed for measuring absolute quantum efficiency of analog photodetectors. Similar to the traditional (Klyshko) method of absolute calibration, the new one is based on the direct detection of two-mode squeezed vacuum at the output of a traveling wave OPA. However, in the new method, one measures the difference-photocurrent variance rather than the correlation function of photocurrents (number of coincidences), which makes the technique applicable for high-gain OPA. In this work we test the new method versus the traditional one for the case of photon-counting detectors where both techniques are valid.

Bell-inequality tests with macroscopic entangled states of light

M. Stobinska, P. Sekatski, A. Buraczewski, N. Gisin, G. Leuchs

Quantum correlations may violate the Bell inequalities. Most experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiments which simultaneously close this loophole and the locality loophole are highly desirable and remain challenging. An approach to loophole-free Bell tests is based on amplification of the entangled photons (i.e., on macroscopic entanglement), for which an optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of the possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell tests and quantum protocols are the subject of an intensive study in the field nowadays.

Intensity correlations of thermal light

T. Iskhakov, A. Allevi, D. A. Kalashnikov, V. G. Sala, M. Takeuchi, M. Bondani, M. Chekhova

We demonstrate measurement of normalized Glauber's intensity correlation functions of different orders using an array photodetector. As the light source, we use a laser beam scattered by a rotating ground-glass disc, which has statistics close to that of thermal light. We compare the measurements of the normalized correlation functions to that of the difference-intensity variance and show that they are in a certain sense complementary. The independence of the variance measurement on the number of temporal modes has been demonstrated for the first time. Different versions of high-order ghost imaging are also realized and characterized quantitatively.

Phase noise suppression in a DPSK transmission system by the use of an attenuation-imbalanced NOLM

C. Stephan, K. Sponsel, G. Onishchukov, B. Schmauss, G. Leuchs

A nonlinear optical loop mirror (NOLM) imbalanced by attenuation has been used for the suppression of nonlinear phase noise in a DPSK transmission system. It has been experimentally shown that such a passive, NOLM-based regenerator can significantly improve the performance of a phase-encoded transmission when it is limited by nonlinear phase noise. A brief overview over the advantages und limitations of different NOLM-based phase-preserving amplitude regenerators is also given. (C) 2011 Elsevier B.V. All rights reserved.

Absolute calibration of photodetectors: photocurrent multiplication versus photocurrent subtraction

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, A. N. Penin, G. O. Rytikov, O. A. Shcherbina

We report testing of the new absolute method of photodetector calibration based on the difference-signal measurement for two-mode squeezed vacuum by comparison with the traditional absolute method based on coincidence counting. Using low-gain parametric downconversion, we have measured the quantum efficiency of a counting detector by both methods. The difference-signal method was adapted for the counting detectors by taking into account the dead-time effect. (c) 2011 Optical Society of America

Classical and quantum properties of cylindrically polarized states of light

Annemarie Holleczek, Andrea Aiello, Christian Gabriel, Christoph Marquardt, Gerd Leuchs

We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electromagnetic field, calculate their total angular momentum and highlight the subtleties of their structure. Furthermore, a hybrid spatio-polarization description for such modes is introduced and developed. In particular, two independent Poincare spheres have been introduced to represent simultaneously the polarization and spatial degree of freedom of CPMs. Possible mode-to-mode transformations accomplishable with the help of Bconventional polarization and spatial phase retarders are shown within this representation. Moreover, the importance of these CPMs in the quantum optics domain due to their classical features is highlighted. (C) 2011 Optical Society of America

Parallel two-step phase-shifting digital holograph microscopy based on a grating pair

Peng Gao, Baoli Yao, Irina Harder, Junwei Min, Rongli Guo, Juanjuan Zheng, Tong Ye

An optical configuration for parallel two-step phase-shifting digital holographic microscopy (DHM) based on a grating pair is proposed for the purpose of real-time phase microscopy. Orthogonally circularly polarized object and reference waves are diffracted twice by a pair of gratings, and two parallel copies for each beams come into being. Combined with polarization elements, parallel two-step phase-shifting holograms are obtained. Based on the proposed configuration, two schemes of DHM, i.e., slightly off-axis and on-axis DHM, have been implemented. The slightly off-axis DHM suppresses the dc term by subtracting the two phase-shifting holograms from each other, thus the requirement on the off-axis angle and sampling power of the CCD camera is reduced greatly. The on-axis DHM has the least requirement on the resolving power of the CCD camera, while it requires that the reference wave is premeasured and its intensity is no less than 2 times the maximal intensity of the object wave. (C) 2011 Optical Society of America

Geometric Spin Hall Effect of Light at polarizing interfaces

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, G. Leuchs

The geometric Spin Hall Effect of Light (geometric SHEL) amounts to a polarization-dependent positional shift when a light beam is observed from a reference frame tilted with respect to its direction of propagation. Motivated by this intriguing phenomenon, the energy density of the light beam is decomposed into its Cartesian components in the tilted reference frame. This illustrates the occurrence of the characteristic shift and the significance of the effective response function of the detector. We introduce the concept of a tilted polarizing interface and provide a scheme for its experimental implementation. A light beam passing through such an interface undergoes a shift resembling the original geometric SHEL in a tilted reference frame. This displacement is generated at the polarizer and its occurrence does not depend on the properties of the detection system. We give explicit results for this novel type of geometric SHEL and show that at grazing incidence this effect amounts to a displacement of multiple wavelengths, a shift larger than the one introduced by Goos-Hanchen and Imbert-Fedorov effects.

Generation of Kerr non-Gaussian motional states of trapped ions

M. Stobinska, A. S. Villar, G. Leuchs

Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally present in this kind of system. We perform detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits generation of all other complex non-Gaussian states with negative Wigner functions resulting from Kerr nonlinear interaction. Especially, superpositions of several coherent states are achieved at a fraction of the time necessary to produce the cat state. Copyright (C) EPLA, 2011

Witnessing effective entanglement over a 2km fiber channel

Christoffer Wittmann, Josef Fuerst, Carlos Wiechers, Dominique Elser, Hauke Haeseler, Norbert Luetkenhaus, Gerd Leuchs

We present a fiber-based continuous-variable quantum key distribution system. In the scheme, a quantum signal of two non-orthogonal weak optical coherent states is sent through a fiber-based quantum channel. The receiver simultaneously measures conjugate quadratures of the light using two homodyne detectors. From the measured Q-function of the transmitted signal, we estimate the attenuation and the excess noise caused by the channel. The estimated excess noise originating from the channel and the channel attenuation including the quantum efficiency of the detection setup is investigated with respect to the detection of effective entanglement. The local oscillator is considered in the verification. We witness effective entanglement with a channel length of up to 2km. (C) 2010 Optical Society of America

Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code

Mikael Lassen, Metin Sabuncu, Alexander Huck, Julien Niset, Gerd Leuchs, Nicolas J. Cerf, Ulrik L. Andersen

A fundamental requirement for enabling fault-tolerant quantum information processing is an efficient quantum error-correcting code that robustly protects the involved fragile quantum states from their environment(1-10). Just as classical error-correcting codes are indispensible in today's information technologies, it is believed that quantum error-correcting code will play a similarly crucial role in tomorrow's quantum information systems. Here, we report on the experimental demonstration of a quantum erasure-correcting code that overcomes the devastating effect of photon losses. Our quantum code is based on linear optics, and it protects a four-mode entangled mesoscopic state of light against erasures. We investigate two approaches for circumventing in-line losses, and demonstrate that both approaches exhibit transmission fidelities beyond what is possible by classical means. Because in-line attenuation is generally the strongest limitation to quantum communication, such an erasure-correcting code provides a new tool for establishing quantum optical coherence over longer distances.

Prospect for detecting squeezed states of light created by a single atom in free space

Magdalena Stobinska, Markus Sondermann, Gerd Leuchs

We discuss the possibilities of studying in detail the dynamics of spontaneous emission of a single photon by a single atom and measuring the transient degree of squeezing by means of full solid angle fluorescence detection. (C) 2009 Elsevier B.V. All rights reserved.

Widely tunable optical delay generator

K. Jamshidi, A. Wiatrek, C. Bersch, G. Onishchukov, G. Leuchs, T. Schneider

We propose and demonstrate a method for quasi storage of light based on periodic spectral filtering realized in the time domain by amplitude modulation using frequency-to-time conversion. The delay can be tuned in a wide range by changing the frequency of an electrical modulation signal. In our experiments, the delay of single 2.5 ps pulses varied by 66 pulse widths. The technique works equally well for more complex optical data packets. Contrary to known approaches, the method has a very large spectral bandwidth and can be implemented by either fiber or integrated solutions using existing technologies. Because of the large bandwidth, fractional delays up to several tens of thousands of pulse widths can be achieved potentially for subpicosecond pulses, which is a tremendous value regarding the implementation simplicity. (C) 2010 Optical Society of America

Experimental demonstration of squeezed-state quantum averaging

Mikael Lassen, Lars Skovgaard Madsen, Metin Sabuncu, Radim Filip, Ulrik L. Andersen

We propose and experimentally demonstrate a universal quantum averaging process implementing the harmonic mean of quadrature variances. The averaged variances are prepared probabilistically by means of linear optical interference and measurement-induced conditioning. We verify that the implemented harmonic mean yields a lower value than the corresponding value obtained for the standard arithmetic-mean strategy. The effect of quantum averaging is experimentally tested for squeezed and thermal states as well as for uncorrelated and partially correlated noise sources. The harmonic-mean protocol can be used to efficiently stabilize a set of squeezed-light sources with statistically fluctuating noise levels.

Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator

J. U. Fuerst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, G. Leuchs

We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering-gallery-mode resonator made of lithium niobate. A conversion efficiency of 9% is achieved at 30 mu W in-coupled continuous wave pump power. The observed saturation pump power of 3.2 mW is almost 2 orders of magnitude lower than the state-of-the-art value. This suggests an application of our frequency doubler as a source of nonclassical light requiring only a low-power pump, which easily can be quantum noise limited. Our theoretical analysis of the three-wave mixing in a whispering-gallery-mode resonator provides the relative conversion efficiencies for frequency doubling in various modes.

Noise-powered probabilistic concentration of phase information

Mario A. Usuga, Christian R. Mueller, Christoffer Wittmann, Petr Marek, Radim Filip, Christoph Marquardt, Gerd Leuchs, Ulrik L. Andersen

Phase-insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state(1-5). However, this fundamental noise penalty in amplification can be circumvented by resorting to a probabilistic scheme as recently proposed and demonstrated in refs 6-8. These amplifiers are based on highly non-classical resources in a complex interferometer. Here we demonstrate a probabilistic quantum amplifier beating the fundamental quantum limit using a thermal-noise source and a photon-number-subtraction scheme(9). The experiment shows, surprisingly, that the addition of incoherent noise leads to a noiselessly amplified output state with a phase uncertainty below the uncertainty of the state before amplification. This amplifier might become a valuable quantum tool in future quantum metrological schemes and quantum communication protocols.

Thermal blinding of gated detectors in quantum cryptography

Lars Lydersen, Carlos Wiechers, Christoffer Wittmann, Dominique Elser, Johannes Skaar, Vadim Makarov

It has previously been shown that the gated detectors of two commercially available quantum key distribution (QKD) systems are blindable and controllable by an eavesdropper using continuous-wave illumination and short bright trigger pulses, manipulating voltages in the circuit [Nat. Photonics 4, 686 (2010)]. This allows for an attack eavesdropping the full raw and secret key without increasing the quantum bit error rate (QBER). Here we show how thermal effects in detectors under bright illumination can lead to the same outcome. We demonstrate that the detectors in a commercial QKD system Clavis2 can be blinded by heating the avalanche photo diodes (APDs) using bright illumination, so-called thermal blinding. Further, the detectors can be triggered using short bright pulses once they are blind. For systems with pauses between packet transmission such as the plug-and-play systems, thermal inertia enables Eve to apply the bright blinding illumination before eavesdropping, making her more difficult to catch. (C) 2010 Optical Society of America

Continuous-variable entanglement distillation of non-Gaussian mixed states

Ruifang Dong, Mikael Lassen, Joel Heersink, Christoph Marquardt, Radim Filip, Gerd Leuchs, Ulrik L. Andersen

Many different quantum-information communication protocols such as teleportation, dense coding, and entanglement-based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical network. The distribution of entanglement in such a network is, however, hampered by loss and noise that is inherent in all practical quantum channels. Thus, to enable faithful transmission one must resort to the protocol of entanglement distillation. In this paper we present a detailed theoretical analysis and an experimental realization of continuous variable entanglement distillation in a channel that is inflicted by different kinds of non-Gaussian noise. The continuous variable entangled states are generated by exploiting the third order nonlinearity in optical fibers, and the states are sent through a free-space laboratory channel in which the losses are altered to simulate a free-space atmospheric channel with varying losses. We use linear optical components, homodyne measurements, and classical communication to distill the entanglement, and we find that by using this method the entanglement can be probabilistically increased for some specific non-Gaussian noise channels.

Coherent state quantum key distribution with multi letter phase-shift keying

Denis Sych, Gerd Leuchs

We present a protocol for quantum key distribution using discrete modulation of coherent states of light. Information is encoded in the variable phase of coherent states which can be chosen from a regular discrete set ranging from binary to continuous modulation, similar to phase-shift keying in classical communication. Information is decoded by simultaneous homodyne measurement of both quadratures and requires no active choice of basis. The protocol utilizes either direct or reverse reconciliation, both with and without postselection. We analyze the security of the protocol and show how to enhance it by the optimal choice of all variable parameters of the quantum signal.

Robustness of bipartite Gaussian entangled beams propagating in lossy channels

F. A. S. Barbosa, A. S. Coelho, A. J. de Faria, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, M. Martinelli

Subtle quantum properties offer exciting new prospects in optical communications. For example, quantum entanglement enables the secure exchange of cryptographic keys(1) and the distribution of quantum information by teleportation(2,3). Entangled bright beams of light are increasingly appealing for such tasks, because they enable the use of well-established classical communications techniques(4). However, quantum resources are fragile and are subject to decoherence by interaction with the environment. The unavoidable losses in the communication channel can lead to a complete destruction of entanglement(5-8), limiting the application of these states to quantum-communication protocols. We investigate the conditions under which this phenomenon takes place for the simplest case of two light beams, and analyse characteristics of states which are robust against losses. Our study sheds new light on the intriguing properties of quantum entanglement and how they may be harnessed for future applications.

The quantum vacuum at the foundations of classical electrodynamics

G. Leuchs, A. S. Villar, L. L. Sanchez-Soto

In the classical theory of electromagnetism, the permittivity epsilon (0) and the permeability mu (0) of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally, our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values of epsilon (0) and mu (0) and for the volume of a virtual pair. Such an interpretation would provide an intriguing connection between the celebrated theory of classical electromagnetism and the quantum theory in the weak-field limit.

Accessing Higher Order Correlations in Quantum Optical States by Time Multiplexing

M. Avenhaus, K. Laiho, M. V. Chekhova, C. Silberhorn

We experimentally measured higher order normalized correlation functions (NCF) of pulsed light with a time-multiplexing detector. We demonstrate excellent performance of our device by verifying unity valued NCF up to the eighth order for coherent light and factorial dependence of the NCF for pseudothermal light. We applied our measurement technique to a type-II parametric down-conversion source to investigate mutual two-mode correlation properties and ascertain nonclassicality.

Free-Space Squeezing Assists Perfectly Matched Layers in Simulations on a Tight Domain

Dzmitry M. Shyroki, Aliaksandra M. Ivinskaya, Andrei V. Lavrinenko

To minimize computer memory consumption in the finite-difference modeling, one tends to place computational domain boundaries as close to the simulated object as possible. Unfortunately, this leads to inaccurate solution in the case when evanescent electromagnetic field is expected to spread far outside the object, as in simulations of eigenmodes or scattering at a wavelength comparable to or larger than the object itself. Here, we show how, in addition to applying the perfectly matched layers (PMLs), outer free space can be squeezed to avoid cutting the evanescent field tails by the PMLs or computational domain borders. Adding the squeeze-transform layers to the standard PMLs requires no changes to the finite-difference algorithms.

Angular momenta and spin-orbit interaction of nonparaxial light in free space

Konstantin Y. Bliokh, Miguel A. Alonso, Elena A. Ostrovskaya, Andrea Aiello

We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin-and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.

Interacting waves on chains of split-ring resonators in the presence of retardation

V. Lomanets, O. Zhuromskyy, G. Onishchukov, O. Sydoruk, E. Tatartschuk, E. Shamonina, G. Leuchs, U. Peschel

Wave propagation is studied experimentally in a one-dimensional periodic chain of magnetically coupled split-ring resonators with a spacing of about one tenth of the resonant wavelength. Retardation leads to a strong interaction between magnetoinductive and free-space waves. Two kinds of guided modes are observed: a slow backward wave which propagates far outside the light cone, and a fast forward wave close to the light cone. The two merge in a region of zero group velocity. The results are relevant for all one- and two-dimensional periodic systems interacting with waves of the surrounding space. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3462314]

Demonstration of a quasi-scalar angular Goos-Hanchen effect

M. Merano, N. Hermosa, A. Aiello, J. P. Woerdman

We show experimentally that the angular Goos-Hanchen (GH) effect can be easily observed, also without employing its resonant enhancement at Brewster incidence. An s-polarized beam was used to decouple the polarization from the propagation dynamics of the beam. We found that, in this case, the angular GH effect can be strongly enhanced by increasing the angular aperture of the Gaussian beam. Our experiments suggest a route toward observing the angular GH effect for true scalar waves, such as acoustic waves and quantum matter waves. (C) 2010 Optical Society of America

Quantum key distribution with multi letter alphabets

D. Sych, G. Leuchs

We present a new protocol for continuous variable quantum key distribution (CV QKD). The novelty of the protocol is a multi letter alphabet represented by coherent states of light with a fixed amplitude and variable phase. Information is encoded in the phase of a coherent state which can be chosen from a regular discrete set consisting, however, of an arbitrary number of letters. We evaluate the security of the protocol against the beam splitting attack. As a result we show the proposed protocol has advantages over the standard two letter coherent state QKD protocol, especially in the case when losses in the communication channel are low.

Phase-shifting point-diffraction interferometry with common-path and in-line configuration for microscopy

Peng Gao, Irina Harder, Vanusch Nercissian, Klaus Mantel, Baoli Yao

A new common-path and in-line point-diffraction interferometer for quantitative phase microscopy is proposed. The interferometer is constructed by introducing a grating pair into the point-diffraction interferometer, thus forming a common-path and in-line configuration for object and reference waves. Achromatic phase shifting is implemented by linearly moving one of the two gratings in its grating vector direction. The feasibility of the proposed configuration is demonstrated by theoretical analysis and experiments. (C) 2010 Optical Society of America

Demonstration of Coherent-State Discrimination Using a Displacement-Controlled Photon-Number-Resolving Detector

Christoffer Wittmann, Ulrik L. Andersen, Masahiro Takeoka, Denis Sych, Gerd Leuchs

We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon-number-resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, prove to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.

On the Analogy between a Single Atom and an Optical Resonator

S. Heugel, A. S. Villar, M. Sondermann, U. Peschel, G. Leuchs

A single atom in free space can have a strong influence on a light beam and a single photon can have a strong effect on a single atom in free space. Regarding this interaction, two conceptually different questions can be asked: can a single atom fully absorb a single photon and can a single atom fully reflect a light beam. The conditions for achieving the full effect in either case are different. Here we discuss related questions in the context of an optical resonator. When shaping a laser pulse properly it will be fully absorbed by an optical resonator, i.e., no light will be reflected and all the pulse energy will accumulate inside the resonator before it starts leaking out. We show in detail that in this case the temporal pulse shape has to match the time-reversed pulse obtained by the cavity's free decay. On the other hand a resonator, made of highly reflecting mirrors which normally reflect a large portion of any incident light, may fully transmit the light, as long as the light is narrow band and resonant with the cavity. The analogy is the single atom-normally letting most of the light pass-which under special conditions may fully reflect the incident light beam. Using this analogy we are able to study the effects of practical experimental limitations in the atom-photon coupling, such as finite pulses, bandwidths, and solid angle coverage, and to use the optical resonator as a test bed for the implementation of the quantum experiment.

A bridge between the single-photon and squeezed-vacuum states

Nitin Jain, S. R. Huisman, Erwan Bimbard, A. I. Lvovsky

The two modes of the Einstein-Podolsky-Rosen quadrature entangled state generated by parametric down-conversion interfere on a beam splitter of variable splitting ratio. Detection of a photon in one of the beam splitter output channels heralds preparation of a signal state in the other, which is characterized using homodyne tomography. By controlling the beam splitting ratio, the signal state can be chosen anywhere between the single-photon and squeezed state. (C) 2010 Optical Society of America

Assessing the Polarization of a Quantum Field from Stokes Fluctuations

A. B. Klimov, G. Bjoerk, J. Soederholm, L. S. Madsen, M. Lassen, U. L. Andersen, J. Heersink, R. Dong, Ch. Marquardt, et al.

We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincare sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.

Continuous-variable quantum information processing

Ulrik L. Andersen, Gerd Leuchs, Christine Silberhorn

Observables of quantum systems can possess either a discrete or a continuous spectrum. For example, upon measurements of the photon number of a light state, discrete outcomes will result whereas measurements of the light's quadrature amplitudes result in continuous outcomes. If one uses the continuous degree of freedom of a quantum system for encoding, processing or detecting information, one enters the field of continuous-variable (CV) quantum information processing. In this paper we review the basic principles of CV quantum information processing with main focus on recent developments in the field. We will be addressing the three main stages of a quantum information system; the preparation stage where quantum information is encoded into CVs of coherent states and single-photon states, the processing stage where CV information is manipulated to carry out a specified protocol and a detection stage where CV information is measured using homodyne detection or photon counting. [GRAPHICS] (C) 2010 by WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim

Hacking commercial quantum cryptography systems by tailored bright illumination

Lars Lydersen, Carlos Wiechers, Christoffer Wittmann, Dominique Elser, Johannes Skaar, Vadim Makarov

The peculiar properties of quantum mechanics allow two remote parties to communicate a private, secret key, which is protected from eavesdropping by the laws of physics(1-4). So-called quantum key distribution (QKD) implementations always rely on detectors to measure the relevant quantum property of single photons(5). Here we demonstrate experimentally that the detectors in two commercially available QKD systems can be fully remote-controlled using specially tailored bright illumination. This makes it possible to tracelessly acquire the full secret key; we propose an eavesdropping apparatus built from off-the-shelf components. The loophole is likely to be present in most QKD systems using avalanche photodiodes to detect single photons. We believe that our findings are crucial for strengthening the security of practical QKD, by identifying and patching technological deficiencies.

Two-color bright squeezed vacuum

Ivan N. Agafonov, Maria V. Chekhova, Gerd Leuchs

In a strongly pumped nondegenerate traveling-wave optical parametric amplifier, we produce a two-color squeezed vacuum with up to millions of photons per pulse. Our approach to registering this macroscopic quantum state is direct detection of a large number of transverse and longitudinal modes, which is achieved by making the detection time and area much larger than the coherence time and area, respectively. Using this approach, we obtain a record value of twin-beam squeezing for direct detection of bright squeezed vacuum. This makes direct detection of macroscopic squeezed vacuum a practical tool for quantum information applications.

Avoiding the blinding attack in QKD reply

Lars Lydersen, Carlos Wiechers, Christoffer Wittmann, Dominique Elser, Johannes Skaar, Vadim Makarov

Transverse angular momentum of photons

Andrea Aiello, Christoph Marquardt, Gerd Leuchs

We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasiparaxial photon beams in vacuum and reproduces the known results for classical beams when applied to coherent states of the field. Both the Poynting vector, alias the linear momentum, and the angular-momentum quantum operators of a light beam are calculated including contributions from first-order transverse derivatives. This permits a correct description of the energy flow in the beam and the natural emergence of both the spin and the angular momentum of the photons. We show that for collimated beams of light, orbital angular-momentum operators do not satisfy the standard commutation rules. Finally, we discuss the application of our theory to some concrete cases.

Tuning the structural properties of femtosecond-laser-induced nanogratings

Lourdes Patricia R. Ramirez, Matthias Heinrich, Soeren Richter, Felix Dreisow, Robert Keil, Alexander V. Korovin, Ulf Peschel, Stefan Nolte, Andreas Tuennermann

We present the results of our investigations on the formation process of nanogratings in fused silica and the influence of fabrication parameters, thereby identifying ways to systematically control the grating properties. Nanogratings, self-organized nanostructures with subwavelength periodicity, are formed in certain parameter ranges during femtosecond-laser processing of transparent materials, resulting in characteristic birefringent modifications. They provide the opportunity for the fabrication of arbitrary three-dimensional birefringent elements with position-dependent retardation. Based on our findings, we were able to fabricate birefringent elements with various precise retardations in otherwise isotropic fused silica.

CaF2 whispering-gallery-mode-resonator stabilized-narrow-linewidth laser

B. Sprenger, H. G. L. Schwefel, Z. H. Lu, S. Svitlov, L. J. Wang

A fiber laser is stabilized by introducing a calcium fluoride (CaF2) whispering-gallery-mode resonator as a filtering element in a ring cavity. It is set up using a semiconductor optical amplifier as a gain medium. The resonator is critically coupled through prisms, and used as a filtering element to suppress the laser linewidth. A three-cornered-hat method is used and shows a stability of 10(-11) after 10 mu s. Using the self-heterodyne beat technique, the linewidth is determined to be 13 kHz. This implies an enhancement factor of 10(3) with respect to the passive cavity linewidth. (C) 2010 Optical Society of America

Extraordinary transmission through a single coaxial aperture in a thin metal film

P. Banzer, J. Kindler (nee Mueller), S. Quabis, U. Peschel, G. Leuchs

We investigate experimentally the transmission properties of single sub-wavelength coaxial apertures in thin metal films (t = 110 nm). Enhanced transmission through a single sub-wavelength coaxial aperture illuminated with a strongly focused radially polarized light beam is reported. In our experiments we achieved up to four times enhanced transmission through a single coaxial aperture as compared to a (hollow) circular aperture with the same outer diameter. We attribute this enhancement of transmission to the excitation of a TEM-mode for illumination with radially polarized light inside the single coaxial aperture. A strong polarization contrast is observed between the transmission for radially and azimuthally polarized illumination. Furthermore, the observed transmission through a single coaxial aperture can be strongly reduced if surface plasmons are excited. The experimental results are in good agreement with finite difference time domain (FDTD) simulations. (C)2010 Optical Society of America

A generator for unique quantum random numbers based on vacuum states

Christian Gabriel, Christoffer Wittmann, Denis Sych, Ruifang Dong, Wolfgang Mauerer, Ulrik L. Andersen, Christoph Marquardt, Gerd Leuchs

Random numbers are a valuable component in diverse applications that range from simulations(1) over gambling to cryptography(2,3). The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics(4-11). However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique(12-15). Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators.

Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector

Christoffer Wittmann, Ulrik L. Andersen, Masahiro Takeoka, Denis Sych, Gerd Leuchs

We investigate quantum measurement strategies capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using nonprobabilistic state discrimination. We apply a postselection strategy to the measurement data of a homodyne detector as well as a photon number resolving detector in order to lower the error probability. We compare the two different receivers with an optimal intermediate measurement scheme where the error rate is minimized for a fixed rate of inconclusive results. The photon number resolving (PNR) receiver is experimentally demonstrated and compared to an experimental realization of a homodyne receiver with postselection. In the comparison, it becomes clear that the performance of the PNR receiver surpasses the performance of the homodyne receiver, which we prove to be optimal within any Gaussian operations and conditional dynamics.

Broadband NIR photoluminescence from Bi-doped Ba2P2O7 crystals: Insights into the nature of NIR-emitting Bismuth centers

Mingying Peng, Benjamin Sprenger, Markus A. Schmidt, Harald G. L. Schwefel, Lothar Wondraczek

We report on a novel type of Bi-doped crystal that exhibits ultrabroadband photoluminescence in the near infrared (NIR). Emission centers can be generated and degenerated reversibly by annealing the material in CO atmosphere and air, respectively, indicating that emission is related to the presence of Bi-species in low valence states. Correlating static and dynamic excitation and emission data with the size and charge of available lattice sites suggests that two types of Bi-0-species, each located on one of the two available Ba2+ lattice sites, are responsible for NIR photoemission. This is further confirmed by the absence of NIR emission in polycrystalline Ca2P2O7:Bi and Sr2P2O7:Bi. Excitation is assigned to transitions between the doubly degenerated ground state S-4(3/2) and the degenerated excited levels D-2(3/2), D-2(5/2) and P-2(1/2), respectively. NIR emission is attributed to D-2(3/2) -> S-4(3/2). The NIR emission center can coexist with Bi2+ species. Then, also Bi2+ is accommodated on one of the two Ba2+-sites. Energy transfer between Bi2+ ions occurs within a critical distance of 25.9 angstrom. (C) 2010 Optical Society of America

Low-Threshold Optical Parametric Oscillations in a Whispering Gallery Mode Resonator

J. U. Fuerst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, G. Leuchs

In whispering gallery mode (WGM) resonator light is guided by continuous total internal reflection along a curved surface. Fabricating such resonators from an optically nonlinear material one takes advantage of their exceptionally high quality factors and small mode volumes to achieve extremely efficient optical frequency conversion. Our analysis of the phase-matching conditions for optical parametric down-conversion (PDC) in a spherical WGM resonator shows their direct relation to the sum rules for photons' angular momenta and predicts a very low parametric oscillation threshold. We realized such an optical parametric oscillator (OPO) based on naturally phase-matched PDC in lithium niobate. We demonstrated a single-mode, strongly nondegenerate OPO with a threshold of 6: 7 mu W and linewidth under 10 MHz. This work demonstrates the remarkable capabilities of WGM-based OPOs.

Near-unit-fidelity entanglement distribution scheme using Gaussian communication

Ludmila Praxmeyer, Peter van Loock

We show how to distribute with percentage success probabilities almost perfectly entangled qubit memory pairs over repeater channel segments of the order of the optical attenuation distance. In addition to some weak, dispersive light-matter interactions, only Gaussian state transmissions and measurements are needed for this scheme. Our protocol outperforms the existing coherent-state-based schemes for entanglement distribution, even those using error-free non-Gaussian measurements. This is achieved through two innovations: First, optical squeezed states are utilized instead of coherent states. Second, the amplitudes of the bright signal pulses are reamplified at each repeater station. This latter variation is a strategy reminiscent of classical repeaters and would be impossible in single-photon-based schemes.

Flexible beam shaping system using fly's eye condenser

Norbert Lindlein, Andreas Bich, Martin Eisner, Irina Harder, Maik Lano, Reinhard Voelkel, Ken Weible, Maik Zimmermann

Normally, fly's eye condensers are used to homogenize light. However, in the case of fully coherent light, a fly's eye condenser, in connection with some simple optical elements, such as a diffractive axicon, a grating, and a telescope, can be used as a quite flexible beam shaping system, forming arrays of rings, parts of rings, or other structures with varying diameters. We present the principle, some simulation results, and some first experimental results. (C) 2010 Optical Society of America

Atmospheric channel characteristics for quantum communication with continuous polarization variables

B. Heim, D. Elser, T. Bartley, M. Sabuncu, C. Wittmann, D. Sych, C. Marquardt, G. Leuchs

We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100 m length on the flat roof of our institute's building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are auto-compensated. The LO also acts as a spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.

Environment-assisted quantum-information correction for continuous variables

Metin Sabuncu, Radim Filip, Gerd Leuchs, Ulrik L. Andersen

Quantum-information protocols are inevitably affected by decoherence which is associated with the leakage of quantum information into an environment. In this article we address the possibility of recovering the quantum information from an environmental measurement. We investigate continuous-variable quantum information, and we propose a simple environmental measurement that under certain circumstances fully restores the quantum information of the signal state although the state is not reconstructed with unit fidelity. We implement the protocol for which information is encoded into conjugate quadratures of coherent states of light and the noise added under the decoherence process is of Gaussian nature. The correction protocol is tested using both a deterministic as well as a probabilistic strategy. The potential use of the protocol in a continuous-variable quantum-key distribution scheme as a means to combat excess noise is also investigated.

Multi-pass Shack-Hartmann planeness test: monitoring thermal stress

J. Schwider, G. Leuchs

The multi-pass solution for surface measurements with the help of a Shack-Hartmann sensor (SHS) on the basis of a Fizeau cavity enables fast access to surface deviation data due to the high speed of the SHS and easy referencing of the measured data through difference measurements. The multi-pass solution described in a previous publication [J. Schwider, Opt. Express 16, 362 (2008)], provides highly sensitive measurements of small displacements caused by thermal non-equilibrium states of the test set up. Here, we want to demonstrate how a pulsed thermal load changes the surface geometry. In addition the temporal response for different plate materials is monitored through a fast wave front measurement with very high sensitivity. The thermal load close to a delta-function in time will be applied from the back-side of a plane plate by heating a small Peltier element with a heat impulse of known order of magnitude. The development of the surface deviation on the time axis can be monitored by storing a set of successive deviation pictures. (c) 2010 Optical Society of America

A novel method for polarization squeezing with Photonic Crystal Fibers

Josip Milanovic, Mikael Lassen, Ulrik L. Andersen, Gerd Leuchs

Photonic Crystal Fibers can be tailored to increase the effective Kerr nonlinearity, while producing smaller amounts of excess noise compared to standard silicon fibers. Using these features of Photonic Crystal Fibers we create polarization squeezed states with increased purity compared to standard fiber squeezing experiments. Explicit we produce squeezed states in counter propagating pulses along the same fiber axis to achieve near identical dispersion properties. This enables the production of polarization squeezing through interference in a polarization type Sagnac interferometer. We observe Stokes parameter squeezing of -3.9 +/- 0.3dB and anti-squeezing of 16.2 +/- 0.3dB. (C) 2010 Optical Society of America

Quantum-optical state engineering up to the two-photon level

Erwan Bimbard, Nitin Jain, Andrew MacRae, A. I. Lvovsky

The ability to prepare arbitrary quantum states within a certain Hilbert space is the holy grail of quantum information technology. It is particularly important for light, as this is the only physical system that can communicate quantum information over long distances. We propose and experimentally verify a scheme to produce arbitrary single-mode states of a travelling light field up to the two-photon level. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means of conditional measurements on the idler channel. The measurement consists of bringing the idler field into interference with two ancilla coherent states, followed by two single-photon detectors, which, in coincidence, herald the preparation event. By varying the amplitudes and phases of the ancillae, we can prepare any arbitrary superposition of zero-, one- and two-photon states.

How orbital angular momentum affects beam shifts in optical reflection

M. Merano, N. Hermosa, J. P. Woerdman, A. Aiello

It is well known that reflection of a Gaussian light beam (TEM(00)) by a planar dielectric interface leads to four beam shifts when compared to the geometrical-optics prediction. These are the spatial Goos-Hanchen (GH) shift, the angular GH shift, the spatial Imbert-Fedorov (IF) shift, and the angular IF shift. We report here, theoretically and experimentally, that endowing the beam with orbital angular momentum leads to coupling of these four shifts; this is described by a 4 x 4 mixing

Effect of fabrication errors on the diffraction pattern produced by sawtooth gratings

Francisco Jose Torcal-Milla, Irina Harder, Norbert Lindlein

In this work we investigate, analytically and numerically, the effect on the diffracted field produced by typical fabrication errors in sawtooth gratings. The analysis is carried out for the near and far field, showing the effects on the intensity and on the diffraction orders efficiency. When the grating profile is not perfect but presents a curved profile or overdevelopment error, some different diffraction orders appear, changing the intensity and the efficiency of each order. In addition, when roughness is present, a decreasing of efficiency is produced, but without generating different diffraction orders than the first one. We show the analytical dependence of these modifications in terms of the profile of the grating, corroborating the results with numerical methods. (C) 2010 Optical Society of America

Discrimination of optical coherent states using a photon number resolving detector

Christoffer Wittmann, Ulrik L. Andersen, Gerd Leuchs

The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non-probabilistic state discrimination. We find that appropriate postselection of the measurement data of a photon number resolving detector can be used to discriminate two coherent states with small error probability. We compare our new receiver to an optimal intermediate measurement between minimum error discrimination and unambiguous state discrimination.

Optics in Curved Space

Vincent H. Schultheiss, Sascha Batz, Alexander Szameit, Felix Dreisow, Stefan Nolte, Andreas Tuennermann, Stefano Longhi, Ulf Peschel

We experimentally study the impact of intrinsic and extrinsic curvature of space on the evolution of light. We show that the topology of a surface matters for radii of curvature comparable with the wavelength, whereas for macroscopically curved surfaces only intrinsic curvature is relevant. On a surface with constant positive Gaussian curvature we observe periodic refocusing, self-imaging, and diffractionless propagation. In contrast, light spreads exponentially on surfaces with constant negative Gaussian curvature. For the first time we realized two beam interference in negatively curved space.

Solitons in curved space of constant curvature

Sascha Batz, Ulf Peschel

We consider spatial solitons as, for example, self-confined optical beams in spaces of constant curvature, which are a natural generalization of flat space. Due to the symmetries of these spaces we are able to define respective dynamical parameters, for example, velocity and position. For positively curved space we find stable multiple-hump solitons as a continuation from the linear modes. In the case of negatively curved space we show that no localized solution exists and a bright soliton will always decay through a nonlinear tunneling process.

Complex source beam: A tool to describe highly focused vector beams analytically

S. Orlov, U. Peschel

The scalar-complex-source model is used to develop an accurate description of highly focused radially, azimuthally, linearly, and circularly polarized monochromatic vector beams. We investigate the power and full beam widths at half maximum of vigorous Maxwell equation solutions. The analytical expressions are employed to compare the vector complex source beams with the real beams produced by various high-numerical-aperture (NA) focusing systems. We find a parameter set for which the spatial extents of the analytical beams are the same as those of experimentally realized ones. We ensure the same shape of the considered beams by investigating an overlap of the complex source beams with high-NA beams. We demonstrate that the analytical expressions are good approximations for realistic highly focused beams.

On the experimental investigation of the electric and magnetic response of a single nano-structure

P. Banzer, U. Peschel, S. Quabis, G. Leuchs

We demonstrate an experimental method to separately test the optical response of a single sub-wavelength nano-structure to tailored electric and magnetic field distributions in the optical domain. For this purpose a highly focused y-polarized TEM10-mode is used which exhibits spatially separated longitudinal magnetic and transverse electric field patterns. By displacing a single sub-wavelength nano-structure, namely a single split-ring resonator (SRR), in the focal plane, different coupling scenarios can be achieved. It is shown experimentally that the single split-ring resonator tested here responds dominantly as an electric dipole. A much smaller but yet statistically significant magnetic dipole contribution is also measured by investigating the interaction of a single SRR with a magnetic field component perpendicular to the SRR plane (which is equivalent to the curl of the electric field) as well as by analyzing the intensity and polarization distribution of the scattered light with high spatial resolution. The developed experimental setup as well as the measurement techniques presented in this paper are a versatile tool to investigate the optical properties of single sub-wavelength nano-structures. (C) 2010 Optical Society of America

Triplet-like correlation symmetry of continuous variable entangled states

Gerd Leuchs, Ruifang Dong, Denis Sych

We report on a continuous variable analogue of the triplet two-qubit Bell states. We discuss the symmetry properties of entangled states of either kind, and theoretically and experimentally demonstrate a remarkable similarity of two-mode continuous variable entangled states with triplet Bell states with respect to their correlation patterns. Understanding the symmetry properties helps finding decoherence-free subspaces.

Goos-Hanchen shift for a rough metallic mirror

M. Merano, J. B. Goette, A. Aiello, M. P. van Exter, J. P. Woerdman

We investigate experimentally the dependence of the Goos-Hanchen shift on the surface properties of an air-metal interface. The shift depends on the microscopic roughness of the metal surface but it is insensitive to the large-scale variations associated with surface non-flatness. Both an effective medium model of roughness and the Rayleigh-Rice theory of scattering are used to interpret the observed phenomenon. (C) 2009 Optical Society of America

Nonparaxial polarizers

Andrea Aiello, Christoph Marquardt, Gerd Leuchs

We develop a theoretical description for polarizers that goes beyond the paraxial approximation. By combining existing theories for fields with nonplanar wavefronts, we are able to derive a simple power series expansion expressing the electric field of a light beam after a polarizer as a linear function of the field and its spatial derivatives evaluated before the polarizer. The first few terms of such expansion are explicitly given, and their physical meaning is discussed. (C) 2009 Optical Society of America

Excitation of plasmonic gap waveguides by nanoantennas

Jing Wen, Sergei Romanov, Ulf Peschel

We model and optimize the excitation of a plasmonic gap waveguide by a dipole antenna. The coupling efficiency strongly depends on antenna and waveguide properties where impedanec matching plays a critical role. The optimization of antenna lengths and gap widths shows that concepts of circuit networks can likewise be applied to optical frequencies. Using classical optimization schemes known from electrical engineering we manage to increase the coupling efficiency by a factor of 129 compared with the situation without antennas. (C) 2009 Optical Society of America

Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States

M. Lassen, G. Leuchs, U. L. Andersen

We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially nondegenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of orbital angular momentum modes is mapped on an orbital Poincare sphere, where the mode's position on the sphere is spanned by the three orbital parameters. Using a nondegenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincare sphere.

Transverse Angular Momentum and Geometric Spin Hall Effect of Light

Andrea Aiello, Norbert Lindlein, Christoph Marquardt, Gerd Leuchs

We present a novel fundamental phenomenon occurring when a polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam. This effect has a purely geometric nature and amounts to a polarization-dependent shift or split of the beam intensity distribution evaluated as the time-averaged flux of the Poynting vector across the plane of observation. We demonstrate that such a shift is unavoidable whenever the beam possesses a nonzero transverse angular momentum. This latter result has general validity and applies to arbitrary systems such as, e.g., electronic and atomic beams.

Extra phase noise from thermal fluctuations in nonlinear optical crystals

J. E. S. Cesar, A. S. Coelho, K. N. Cassemiro, A. S. Villar, M. Lassen, P. Nussenzveig, M. Martinelli

We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature.

Nonlinear Phase Noise Reduction in a DPSK Transmission System Using Cascaded Nonlinear Amplifying Loop Mirrors

C. Stephan, K. Sponsel, G. Onishchukov, B. Schmauss, G. Leuchs

The performance of a nonlinear amplifying loop mirror as a phase-preserving amplitude 2R regenerator in a differential phase-shift-keying transmission system with nonlinear phase noise as dominant limiting effect has been investigated in a recirculating fiber-loop setup. The experimental results show that cascaded regenerators can efficiently prevent the accumulation of nonlinear phase noise in such systems. It was possible to significantly increase the transmission quality; alternatively, a considerable increase of fiber launch power could be achieved for the same bit-error ratio. As a limiting effect, the amplified Rayleigh backscattering in the highly nonlinear fiber is identified when the regenerator is passed multiple times.

Feasibility of free space quantum key distribution with coherent polarization states

D. Elser, T. Bartley, B. Heim, Ch Wittmann, D. Sych, G. Leuchs

We demonstrate for the first time the feasibility of free space quantum key distribution with continuous variables under real atmospheric conditions. More specifically, we transmit coherent polarization states over a 100m free space channel on the roof of our institute's building. In our scheme, signal and local oscillator (LO) are combined in a single spatial mode, which auto-compensates atmospheric fluctuations and results in an excellent interference. Furthermore, the LO acts as a spatial and spectral filter, thus allowing unrestrained daylight operation.

An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane

Harald G. L. Schwefel, Christopher G. Poulton

We present a numerically improved multipole formulation for the calculation of resonances of multiple disks located at arbitrary positions in a 2-d plane, and suitable for the accurate computation of the resonances of large numbers of disks and of high-wavenumber eigenstates. Using a simple reformulation of the field expansions and boundary conditions, we are able to transform the multipole formalism into a linear eigenvalue problem, for which fast and accurate methods are available. Observing that the motion of the eigenvalues in the complex plane is analytic with respect to a two parameter family, we present a numerical algorithm to compute a range of multiple-disk resonances and field distributions using only two diagonalizations. This method can be applied to photonic molecules, photonic crystals, photonic crystal fibers, and random lasers. (C) 2009 Optical Society of America

Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, G. Leuchs

An optical low-coherence interferometry technique has been used to simultaneously resolve the mode profile and to measure the intermodal dispersion of guided modes of a few-mode fiber. Measurements are performed using short samples of fiber (about 50 cm). There is no need for a complex mode-conversion technique to reach a high interference visibility. Four LP mode groups of the few-mode fiber are resolved. Experimental results and numerical simulations show that the ellipticity of the fiber core leads to a distinct splitting of the degenerate high-order modes in group index. For the first time, to the best of our knowledge, it has been demonstrated that degenerate LP11 modes are much more sensitive to core shape variations than the fundamental modes and that intermodal dispersion of high-order degenerate modes can be used for characterizing the anisotropy of an optical waveguide.

Optomechanical stochastic resonance in a macroscopic torsion oscillator

F. Mueller, S. Heugel, L. J. Wang

Linear mechanical oscillators have been applied to measure very small forces, mostly with the help of noise suppression. In contrast, adding noise to nonlinear oscillators can improve the measurement conditions. Here, this effect of stochastic resonance is demonstrated in a macroscopic torsion oscillator, for an optomechanical nonlinear potential. The signal output is enhanced for a subthreshold electronic signal. This nonlinear oscillator serves as a model system for the enhancement of signal-to-noise ratio in high precision optomechanical experiments.

The information of ambiguity

Ludmila Praxmeyer, Stig Stenholm, Nikolay V. Vitanov

The phase space characteristics of a quantum state are best captured by the Wigner distribution. This displays transparently the diagonality information of the density matrix. The complementary function offering transparently the off-diagonal elements is captured by a function called the S-function, or the ambiguity. In carrying the maximal information about the quantum coherences it represents the uncertainties or ambiguity of the diagonal information. Mathematically this is manifested in its role as the phase space moment generating function. Formally it complements the information in the Wigner function. These formal relations provide the starting point for the present investigations. As a measure of quantum uncertainties, ambiguity may be used to define a probability measure on the off-diagonality. The mathematical and physical consistency of this view is presented in this paper. For a pure state, we find the extraordinary result that such distributions are their own Fourier transforms. The physical interpretation of this distribution as a carrier of classical signal fuzziness suggests the introduction of heuristic approximations to the observational uncertainties. We illustrate the properties and interpretation of the ambiguity function by some specific examples. We find that for smooth, 'Gaussian-like' distributions, the heuristic considerations provide good approximations. On the other hand, representing quantum interferences, the ambiguity serves as the most positive probe for the ultimate quantum structures which have been called sub-Planckian. They are interesting because it has been argued that such structures are physically observable.

A complete basis of generalized Bell states

Denis Sych, Gerd Leuchs

A generalization of the Bell states and Pauli matrices to dimensions which are powers of 2 is considered. A basis of maximally entangled multidimensional bipartite states (MEMBS) is chosen very similar to the standard Bell states and constructed of only symmetric and antisymmetric states. This special basis of MEMBS preserves all basic properties of the standard Bell states. We present a recursive and non-recursive method for the construction of MEMBS and discuss their properties. The antisymmetric MEMBS possess the property of rotationally invariant exclusive correlations which is a generalization of the rotational invariance of the antisymmetric singlet Bell state.

Phase-Preserving Amplitude Regeneration in DPSK Transmission Systems Using a Nonlinear Amplifying Loop Mirror

Christian Stephan, Klaus Sponsel, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

A phase-preserving 2R regenerator based on a nonlinear amplifying loop mirror was implemented in a RZ-DPSK transmission system. Its performance has been investigated in numerical simulations and experimentally. The results show that amplitude regeneration using a NALM can efficiently prevent accumulation of nonlinear phase noise in a 10 Gb/s DPSK transmission system. In the experiments, significant improvements of eye opening and of BER as well as a 3 dB increase in fiber launch power have been demonstrated. Simulations at 10 Gb/s and 100 Gb/s indicated that the enhancement of the transmission quality is smaller at 100 Gb/s. The reason is that at 100 Gb/s nonlinear intra-channel effects rather than pure nonlinear phase noise are the main limiting factor and the NALM can only reduce the accumulation of amplitude noise in that case.

Experimental observation of spectral Bloch oscillations

Christoph Bersch, Georgy Onishchukov, Ulf Peschel

We report on the first, to our knowledge, experimental observation of spectral Bloch oscillations in an optical fiber employing the interaction between a probe signal and a traveling-wave periodic potential. The spectrum of weak probe pulses is shown to oscillate on account of their group-velocity mismatch to the periodic field. The behavior of a cw probe spectrum reveals the actual discrete nature of the effect. Recurrences of the spectrum after one and two Bloch periods are demonstrated. (C) 2009 Optical Society of America

Perfect excitation of a matter qubit by a single photon in free space

M. Stobinska, G. Alber, G. Leuchs

We propose a scheme for perfect excitation of a single two-level atom by a single photon in free space. The photon state has to match the time reversed photon state originating from spontaneous decay of a two-level system. Here, we discuss its experimental preparation. The state is characterized by a particular asymmetric exponentially shaped temporal profile. Any deviations from this ideal state limit the maximum absorption. Although perfect excitation requires an infinite amount of time, we demonstrate that there is a class of initial one-photon quantum states which can achieve almost perfect absorption even for a finite interaction time. Our results pave the way for realizing perfect coupling between flying and stationary qubits in free space thus opening a possibility for building scalable quantum networks. Copyright (C) EPLA, 2009

Microwave whispering-gallery resonator for efficient optical up-conversion

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, N. Yu

Conversion of microwave radiation into the optical range has been predicted to reach unity quantum efficiency in whispering-gallery resonators made from an optically nonlinear crystal and supporting microwave and optical modes simultaneously. In this work, we theoretically explore and experimentally demonstrate a resonator geometry that can provide the required phase matching for such a conversion at any desired frequency in the sub-THz range. We show that such a ring-shaped resonator not only allows for the phase matching but also maximizes the overlap of the interacting fields. As a result, unity-efficient conversion is expected in a resonator with feasible parameters.

Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, G. Leuchs

This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell's theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.

Interferometric quasi-absolute tests for aspherics using a radial shear position

Klaus Mantel, Eduard Geist, Irina Harder, Norbert Lindlein, Gerd Leuchs

Increasing accuracy requirements in aspheric metrology make the development of absolute testing procedures for aspheric surfaces important. One strategy is transferring the standard practice three-position test for spheres to aspherics. The three-position test, however, involves a cat's eye position and therefore has certain drawbacks. We propose an absolute testing method for rotationally symmetric aspherics where the cat's eye position is replaced with a radially sheared position. Together with rotational movements of the specimen, the surface deviations can be obtained in an absolute manner. To demonstrate the validity of the procedure, we present a measurement result for a sphere and compare it with a result obtained by the standard three-position test. (C) 2009 Optical Society of America

Correlation measurement of squeezed light

Leonid A. Krivitsky, Ulrik L. Andersen, Ruifang Dong, Alexander Huck, Christoffer Wittmann, Gerd Leuchs

We study the implementation of a correlation measurement technique for the characterization of squeezed light which is nearly free of electronic noise. With two different sources of squeezed light, we show that the sign of the covariance coefficient, revealed from the time-resolved correlation data, is witnessing the presence of squeezing in the system. Furthermore, we estimate the degree of squeezing using the correlation method and compare it to the standard homodyne measurement scheme. We show that the role of electronic detector noise is minimized using the correlation approach as opposed to homodyning where it often becomes a crucial issue.

Stylus ion trap for enhanced access and sen