Publications

2020

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

Nature Photonics 15 156-161 (2020) | Preprint | Journal

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

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

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

Frontiers in Physics 8 527734 (2020) | Preprint | Journal | PDF | PDF

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

Extremal quantum states

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

AVS QUANTUM SCIENCE 2 (4) 044701 (2020) | Journal | PDF

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

Quantum Fisher Information with Coherence

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

Optica 6 (11) 1437-1440 (2020) | Preprint | Journal | PDF

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

Compressively certifying quantum measurements

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

Physical Review X Quantum 1 (2) 307 | Preprint | Journal | PDF

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

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

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

Optics Express 28 (21) 30784-30796 (2020) | Journal | Preprint | PDF

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

Optica 7 (10) 1228-1231 (2020) | Journal | PDF

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

Chalcogenide fibers for Kerr squeezing

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

OPTICS LETTERS 45 (19) 5299-5302 (2020) | Journal

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

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

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

PHOTONICS 7 (3) 72 (2020) | Journal | PDF

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

Wigner function for SU(1,1)

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

Quantum 4 (2020) | Journal | PDF

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

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

Alexey Andrianov, Nikolay Kalinin, Elena Anashkina, Gerd Leuchs

OPTICS LETTERS 45 (17) 4774-4777 (2020) | Journal

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

Fundamental quantum limits in ellipsometry

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

Optics Letters 45 (16) 4607-4610 (2020) | Journal

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

Laser & Photonics Reviews 2000110 (2020) | Journal | PDF

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

New Journal of Physics 22 (7) 073045 (2020) | Journal | PDF

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

Nanomaterials 10 (7) 1376 (2020) | Journal | PDF

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.

Applied Physics B 126 (8) 130 (2020) | Journal | PDF

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

Nature Communications 11 2915 (2020) | Preprint | Journal | PDF

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

Physical Review Letters 124 (21) 210401 (2020) | Preprint | Journal | PDF

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

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

Markus Sondermann, Martin Fischer, Gerd Leuchs

SI 3 (11) 2000022 (2020) | Journal | PDF

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

Chiral Surface Lattice Resonances

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

Advanced Materials 2001330 (2020) | Journal | PDF

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

Properties of bright squeezed vacuum at increasing brightness

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

Physical Review Research 2 (1) 013371 (2020) | Journal | PDF

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

Optics Express 28 (7) 10239-10252 (2020) | Preprint | Journal | PDF

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

Roadmap on quantum light spectroscopy

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

Journal of Physics B: Atomic, Molecular and Optical Physics; IOP Publishing, Bristol 53 7 (2020) | Journal

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

Helstrom measurement: A nondestructive implementation

Rui Han, Gerd Leuchs, Janos A. Bergou

PHYSICAL REVIEW A 101 (3) 032103 (2020) | Journal | PDF

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

Objective Compressive Quantum Process Tomography

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

Physical Review A 101 (2) 022334 (2020) | Preprint | Journal

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

Shaping Field Gradients for Nanolocalization

Sergey Nechayev, Jörg Eismann, Martin Neugebauer, Peter Banzer

ACS Photonics 7 (3) 581-587 (2020) | Preprint | Journal | PDF

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

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

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

PHYSICA SCRIPTA 95 (3) 034012 (2020) | Journal

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

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

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

QUANTUM ELECTRONICS 50 (4) 386-391 (2020) | Journal

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

Vector-light quantum complementarity and the degree of polarization

Andreas Norrman, Ari T. Friberg, Gerd Leuchs

OPTICA 7 (2) 93-97 (2020) | Journal | PDF

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

QED Response of the Vacuum

Gerd Leuchs, Margaret Hawton, Luis Sanchez-Soto

PHYSICS 2 (1) 14-21 (2020) | Journal | PDF

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

Efficient generation of temporally shaped photons using nonlocal spectral filtering

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

Physical Review A 101 (1) 013808 (2020) | Journal | Preprint | PDF

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

Physical Review Letters 124 (1) 013607 (2020) | Journal

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

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

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

JOURNAL OF OPTICS 22 (2) 024001 (2020) | Journal | PDF

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

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