Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology

Aaron Z. Goldberg, Luis Sanchez-Soto, Hugo Ferretti

The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits tradeoffs in the precision with which each parameter can be estimated. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix as the metric tensor linked to the geometry of the underlying algebra su(n). This ensures an intrinsic bound that is independent of the choice of parametrization.

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.

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(10), 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.

Comment on “An encryption protocol for NEQR images based on one-particle quantum walks on a circle”

Markus Grassl

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 still are 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 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 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.

Effects of coherence on temporal resolution

Syamsundar De, Jano Gil-Lopez, Benjamin Brecht, Christine Silberhorn, Luis Sanchez-Soto, Z. Hradil, J. Rehacek

Measuring small separations between two optical sources, either in space or in time, constitute 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. Our experiment demonstrates that coherent mode projections are optimal for any degree of coherence.

Benchmarking quantum tomography completeness and fidelity with machine learning

Yong Siah Teo, Seongwook Shin, Hyunseok Jeong, Yosep Kim, Yoon-Ho Kim, Gleb I. Struchalin, Egor V. Kovlakov, 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 through collective encoding of quantum measurements, data and target states into grayscale images. By gradually accumulating measurements and data, these convolutional networks can efficiently certify a low-measurement-cost quantum-state characterization scheme. 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 with noise recognition when the networks are trained with additional bootstrapped training sets from real experimental data.

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

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

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.

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

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

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.

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.

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

Chiral Surface Lattice Resonances

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

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, 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. 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 the conventional beam-path of commercial Raman systems. Using this excitation scheme, we experimentally show that the recorded Raman spectra of individual gallium-nitride nanostructures of sub-wavelength diameter used as a test 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 of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. This Roadmap article focuses on using quantum light as a powerful sensing and spectroscopic tool to reveal novel information about complex molecules that is not accessible by classical light. It aims at bridging the quantum optics and spectroscopy communities which normally have opposite goals: manipulating complex light states with simple matter e.g. qubits versus studying complex molecules with simple classical light, respectively. Articles cover advances in the generation and manipulation of state-of-the-art quantum light sources along with applications to sensing, spectroscopy, imaging and interferometry.

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 Poincaré 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 Poincaré 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.

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

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.

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.

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 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 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 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.

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.

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.

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 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.

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 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 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 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.

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 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, 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.

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.

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.

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 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 down to few Angstroms can be resolved with sub-Angstrom precision using an all-optical method. 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 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.

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.

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

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 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).

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.

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

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.

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.

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.

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.

Satellite-Based QKD

Imran Khan, Bettina Heim, Andreas Neuzner, Christoph Marquardt

A global network of spacecraft and ground stations, distributing secret encryption keys by meansof quantum technology, could meet emerging and long-term threats to data security.

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.

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.

Tackling Africa’s digital divide

Martin P. J. Lavery, Mojtaba Mansour Abadi, Ralf Bauer, Gilberto Brambilla, Ling Cheng, Mitchell A. Cox, Angela Dudley, Andrew D. Ellis, Nicolas K. Fontaine, et al.

Innovations in ‘sustainable’ photonics technologies such as free-space optical links and solar-powered equipment provide developing countries with new cost-effective opportunities for deploying future-proof telecommunication networks.

"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.

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.

Quantum Limits of Coherent Beam Combining

Gerd Leuchs, Christian Müller, Florian Sedlmeir, Sourav Chatterjee, Nicoletta Haarlammert, Cesar Jauregui, Thomas Schreiber, Jens Limpert, Andreas Tünnermann, et al.

Coherent beam combining refers to the process of generating a bright output beam by merging independent input beams with locked relative phases. We report the first quantum mechanical noise limit calculations for coherent beam combining and compare our results to quantum-limited amplification. We highlight a favourable noise scaling for both pure and noisy input states.

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.

Joint measurement of complementary observables in moment tomography

Yong Siah Teo, Christian R. Mueller, Hyunseok Jeong, Zdenek Hradil, Jaroslav Rehacek, Luis L. Sanchez-Soto

Wigner and Husimi quasi-distributions, owing to their functional regularity, give the two archetypal and equivalent representations of all observable-parameters in continuous-variable quantum information. Balanced homodyning (HOM) and heterodyning (HET) that correspond to their associated sampling procedures, on the other hand, fare very differently concerning their state or parameter reconstruction accuracies. We present a general theory of a now-known fact that HET can be tomographically more powerful than balanced homodyning to many interesting classes of single-mode quantum states, and discuss the treatment for two-mode sources.

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 constitutes a remarkable example of this quantum-enhanced precision. The recently introduced Kings of Quantumness are especially germane for this task 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 experimental realization of these states by generating up to 21-dimensional orbital angular momentum states of single photons, and confirm their high metrological abilities.

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.

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 $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of $\rho$ and the entries of a unitary matrix $U$ relating both bases. The obtained results 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 uncertainty relation for the sum of conditional entropies.

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.

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.

Codes for Simultaneous Transmission of Quantum and Classical Information

M. Grassl, Sirui Lu, Bei Zeng

We consider the characterization as well as the construction of quantum codes that allow to transmit both quantum and classical information, which we refer to as `hybrid codes'. We construct hybrid codes $[\![n,k{: }m,d]\!]_q$ with length $n$ and distance $d$, that simultaneously transmit $k$ qudits and $m$ symbols from a classical alphabet of size $q$. Many good codes such as $[\![7,1{: }1,3]\!]_2$, $[\![9,2{: }2,3]\!]_2$, $[\![10,3{: }2,3]\!]_2$, $[\![11,4{: }2,3]\!]_2$, $[\![11,1{: }2,4]\!]_2$, $[\![13,1{: }4,4]\!]_2$, $[\![13,1{: }1,5]\!]_2$, $[\![14,1{: }2,5]\!]_2$, $[\![15,1{: }3,5]\!]_2$, $[\![19,9{: }1,4]\!]_2$, $[\![20,9{: }2,4]\!]_2$, $[\![21,9{: }3,4]\!]_2$, $[\![22,9{: }4,4]\!]_2$ have been found. All these codes have better parameters than hybrid codes obtained from the best known stabilizer quantum codes.

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 phase space to produce a coarse-grained version with reduced effective size. Our coarse-grained spaces inherit key properties of the original ones. In 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.

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).

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.

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

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.

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.

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.

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.

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 field theory and classical optics: determining the fine structure constant

Gerd Leuchs, Margaret Hawton, Luis L. Sanchez-Soto

The properties of the vacuum are described by quantum physics including the response to external fields such as electromagnetic radiation. Of the two parameters that govern the details of the electromagnetic field dynamics in vacuum, one is fixed by the requirement of Lorentz invariance c = 1/root epsilon(0)mu(0) The other one, Z(0) = root mu(0)/epsilon(0) = 1/(c epsilon(0)) and its relation to the quantum vacuum, is discussed in this contribution. Deriving epsilon(0) from the properties of the quantum vacuum implies the derivation of the fine structure constant.

Photonic crystal fibers for generating three-photon states

Maria V. Chekhova, Andrea Cavanna, M. Taheri, Cameron Okoth, Xin Jiang, Nicolas Joly, Philip St. J. Russell

Direct decay of pump photons into triplets is an interesting but not-yet-realized nonlinear effect. We are exploring two approaches using photonic crystal fibers: a gas-filled hollow-core PCF and the recently designed hybrid solid-core PCF.

Temporal and spectral properties of quantum light

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

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.

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.

How Latitude Location on a Micro-World Enables Real-Time Nanoparticle Sizing

Steve Arnold, D. Keng, E. Treasurer, M. R. Foreman

We have devised a method for using the nanoparticle induced frequency shift of whispering gallery modes (WGMs) in a microspheroid for the accurate determination of the nanoparticle size in real time. Before the introduction of this technique, size determination from the mode shift could only be obtained statistically based on the assumption that the largest perturbation occurs for binding at the equator. Determining the latitude of the binding event using two polar WGMs results in an analytic method for size determination using a single binding event. The analysis proceeds by incorporating the binding latitude into the Reactive Sensing Principle (RSP), itself containing a shape dependent form factor found using the Born approximation. By comparing this theory with experiments we find that our theoretical approach is more accurate than point dipole theory even though the optical size (circumference/wavelength) is considerably less than one.

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.

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.

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.

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.

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.

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.

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

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'.

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.

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.

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.

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.

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.

Reduction of phase singularities in a speckle Michelson setup

K. Mantel, V. Nercissian

Speckle interferometry is an optical metrology technique for characterizing rough surfaces. In one application, the deformation of a specimen under a load may be determined by comparing measurements before and after the load is applied. Owing to the surface roughness, however, the results are impaired by phase singularities, leading to a strong noise in the measurement results. Usually, filtering and smoothing operations are performed to reduce the noise. However, these procedures also affect the underlying systematic phase and are therefore disadvantageous. Instead, we examine incoherent averaging, a physical procedure, to reduce the number of phase singularities in the first place. We tailor the spatial coherence of the light using extended light sources of continuous or multipoint shape, achieving smoother phase distributions. The mechanism behind the reduction process involves subtle effects like enhancing phase singularity correlations in the fields before and after the deformation takes place.

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.

Preparation of single photon states with rising exponential shape

Bharath Srivathsan, Curpreet Kaur Gulati, Victor Leong, Mathias Seidler, Matthias Steiner, Alessandro Cere, Christian Kurtsiefer

We prepare single photons with a temporal envelope with rising exponential shape, resembling the time-reversed version of photons from the spontaneous decay process using a parametric conversion process in a cold atomic vapor. The mechanism is based on correlated photon pair preparation and heralding of one photon by the other one after engineering the temporal envelope of the herald.(1) Such a temporal single photon profile is ideal for absorption by a two level system.(2, 3) We demonstrate this in an experiment showcasing the absorption by a single Rubidium atom.(4)

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.

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

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.

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.

Codes for Simultaneous Transmission of Quantum and Classical Information

Markus Grassl, Sirui Lu, Bei Zeng

We consider the characterization as well as the construction of quantum codes that allow to transmit both quantum and classical information, which we refer to as 'hybrid codes'. We construct hybrid codes [[n, k:m, d]](q) with length n and distance d, that simultaneously transmit k qudits and m symbols from a classical alphabet of size q. Many good codes such as [[7,1:1,3]](2), [[9,2:2,3]](2), [[10,3:2,3]](2), [[11,4:2,3]](2), [[11,1:2,4]](2), [[13,1:4,4]](2), [[13,1:1,5]](2), [[14,1:2,5]](2), [[15,1:3,5]](2), [[19,9:1,4]](2), [[20,9:2,4]](2), [[21,9:3,4]](2), [[22,9:1,4]](2) have been found. All these codes have better parameters than hybrid codes obtained from the best known stabilizer quantum codes.

Directivity Based Nanoscopic Position Sensing

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

Precise position sensing of a nanoparticle or a biomolecule is of paramount importance for the field of photonics, specifically in medicine and biophysics. This is a fundamental step towards several super-resolution imaging techniques, such as fluorescence based photoactivated localization microscopy (PALM) [1]. In the last decade, using different nonlinear or linear techniques, a localization precision down to few nanometers, even Angstrom has been achieved [2]. Here, we present a new concept of position sensing enabling Angstrom accuracy, based on strongly directional light emission off a single subwavelength dielectric scatterer. To realize the strong directional emission, we take advantage of a high refractive index dielectric silicon nanosphere, which supports both electric as well as magnetic resonances in the visible spectra [3]. As a probe beam, we use a radially polarized vector beam, which upon tight focusing provides an inhomogeneous field distribution, with a strong longitudinal electric field component present on-axis [4]. While, the transverse electric field components vanish on-axis, but increase linearly with radial distance (linearity holds in close vicinity to optical axis, around 50 nm). Using this tailored electromagnetic field, electric and magnetic dipoles resonances can be induced in the dielectric scatterer, when it is located off-axis; and interference of those dipole emissions may yield strong directional emission (see Fig. 44.1). By appropriately choosing the wavelength of the probe beam, this directivity has been maximized to get a strong position dependence. With proper calibration of this strong position dependent directivity, it was possible to show that a displacement of 5 nm can be easily distinguished whereas with further statistical analysis, it was possible to resolve smaller displacement with position uncertainty of 0: 2 nm. This fast, easy to calibrate, linear technique can be very much useful for high resolution spatial and temporal particle localization and several other applications, also might constitute an alternative pathway towards linear high resolution imaging.

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.

Polarization and phase shifting interferometry

Sergej Rothau, Klaus Mantel, Norbert Lindlein

This publication presents a novel interferometric method for the simultaneous measurement of the phase and state of polarization of a light wave with arbitrary, in particular locally varying elliptical polarization. The measurement strategy is based on variations of the reference wave concerning phase and polarization and processing the interference patterns so obtained. With this method, that is very similar to the classical phase shifting interferometry, a complete analysis of spatially variant states of polarization and their phase fronts can be done in one measurement cycle. Furthermore, a direct analysis of specimens under test regarding birefringence and the impact on the phase of the incoming light can be realized. The theoretical description of the investigated methods and their experimental implementation are presented.

Gaussian and Non-Gaussian Highly Multimode Quantum Light

C. Fabre, F. Arzani, V. Averchenko, A. Dufour, C. Jacquard, Y. Ra, V. Thiel, N. Treps

We show that non-linear processes pumped by ultrashort pulses of adjustable spectral shape are ideal tools to produce highly multimode quantum states in specific light modes, featuring either Gaussian squeezed, or non-Gaussian negative, Wigner functions

Exploring Exotic Polarization Topologies in Complex 3D Electromagnetic Fields

Peter Banzer

If electromagnetic fields are spatially confined, exotic polarization phenomena and topologies can be observed. Here, we discuss the appearance and experimental study of optical polarization M\"obius strips and ribbons at the nanoscale.

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.

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.

Efficient Up-Conversion of Weak THz Signals into the Optical Domain Using a Whispering Gallery Mode Resonator

Florian Sedlmeir, Alfred Rueda, Sascha Preu, L. Enrique Garcia-Munoz, Harald G. L. Schwefel

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.

The many facets of the Fabry-Perot

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

Codeword Stabilized Quantum Codes for Asymmetric Channels

Tyler Jackson, Markus Grassl, Bei Zeng

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.

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

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

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

Nonlinear interferometers in quantum optics

M. V. Chekhova, Z. Y. Ou

A Classical Analog of Random Quantum States

Denis Sych

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.

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

Gerd Leuchs, Roy J. Glauber, Wolfgang P Schleich

Dimension of quantum phase space measured by photon correlations

Gerd Leuchs, Roy J. Glauber, Wolfgang P Schleich

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.

A chaotic approach clears up imaging

Harald G. L. Schwefel, Hakan E. Tuereci

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

Entanglement Creation by Locally Splitting a Discordant State

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

We introduce and experimentally implement counter-intuitive entanglement creation by locally splitting a classical mode that is part of a larger discordant state. Possible applications are quantum advantage in information encoding and assisted dense coding. (C) 2014 Optical Society of America

AFM-Based Pick-and-Place Handling of Individual Nanoparticles inside an SEM for the Fabrication of Plasmonic Nano-Patterns

Uwe Mick, Peter Banzer, Silke Christiansen, Gerd Leuchs

Integrating AFM technology into an SEM enables the interactive assembling of individual nanoparticles by in-situ pick-and-place handling. We present a hardware setup and introduce examples for the nanofabrication of plasmonic patterns.

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.

Experimental Investigation of a Single Chrial Nano-Structure Made of a Composite Material

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

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.

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.

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.

Bound states in a temporal fiber network with parity-time symmetry

Alois Regensburger, Mohammad-Ali Miri, Christoph Bersch, Jakob Naeger, Georgy Onishchukov, Demetrios N. Christodoulides, Ulf Peschel

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

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 macroscopic Bell states

T. Iskhakov, B. Kanseri, G. Rytikov, M. Chekhova, G. Leuchs

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.

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

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.

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.

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.

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.

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.

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.

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.

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

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

Experimental Comparison of All-Optical Phase-Preserving Amplitude Regeneration Techniques

Daniel Endres, Christian Stephan, Klaus Sponsel, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

Performance of a nonlinear amplifying loop mirror and a fiber optical parametric amplifier in saturation used as phase-preserving amplitude limiters was investigated in a setup simulating a DPSK transmission system. The Q-factor improvement as well as the power penalty reduction have been compared under identical conditions. Both regenerators provide a similar Q-factor improvement, but the nonlinear amplifying loop mirror yields a better power penalty reduction.

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)].

Concentrating the phase of a coherent state by means of probabilistic amplification

Mario A. Usuga, Christian R. Mueller, Christoffer Wittmann, Petr Marek, Radim Filip, Christoph Marquardt, Gerd Leuchs, Ulrik L. Andersen

We discuss the recent implementation of phase concentration of an optical coherent state by use of a probabilistic noiseless amplifier. The operation of the amplifier is described pictorially with phase space diagrams, and the experimental results are outlined.

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.

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.

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

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.

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.

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.

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

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

Nonlinear Phase-Shift Compensation for DQPSK Signals Using a Nonlinear Amplifying Loop Mirror

Klaus Sponsel, Christian Stephan, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

The application of a Nonlinear Amplifying Loop Mirror (NALM) as a nonlinear phase-shift compensator (NPSC) in phase-shift keyed transmission is investigated with emphasis on Differential Quadrature Phase-Shift Keying (DQPSK). The origin of the effective negative nonlinear phase shift in a NALM and the effects of the NALM parameters on the phase-shift compensation are discussed. Two possible application modes of the NALM as NPSC have been found: sole nonlinear phase-shift compensation up to 3 rad, and phase-shift compensation in a smaller range with simultaneous amplitude equalization. The points of operation for both modes and the limitations in their implementation are presented. Results show that the use of a NALM, optimized for phase-shift compensation, seems to be very promising, especially for the application as post-compensator in differential phase-shift-keyed transmission systems. To evaluate the performance of a NALM as post-compensator a simplified model of the NALM and a DQPSK transmission system was used. The BER with and without the NALM was calculated in dependence on the average nonlinear phase shift and on the input noise. The results show that with a NALM as NPSC the amount of nonlinear phase shift in a preceding transmission system can be approximately doubled for the same BER.

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.

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

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

Quantum Electrodynamics of One-Photon Wave Packets

M. Stobinska, G. Alber, G. Leuchs

Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum state of the electromagnetic radiation field which contains a small number or even a single photon only. Despite much recent work in cavity quantum electrodynamics, which has explored this problem successfully in cases in which the number of accessible electromagnetic field modes is strongly restricted by a cavity, currently still much less is known about ideal quantum state transfer between matter and few-photon quantum states of the electromagnetic field in the extreme opposite case of free space. In this contribution we review recent work which explores characteristic quantum electrodynamical phenomena governing the interaction of a material quantum system with the electromagnetic field in extreme many-mode cases which are close to cavity-free situations. For this purpose the simplest possible quantum electrodynamical situation, namely the interaction of a single material two-level system with the wave packet of a single optical photon, is investigated in free space and in situations in which a large cavity modifies the mode structure of the electromagnetic field modes. It is demonstrated that perfect excitation of an atom by a properly shaped single-photon wave packet is possible even in free space. In particular, it is demonstrated that perfect excitation of an atom can be achieved by a single optical photon which is prepared initially in an appropriate superposition of plane-wave modes, provided this photon is focused subsequently onto the absorbing atom by a parabolic cavity.

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.

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

Optimization of Dispersion-Imbalanced Loop Mirror for Phase-Preserving Amplitude Regeneration

T. Roethlingshoefer, K. Sponsel, C. Stephan, G. Onishchukov, B. Schmauss, G. Leuchs

The adaptation and optimization of a dispersion-imbalance loop mirror for phase-preserving amplitude 2R regeneration is shown by numerical simulations. Its performance has been evaluated for DPSK transmission. A 4.8dB Q-factor improvement has been demonstrated.

Cascaded Phase-Preserving Amplitude Regeneration in a DPSK Transmission System

Ch Stephan, K. Sponsel, G. Onishchukov, B. Schmauss, G. Leuchs

Experimental results obtained on 10 Gb/s RZ-DPSK transmission in a recirculating fiber-loop setup show that nonlinear amplifying loop mirrors can efficiently enhance system performance. Main limiting factor is amplified Rayleigh backscattering in highly nonlinear fiber.

Generation and Direct Detection of Broadband Mesoscopic Polarization-Squeezed Vacuum

Timur Iskhakov, Maria V. Chekhova, Gerd Leuchs

Using a traveling-wave optical parametric amplifier with two orthogonally oriented type-I BBO crystals pumped by picosecond pulses, we generate vertically and horizontally polarized squeezed vacuum states within a broad frequency-angular range. Depending on the phase between these states, fluctuations in one or another Stokes parameter are suppressed below the shot-noise limit. Because of the large number of photon pairs produced, no local oscillator is required, and 3 dB squeezing is observed by means of direct detection.

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.

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

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

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.

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.

Quadrature measurements of a bright squeezed state via sideband swapping

Jessica Schneider, Oliver Gloeckl, Gerd Leuchs, Ulrik L. Andersen

The measurement of an arbitrary quadrature of a bright quantum state of light is a commonly requested action in many quantum information protocols, but it is experimentally challenging with previously proposed schemes. We suggest that the quadrature be measured at a specific sideband frequency of a bright quantum state by transferring the sideband modes under interrogation to a vacuum state and subsequently measuring the quadrature via homodyne detection. The scheme is implemented experimentally, and it is successfully tested with a bright squeezed state of light. (C) 2009 Optical Society of America

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.

Phase-preserving amplitude regeneration for a WDM RZ-DPSK signal using a nonlinear amplifying loop mirror

K. Cvecek, K. Sponsel, C. Stephan, G. Onishchukov, R. Ludwig, C. Schubert, B. Schmauss, G. Leuchs

We propose a modified nonlinear amplifying loop mirror (NALM) for phase-preserving 2R regeneration of wavelength division multiplexed (WDM) return-to-zero differential phase-shift-keyed signals. As proof of principle the regeneration capability of this NALM setup has been investigated experimentally for two 10 Gbit/s wavelength channels. A significant eye-opening improvement and a negative power penalty of 1.2 dB have been observed in both channels. (C) 2008 Optical Society of America.

Electronic noise-free measurements 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. We show that the sign of the covariance coefficient revealed from the time-resolved correlation data allow us to distinguish among squeezed, coherent, and thermal states. In contrast to the traditional method of characterizing squeezed light, involving measurement of the variation of the difference photocurrent, the correlation measurement method allows one to eliminate the contribution of the electronic noise, which becomes a crucial issue in experiments with dim sources of squeezed light. (C) 2008 Optical Society of America

Effective Negative Nonlinearity of a Nonlinear Amplifying Loop Mirror for Compensating Nonlinearity-Induced Signal Distortions

Klaus Sponsel, Kristian Cvecek, Christian Stephan, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

Conditions for realizing effective negative nonlinearity using a NALM are analyzed. Efficient compensation of SPM-induced nonlinear phase noise in a 100Gb/s DPSK system is confirmed in numerical simulations.

Experimental Demonstration of Macroscopic Quantum Coherence in Gaussian States

Ch. Marquardt, U. L. Andersen, G. Leuchs, Y. Takeno, M. Yukawa, H. Yonezawa, A. Furusawa

We experimentally proved the existence of macroscopic coherences in Gaussian quantum states using a recently proposed criterion [I]. We show interferences with remarkable distances in phase space for squeezed, entangled and even for coherent states. (C) 2008 Optical Society of America

Experimental Demonstration of Continuous Variable Entanglement Distillation

R. F. Dong, M. Lassen, Ch. Marquardt, R. Filip, U. L. Andersen, G. Leuchs

We experimentally demonstrate distillation of continuous variable entanglement through an attenuating quantum channel. Through a simple protocol based entirely on linear optics and homodyne detection we probabilistically filter out a highly entangled state from a less non-entangled mixed state. (C) 2008 Optical Society of America

Experimental continuous-variable cloning of partial quantum information

Metin Sabuncu, Gerd Leuchs, Ulrik L. Andersen

The fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed. We illustrate this interesting point by proposing and demonstrating the superior cloning of coherent states with prior partial information. More specifically, we propose two simple transformations that under the Gaussian assumption optimally clone symmetric Gaussian distributions of coherent states as well as coherent states with known phases. Furthermore, we implement for the first time near-optimal state-dependent cloning schemes relying on simple linear optics and feedforward.

Interferometric null test of a parabolic reflector generating a Hertzian dipole field

G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, J. Schwider

Interferometric surface tests of stigmatic aspherics can be carried out in a null test configuration. Null tests require reference null elements either plane or spherical surfaces or both. A parabolic reflector transforms a plane into a spherical wave which converges to the focus of the paraboloid. Therefore, a spherical ball lens or a steel ball can be placed into the focus enabling a double-pass geometry for the null test. Here a Fizeau interferometer geometry has been selected in order to guarantee invariance against polarization distortions under the assumption that radially polarized laser light is used for the interferometer. Radial polarized light is necessary to mimic a Hertzian dipole field. Due to the extreme solid angle produced by the paraboloid the alignment of the setup is very critical and needs auxiliary systems for the control. Aberrations caused by misalignments are removed via fitting of suitable functionals provided through ray-trace simulations. It turned out that the usual vector approximations fail under these extreme circumstances. Test results arc given for a paraboloid with 2mm focal length transforming a plane wave into a near dipole wave comprising a solid angle of about 3,4 pi.

Experimental evidence for Raman-induced limits to efficient squeezing in optical fibers

Ruifang Dong, Joel Heersink, Joel F. Corney, Peter D. Drummond, Ulrik L. Andersen, Gerd Leuchs

We report new experiments on polarization squeezing using ultrashort photonic pulses in a single pass of a birefringent fiber. We measure what is to our knowledge a record squeezing of -6.8 +/- 0.3 dB in optical fibers, which when corrected for linear losses is -10.4 +/- 0.8 dB. The measured polarization squeezing as a function of optical pulse energy, which spans a wide range from 3.5-178.8 pJ, shows a very good agreement with the quantum simulations, and for the first time we see the proof experimentally that Raman effects limit and reduce squeezing at high pulse energy. (c) 2008 Optical Society of America.

Quantum filtering of optical coherent states

C. Wittmann, D. Elser, U. L. Andersen, R. Filip, P. Marek, G. Leuchs

We propose and experimentally demonstrate nondestructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors, i.e., vacuum states in the quantum information are diagnosed through a weak measurement, and on that basis, probabilistically filtered out. We consider three different filters based on on-off detection, phase stabilized, and phase randomized homodyne detection. We find that on-off detection, optimal in the ideal theoretical setting, is superior to the homodyne strategy also in a practical setting.

Phase-preserving 2R regeneration of a WDM RZ-DPSK signal using a nonlinear amplifying loop mirror

K. Cvecek, K. Sponsel, C. Stephan, G. Onishchukov, R. Ludwig, C. Schubert, B. Schmauss, G. Leuchs

A modified NALM setup for phase-preserving amplitude regeneration of WDM-DPSK signals is proposed. Demultiplexing-multiplexing within the NALM fiber loop is used to avoid WDM channel crosstalk. A negative power penalty of 1.2 dB was obtained. (C) 2007 Optical Society of America.

Optical amplification at the quantum limit

Ulrik L. Andersen, Gerd Leuchs

In this paper we evaluate experimentally measured signal-to-noise ratio performance of different types of optical amplifiers [V. Josse, M. Sabuncu, N. Cerf, et al., Phys. Rev. Lett. 96 163602 ( 2006); Z. Y. Ou, S. F. Pereira and H. J. Kimble, Phys. Rev. Lett. 70 3239 ( 1993)]. We pay particular attention to the low gain regime where the quantum limit of the amplifier varies with gain. Independent of the amplifier type the noise performance is remarkably close to the quantum limit. Low gain optical amplifiers are of interest for quantum communication.

Optimization of a nonlinear amplifying loop mirror for amplitude regeneration in phase-shift-keyed transmission

Klaus Sponsel, Kristian Cvecek, Christian Stephan, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

We present the numerical optimization of the transmission characteristics of a nonlinear amplifying loop mirror for amplitude regeneration of phase-encoded optical transmission formats. Adjusting the splitting factor, the amplifier gain and the phase bias, minimal phase distortions can be achieved while strong amplitude fluctuations are regenerated. The limiting effects of noise from the built-in amplifier and of amplified Rayleigh backscattering are also discussed.

A new 4 pi geometry optimized for focusing on an atom with a dipole-like radiation pattern

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, G. Leuchs

Focusing electromagnetic radiation efficiently onto an atom requires an open geometry, which is as close to the full solid angle as possible. Additionally, the radiant intensity should be as close as possible to a dipole radiation in order to have a similar field distribution as in the emission process. Here, we propose to make use of a novel combination of a parabolic mirror and a diffractive optical element.

High numerical aperture imaging with different polarization patterns

N. Lindlein, S. Quabis, U. Peschel, G. Leuchs

The modulation transfer function (MTF) is calculated for imaging with linearly, circularly and radially polarized light as well as for different numerical apertures and aperture shapes. Special detectors are only sensitive to one component of the electric energy density, e. g. the longitudinal component. For certain parameters this has advantages concerning the resolution when comparing to polarization insensitive detectors. It is also shown that in the latter case zeros of the MTF may appear which are purely due to polarization effects and which depend on the aperture angle. Finally some ideas are presented how to use these results for improving the resolution in lithography. (c) 2007 Optical Society of America

Tailored polarization patterns for performance optimization of optical devices

Gerd Leuchs, Susanne Quabis

In the case of strong focusing the smallest possible focal spot can be reached, provided one uses a specially designed polarization pattern. Other optical set-ups also employing high numerical aperture imaging are likewise expected to improve performance under polarization optimization. We propose a strategy for calculating the polarization pattern required for system optimization. A single element modulating only the polarization and not amplitude and phase may lead to satisfactory performance in some cases.

Guided acoustic wave Brillouin scattering in photonic crystal fibers

D. Elser, Ch Wittmann, U. L. Andersen, O. Gloeckl, S. Lorenz, Ch Marquardt, G. Leuchs

In silica glass fibers, thermally excited acoustic phonons scatter light into the beam propagating in the forward direction. At acoustic frequencies up to several hundreds of megahertz, the wave vectors of the phonons interacting with the light propagate essentially transversally to the fiber axis. This effect is known as Guided Acoustic Wave Brillouin Scattering (GAWBS) and leads to phase and polarization noise in the guided light. For fiber-based quantum optics experiments, this excess noise is a major limitation. In Photonic Crystal Fibers (PCFs), light is guided by a microstructure simultaneously acting as a 2D transversal phononic crystal which modifies the acoustic noise spectrum. We demonstrate a GAWBS-noise reduction in commercially available PCFs. This gives rise to the prospect of fiber-based quantum optic devices exhibiting less excess noise, thus resulting in higher quantum state purity. Further improvement can be achieved by tailoring the photonic microstructure such that a reduction of phonon noise by design is achieved.

Achieving Gaussian outputs from large-mode-area higher-order-mode fibers

Norbert Lindlein, Gerd Leuchs, Siddharth Ramachandran

We describe an alternative to fiber-gratings for converting higher-order LP0m (m > 1) fiber modes into a nearly fundamental Gaussian shape at the output of a fiber. This schematic enables the use of light propagation in higher-order modes of a fiber, a fiber-platform that has recently shown great promise for achieving very large mode areas needed for future high-power lasers and amplifiers. The conversion will be done by using a binary phase plate in the near field of the fiber, which emits the LP0m mode. Since the binary phase plate alone cannot increase the quality factor M-2 of the laser beam because of some broad sidebands, a filtering of the sidebands is done in the Fourier plane of a telescope. Of course, this will cost some of the total light power, but on the other side the M-2 factor can be reduced to nearly the ideal value near 1.0, and it is shown that similar to 76% of the total light power can be conserved for all investigated modes (2 <= m <= 8). A tolerance analysis for the phase plate and its adjustment is made, and different optical imaging systems to form a magnified image of the fiber mode on the phase plate are discussed in order to have more tolerance for the adjustment of the phase plate. (c) 2007 Optical Society of America.

Polarization effect in the transmission through a single nanoscopic aperture

J. Mueller, P. Banzer, S. Quabis, G. Leuchs

Transmission of a strongly focused light beam through a nanoscopic aperture differs for radial and azimuthal polarization and for holes and coaxial structures. Experimental results are compared with FDTD-calculations showing the relevance of surface plasmons. (c) 2006 Optical Society of America

2R-regeneration of an RZ-DPSK signal using a nonlinear amplifying loop mirror

K. Cvecek, K. Sponsel, G. Onishchukov, B. Schmauss, G. Leuchs

The performance of a nonlinear amplifying loop mirror as a 2R-regenerator for return-to-zero differential-phase-shift-keyed signals has been investigated experimentally. The measured power characteristics and phase functions show that the signal amplitude is regenerated while the signal phase is preserved in the setup. A significant eye-opening improvement and a negative power penalty of about 1.5 dB were obtained.

2R-Regeneration of an 80-Gb/s RZ-DQPSK signal by a nonlinear amplifying loop mirror

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, G. Leuchs

The performance of a nonlinear amplifying loop mirror as a 2R-regenerator for an 80-Gb/s return-to-zero differential-quadrature-phase-shift-keyed signal has been investigated. experimentally. A significant eye-opening improvement and a negative power penalty of up to 2.6 dB were obtained.

TE- and TM-polarization-resolved spectroscopy on quantum wells under normal incidence

M Schardt, A Winkler, G Rurimo, M Hanson, D Driscoll, S Quabis, S Malzer, G Leuchs, GH Doehler, et al.

We present TE- and TM-polarization-resolved photocurrent measurements on quantum well pin diodes under normal incidence. Usually, optical experiments performed in such a geometry yield information only about transitions involving in-plane (p, and p,) components of the hole wave functions because of the in-plane (TE) polarization of the light. Information on transitions sensitive to the p, components can be obtained by focussing a radially polarized laser beam through a microscope objective with high numerical aperture (NA = 0.9). With our setup, the electrical field vector at the focal tail has a significant component along the optical axis (TM-polarization!) which enables excitation of transitions sensitive to p, components also. Additionally, the existence of a degenerate (azimuthally polarized) optical mode enables switching these p. components on and off easily. Experimental evidence of these features has been achieved by exploiting the selection rules for e-hh and e-lh transitions in a quantum well structure. We present a comparison of our recorded spectra with theoretical predictions obtained from simple geometric optics assumptions. For our quantum wells the polarization effects are small because our measurement averages the intensity distribution of the whole focal plane. We plan to extend our measurements to polarization resolved single quantum dot spectroscopy. By restricting the detection region to the spatial extent of a single dot, one can exploit the almost pure TM-polarization on the optical axis for obtaining high contrast between heavy- and light-hole exciton absorption. (c) 2006 Published by Elsevier B.V.

Distillation of squeezing from non-Gaussian quantum states

J. Heersink, Ch. Marquardt, R. Dong, R. Filip, S. Lorenz, G. Leuchs, U. L. Andersen

We show that single copy distillation of squeezing from continuous variable non-Gaussian states is possible using linear optics and conditional homodyne detection. A specific non-Gaussian noise source, corresponding to a random linear displacement, is investigated experimentally. Conditioning the signal on a tap measurement, we observe probabilistic recovery of squeezing.

All-fibre source of continuous variable entangled light

A Nandan, M Sabuncu, J Heersink, O Glockl, G Leuchs, UL Andersen

We experimentally demonstrate the production of continuous variable entanglement of femto second laser pulses from an all-fibre asymmetric Sagnac interferometer exploiting the Kerr effect. Contrary to the experiment of Silberhorn et at. [Phys. Rev. Lett. 86,4267 (2001)], the asymmetric coupler in the Sagnac loop is fully integrated in the fibre, making the source extremely compact, reliable and robust. Employing a simple detection scheme, comprising a beam splitter and two intensity detectors, we clearly observe quantum correlations of conjugate quadratures, hereby witnessing entanglement.

Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers

D. Elser, U. L. Andersen, A. Korn, O. Gloeckl, S. Lorenz, Ch. Marquardt, G. Leuchs

Guided acoustic wave Brillouin scattering (GAWBS) generates phase and polarization noise of light propagating in glass fibers. This excess noise affects the performance of various experiments operating at the quantum noise limit. We experimentally demonstrate the reduction of GAWBS noise in a photonic crystal fiber in a broad frequency range by tailoring the acoustic modes using the photonic also as a phononic crystal. We compare the noise spectrum to the one of a standard fiber and observe a tenfold noise reduction in the frequency range up to 200 MHz. Based on our measurement results as well as on numerical simulations, we establish a model for the reduction of GAWBS noise in photonic crystal fibers.

Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Dohler, D. Driscoll, et al.

We report a method to measure the electric energy density of longitudinal and transverse electric field components of strongly focused polarized laser beams. We used a quantum well photodetector and exploited the polarization dependent optical transitions of light holes and heavy holes to probe the electric field distribution in the focal region. A comparison of the measured photocurrent spectra for radially and azimuthally polarized beams at the light and heavy hole absorption peaks provides a measure of the amount of the longitudinal electric field component. (c) 2006 American Institute of Physics.

Experimental investigation of a modified NOLM for phase-encoded signal regeneration

K. Cvecek, G. Onishchukov, K. Sponsel, A. G. Striegler, B. Schmauss, G. Leuchs

We experimentally investigate the amplitude and phase transfer characteristics of a modified nonlinear optical loop mirror (NOLM) with a directional attenuator (DA-NOLM) optimized for differential phase-shift keying signal regeneration. The results show that the phase relation is preserved in the setup and thus the DA-NOLM is suitable for amplitude regeneration of phase-shift-keyed signals.

Verifying continuous-variable entanglement of intense light pulses

O Glockl, UL Andersen, G Leuchs

Three different methods have been discussed to verify continuous variable entanglement of intense light beams. We demonstrate all three methods using the same setup to facilitate the comparison. The nonlinearity used to generate entanglement is the Kerr effect in optical fibers. Due to the brightness of the entangled pulses, standard homodyne detection is not an appropriate tool for the verification. However, we show that by using large asymmetric interferometers on each beam individually, two noncommuting variables can be accessed and the presence of entanglement verified via joint measurements on the two beams. Alternatively, we witness entanglement by combining the two beams on a beam splitter that yields certain linear combinations of quadrature amplitudes which suffice to prove the presence of entanglement.

Nonunity gain quantum nondemolition measurements based on measurement and repreparation

Jessica Schneider, Oliver Gloeckl, Gerd Leuchs, Ulrik L. Andersen

We demonstrate experimentally a nonunity gain quantum nondemolition measurement based on a simple homodyne measurement and recreation strategy. Although the output state is an amplified version of the input state, the device meets standard criteria for QND measurements: the transfer coefficient was measured to 1,78, and the conditional variance was measured to 0.66. (c) 2006 Optical Society of America.

THE QUANTUM PROPERTIES OF MULTIMODE OPTICAL AMPLIFIERS REVISITED

G. Leuchs, U. L. Andersen, C. Fabre

There are a number of physically different realizations of an optical amplifier and yet they all share the same fundamental quantum limit as far as their noise characteristics are concerned. We review the underlying mathematical formalism without the restriction of a minimum number of modes being involved, its physical implications and relate it to the phenomenological models for the various amplifiers.

Optimum splitting ratio for amplifier noise reduction by an asymmetric nonlinear optical loop mirror

M Meissner, M Rosch, B Schmauss, G Leuchs

We theoretically and experimentally analyze the influence of the splitting ratio and the input power on the noise reduction capability of an asymmetric nonlinear optical loop mirror (NOLM) for different input noise levels. An easy method to calculate the optimum parameters for noise reduction is also presented. The best noise reduction is found at NOLM input powers at which the nonlinear transfer function has a slope close to zero. Additionally, the splitting ratio of the NOLM has to be adapted to its input noise level to suppress amplitude fluctuations effectively. Since the noise reduction by the NOLM is due to the Kerr nonlinearity, which has a timescale below a few femtoseconds, the noise reduction is applicable to short pulses in the picosecond and femtosecond range. This makes the NOLM applicable as an optical regenerator in an optical data transmission system at high bit rates, such as 160 GBit/s.

NOLM-based RZ-DPSK signal regeneration

AG Striegler, M Meissner, K Cvecek, K Sponsel, G Leuchs, B Schmauss

We present a nonlinear optical loop mirror (NOLM)-based 2R-regenerator setup, which signals modulated in phase-sensitive modulation formats. In a conventional NOLM, fluctuations of the signal amplitude are converted into phase fluctuations. Therefore, it is not suitable for regeneration of signals, modulated in formats such as differential phase-shift keying (DPSK) or duobinary. In this letter, we present a modified NOLM setup for 2R-regeneration taking return-to-zero DPSK as an example.

Unconditional quantum cloning of coherent states with linear optics

Ulrik L. Andersen, V Josse, Gerd Leuchs

A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is limited only by detection inefficiencies. Experimentally, we achieved a cloning fidelity of about 65%, which almost touches the optimal value of 2/3.

The effect of dissipation on nonclassical states of the radiation field

G Leuchs, UL Andersen

We point out similarities in the evolution of different types of nonclassical light fields. Generally, Fock and cat states are considered to decay much faster under dissipation than do squeezed states. We connect measurements of the intensity correlation function of nonclassical light to the second moment of the photon number distribution function. It is shown that all these nonclassical fields behave in a similar manner when one is looking at an appropriate property. Finally it is shown how the electronic-detection noise floor, typically present in measurements of the variance of a photocurrent, can be eliminated based upon a procedure that is well-established for intensity correlation measurements.

Experimental purification of coherent states

Ulrik Andersen, R Filip, J Fiurasek, V Josse, Gerd Leuchs

We propose a scheme for optimal Gaussian purification of coherent states from several imperfect copies. The proposal is experimentally demonstrated for the case of two copies of a coherent state sent through independent noisy channels. Our purification protocol relies on only linear optics and an ancilla vacuum state, rendering this approach an interesting alternative to the more complex protocols of entanglement distillation and quantum error correction.

Generation of a radially polarized doughnut mode of high quality

Susanne Quabis, Ralf Dorn, Gerd Leuchs

We present an experimental set-up to generate laser beams with locally varying polarization distribution. In a linear set-up, a radially polarized beam of high quality regarding intensity distribution, polarization and phase-front distortion is generated. This beam can be used for tight focusing. Further applications are discussed.

Efficient polarization squeezing in optical fibers

J Heersink, V Josse, G Leuchs, UL Andersen

We report on a novel and efficient source of polarization squeezing that uses a single pass through an optical fiber. Using the fiber's two orthogonal polarization axes produces two identical squeezed beams. Combining these in a Stokes measurement generates polarization squeezing of up to 5.1 &PLUSMN; 0.3 dB. Furthermore, this scheme enables us to directly measure, for both polarizations, the noise of any given quadrature. &COPY; 2005 Optical Society of America.

Quantum information processing and communication - Strategic report on current status, visions and goals for research in Europe

P Zoller, T Beth, D Binosi, R Blatt, H Briegel, D Bruss, T Calarco, JI Cirac, D Deutsch, et al.

We present an excerpt of the document "Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe", which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the European Commission, http://www.cordis.lu/ist/fet/qipc-sr.htm). This document has been elaborated, following a former suggestion by FET, by a committee of QIPC scientists to provide input towards the European Commission for the preparation of the Seventh Framework Program. Besides being a document addressed to policy makers and funding agencies (both at the European and national level), the document contains a detailed scientific assessment of the state-of-the-art, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC sub-fields, that we report here.

BER improvement using a 2-R regenerator based on an asymmetric nonlinear optical loop mirror

M Meissner, K Sponsel, K Cvecek, A Benz, S Weisser, B Schmauss, G Leuchs

BER improvement of 15 decades is observed using an asymmetric NOLM at a bitrate of 40Gbit/s and an input OSNR of 28.7dB. The BER improvement can be converted into 3.9dB of OSNR gain. Both were achieved by optimizing NOLM input power and splitting ratio. This allows for longer spans and thus reduces the over all amount of amplifiers or allows for an increased system reach.

Demonstration of the spatial separation of the entangled quantum sidebands of an optical field

EH Huntington, GN Milford, C Robilliard, TC Ralph, O Glockl, Ulrik L. Andersen, S Lorenz, Gerd Leuchs

Quantum optics experiments on "bright" beams are based on the spectral analysis of field fluctuations and typically probe correlations between radio-frequency sideband modes. However, the extra degree of freedom represented by this dual-mode picture is generally ignored. We demonstrate the experimental operation of a device which can be used to separate the quantum sidebands of an optical field. We use this device to explicitly demonstrate the quantum entanglement between the sidebands of a squeezed beam.

Sub-shot-noise phase quadrature measurement of intense light beams

O Glockl, Ulrik L. Andersen, S Lorenz, Christine Silberhorn, N Korolkova, Gerd Leuchs

We present a setup for performing sub-shot-noise measurements of the phase quadrature of intense pulsed light without the use of a separate local oscillator. A Mach-Zehnder interferometer with an unbalanced arm length is used to detect the fluctuations of the phase quadrature at a single sideband frequency. With this setup, the nonseparability of a pair of quadrature-entangled beams is demonstrated experimentally. (C) 2004 Optical Society of America.

Experimental demonstration of continuous variable quantum erasing

UL Andersen, O Glockl, S Lorenz, G Leuchs, R Filip

We experimentally demonstrate the concept of continuous variable quantum erasing. The amplitude quadrature of the signal state is labeled to another state via a quantum nondemolition interaction, leading to a large uncertainty in the determination of the phase quadrature due to the inextricable complementarity of the two observables. We show that by erasing the amplitude quadrature information we are able to recover the phase quadrature information of the signal state.

3.9-dB OSNR gain by an NOLM-based 2-R regenerator

M Meissner, K Spionsel, K Cvecek, A Benz, S Weisser, B Schmauss, G Leuchs

We experimentally demonstrate bit-error-rate (BER) improvement of more than nine decades by an asymmetric nonlinear optical loop mirror (NOLM). This can be related to an optical signal-to-noise ratio (OSNR) gain of up to 3.9 dB with respect to the NOLM input OSNR at a bit rate of 40 GB/s. The principle of operation of NOLM-based 2-R regeneration with respect to BER improvement is investigated and it is experimentally shown that BER improvement cannot be detected directly at the regenerator's output.

All-fibre source of amplitude squeezed light pulses

M Meissner, C Marquardt, J Heersink, T Gaber, A Wietfeld, G Leuchs, UL Andersen

An all-fibre source of amplitude squeezed solitons utilizing the self-phase modulation in an asymmetric Sagnac interferometer is experimentally demonstrated. The asymmetry of the interferometer is passively controlled by an integrated fibre coupler, allowing for the optimization of the noise reduction. We have carefully studied the dependence of the amplitude noise on the asymmetry and the power launched into the Sagnac interferometer. Qualitatively, we find good agreement between the experimental results, a semi-classical theory and earlier numerical calculations (Schmitt et al 1998 Phys. Rev. Lett. 81 2446). The stability and flexibility of this all-fibre source makes it particularly well suited to applications in quantum information science.

Continuous-variable quantum key distribution using polarization encoding and post selection

S Lorenz, N Korolkova, G Leuchs

We present an experimental demonstration of a quantum key distribution protocol using coherent polarization states. Post selection is used to ensure a low error rate and security against beam-splitting attacks even in the presence of high losses. Signal encoding and readout in polarization bases avoids the difficult task of sending a local oscillator with the quantum channel. This makes our setup robust and easy to implement. A shared key was established for losses up to 64%.

Polarization optimized focusing of light and coupling to sub-wavelength antennae

Gerd Leuchs, Susanne Quabis

This chapter describes the polarization optimized focusing of light and coupling to sub-wavelength antennae. In a set-up for focusing of light, the lens system transforms the transverse field distribution at the input into the transverse field distribution at the focal plane. The parameters of the input beam are the transverse intensity and phase distribution as well as its state of polarization. The various optical rays directed by the lens to the focal spot typically carry different polarizations even if the input beam has a homogeneous polarization distribution across the beam. Locally the polarization is linear everywhere but the direction of the electric field vector depends on the transverse coordinates within the cross section of the beam in such a way that the electric field vectors oscillate in the radial direction. In the limit of high numerical aperture, focusing the field distribution at and near the focus is calculated using the Debye approximation. The effects of the vector properties of light on the structure of the focus are best observed if two special input beams are compared with identical intensity distribution but different polarization properties