Testing local realistic hidden-variable theories without inequalities

Andrea Aiello

Many of the tests of local realistic hidden-variable theories against quantum mechanics are based on inequalities such as Bell's inequality and Clauser Horne, Shimony, and Holt's inequality. In this work we present a simple alternative test which does not involve inequalities, but direct comparison between correlation functions. The main advantage of this test is that it does not require measuring incompatible observables separately and simultaneously. This implies that our result, differently from traditional inequalities, does not involve counterfactual reasoning.

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

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

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

An inconsistency in the CHSH inequality

Andrea Aiello

Violation of the CHSH inequality supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. We show that the mathematical assumptions underlying the proof of the CHSH inequality are, in fact, incompatible with the physics of the experiments testing such inequality. This implies that we cannot dismiss local realistic hidden variable theories on the basis of currently available experimental data yet. However, we also show that an experimental proof of CHSH inequality is, in principle, possible, but it is unclear how to implement, in practice, such an experiment.

Against Bell's Theorem

Andrea Aiello

Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. In this paper we show that all experiments that aim to prove Bell's theorem do not actually achieve this goal. Our conclusions are based on a straightforward statistical analysis of the outcomes of these experiments. The key tool in our study is probability theory and, in particular, the concept of sample space for the dichotomic random variables that quantifies the outcomes of such experiments.We also show that an experimental proof of Bell's theorem is not, in principle, impossible, but it would require a completely different experimental apparatus than those commonly used to allegedly achieve this objective. The main consequence of our work is that we cannot dismiss local realistic hidden variable theories on the basis of currently available experimental data.

Measuring the Tensorial Flow of Mosaic Vector Beams in Disordered Media

Davide Pierangeli, Andrea Aiello, Claudio Conti

Optical beams with nonuniform polarization offer enhanced capabilities for information transmission, boasting increased capacity, security, and resilience. These beams possess vectorial features that are spatially organized within localized three-dimensional regions, forming tensors that can be harnessed across a spectrum of applications spanning quantum physics, imaging, and machine learning. However, when subjected to the effect of the transmission channel, the tensorial propagation leads to a loss of data integrity due to the entanglement of spatial and polarization degrees of freedom. The challenge of quantifying this spatial-polarization coupling poses a significant obstacle to the utilization of vector beams in turbulent environments, multimode fibers, and disordered media. Here, we introduce and experimentally investigate mosaic vector beams, which consist of localized polarization tesserae that propagate in parallel, demonstrating accurate measurement of their behavior as they traverse strongly disordered channels and decoding their polarization structure in single-shot experiments. The resultant transmission tensor empowers polarization-based optical communication and imaging in complex media. These findings also hold promise for photonic machine learning, where the engineering of tensorial flow can enable optical computing with high throughput.

Brillouin light storage for 100 pulse widths

Birgit Stiller, Kevin Jaksch, Johannes Piotrowski, Moritz Merklein, Mikolaj K. Schmidt, Khu Vu, Pan Ma, Stephen Madden, Michael J. Steel, et al.

Signal processing based on stimulated Brillouin scattering (SBS) is limited by the narrow linewidth of the optoacoustic response, which confines many Brillouin applications to continuous wave signals or optical pulses longer than several nanoseconds. In this work, we experimentally demonstrate Brillouin interactions at the 150 ps time scale and a delay for a record 15 ns which corresponds to a delay of 100 pulse widths. This breakthrough experimental result was enabled by the high local gain of the chalcogenide waveguides as the optoacoustic interaction length reduces with pulse width. We successfully transfer 150 ps-long pulses to traveling acoustic waves within a Brillouin-based memory setup. The information encoded in the optical pulses is stored for 15 ns in the acoustic field. We show the retrieval of eight amplitude levels, multiple consecutive pulses, and low distortion in pulse shape. The extension of Brillouin-based storage to the ultra-short pulse regime is an important step for the realization of practical Brillouin-based delay lines and other optical processing applications.

A Bohmian trajectory analysis of singular wave functions

Ángel S. Sanz, Luis L. Sánchez-Soto, Andrea Aiello

The Schrödinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time evolution. We resort to the notion of quantum Bohmian trajectories to relate this singular behavior to local phase variations, which generate an underlying velocity field responsible for driving the quantum flux toward the singular region.

Metasurface-Based Hybrid Optical Cavities for Chiral Sensing

Nico S. Baßler, Andrea Aiello, Kai P. Schmidt, Claudiu Genes, Michael Reitz

Quantum metasurfaces, i.e., two-dimensional subwavelength arrays of quantum emitters, can be employed as mirrors towards the design of hybrid cavities, where the optical response is given by the interplay of a cavity-confined field and the surface modes supported by the arrays. We show that stacked layers of quantum metasurfaces with orthogonal dipole orientation can serve as helicity-preserving cavities. These structures exhibit ultranarrow resonances and can enhance the intensity of the incoming field by orders of magnitude, while simultaneously preserving the handedness of the field circulating inside the resonator, as opposed to conventional cavities. The rapid phase shift in the cavity transmission around the resonance can be exploited for the sensitive detection of chiral scatterers passing through the cavity. We discuss possible applications of these resonators as sensors for the discrimination of chiral molecules. Our approach describes a new way of chiral sensing via the measurement of particle-induced phase shifts.

Eavesdropper localization for quantum and classical channels via nonlinear scattering

Alexandra Popp, Florian Sedlmeir, Birgit Stiller, Christoph Marquardt

Optical fiber networks are part of the important critical infrastructure and known to be prone to eavesdropping attacks. Hence, cryptographic methods have to be used to protect communication. Quantum key distribution (QKD), at its core, offers information theoretical security based on the laws of physics. In deployments, one has to take into account practical security and resilience. The latter includes the localization of a possible eavesdropper after an anomaly has been detected by the QKD system to avoid denial-of-service. Here, we present an approach to eavesdropper location that can be employed in quantum as well as classical channels using stimulated Brillouin scattering. The tight localization of the acoustic wave inside the fiber channel using correlated pump and probe waves allows discovery of the coordinates of a potential threat within centimeters. We demonstrate that our approach outperforms conventional optical time-domain reflectometry (OTDR) in the task of localizing an evanescent outcoupling of 1% with centimeter precision inside standard optical fibers. The system is furthermore able to clearly distinguish commercially available standard SMF28 from different manufacturers, paving the way for fingerprinted fibers in high-security environments.

A probabilistic view of wave-particle duality for single photons

Andrea Aiello

One of the most puzzling consequences of interpreting quantum mechanics in terms of concepts borrowed from classical physics, is the so-called wave-particle duality. Usually, wave-particle duality is illustrated in terms of complementarity between path distinguishability and fringe visibility in interference experiments. In this work, we instead propose a new type of complementarity, that between the continuous nature of waves and the discrete character of particles. Using the probabilistic methods of quantum field theory, we show that the simultaneous measurement of the wave amplitude and the number of photons in the same beam of light is, under certain circumstances, prohibited by the laws of quantum mechanics. Our results suggest that the concept of “interferometric duality'' could be eventually replaced by the more general one of “continuous-discrete duality''.

Quantum-enhanced interferometer using Kerr squeezing

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

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

Extreme thermodynamics in nanolitre volumes through stimulated Brillouin–Mandelstam scattering

Andreas Geilen, Alexandra Popp, Debavan Das, Saher Junaid, Christopher G. Poulton, Mario Chemnitz, Christoph Marquardt, Markus A. Schmidt, Birgit Stiller

Examining the physical properties of materials—particularly of toxic liquids—under a wide range of thermodynamic states is a challenging problem due to the extreme conditions the material has to experience. Such temperature and pressure regimes, which result in a change in the refractive index and sound velocity, can be accessed by optoacoustic interactions such as Brillouin–Mandelstam scattering. Here we demonstrate the Brillouin–Mandelstam measurements of nanolitre volumes of liquids in extreme thermodynamic regimes. This is enabled by a fully sealed liquid-core optical fibre containing carbon disulfide. Within this waveguide, which exhibits tight optoacoustic confinement and a high Brillouin gain, we are able to conduct spatially resolved measurements of the local Brillouin response, giving us access to a resolved image of the temperature and pressure values along the liquid channel. We measure the material properties of the liquid core at very large positive pressures (above 1,000 bar) and substantial negative pressures (below –300 bar), as well as explore the isobaric and isochoric regimes. The extensive thermodynamic control allows the tunability of the Brillouin frequency shift of more than 40% using only minute volumes of liquid.

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

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

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

The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics

Makan Mohageg, Luca Mazzarella, Charis Anastopoulos, Jason Gallicchio, Bei-Lok Hu, Thomas Jennewein, Spencer Johnson, Shih-Yuin Lin, Alexander Ling, et al.

The National Aeronautics and Space Administration’s Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.

Quantum physics in space

Alessio Belenchia, Matteo Carlesso, Ömer Bayraktar, Daniele Dequal, Ivan Derkach, Giulio Gasbarri, Waldemar Herr, Ying Lia Li, Markus Rademacher, et al.

Advances in quantum technologies are giving rise to a revolution in the way fundamental physics questions are explored at the empirical level. At the same time, they are the seeds for future disruptive technological applications of quantum physics. Remarkably, a space-based environment may open many new avenues for exploring and employing quantum physics and technologies. Recently, space missions employing quantum technologies for fundamental or applied studies have been proposed and implemented with stunning results. The combination of quantum physics and its space application is the focus of this review: we cover both the fundamental scientific questions that can be tackled with quantum technologies in space and the possible implementation of these technologies for a variety of academic and commercial purposes.

The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics

Makan Mohageg, Luca Mazzarella, Charis Anastopoulos, Jason Gallicchio, Bei-Lok Hu, Thomas Jennewein, Spencer Johnson, Shih-Yuin Lin, Alexander Ling, et al.

The National Aeronautics and Space Administration’s Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.

Quantum technologies in space

Rainer Kaltenbaek, Antonio Acin, Laszlo Bacsardi, Paolo Bianco, Philippe Bouyer, Eleni Diamanti, Christoph Marquardt, Yasser Omar, Valerio Pruneri, et al.

Recently, the European Commission supported by many European countries has announced large investments towards the commercialization of quantum technology (QT) to address and mitigate some of the biggest challenges facing today’s digital era – e.g. secure communication and computing power. For more than two decades the QT community has been working on the development of QTs, which promise landmark breakthroughs leading to commercialization in various areas. The ambitious goals of the QT community and expectations of EU authorities cannot be met solely by individual initiatives of single countries, and therefore, require a combined European effort of large and unprecedented dimensions comparable only to the Galileo or Copernicus programs. Strong international competition calls for a coordinated European effort towards the development of QT in and for space, including research and development of technology in the areas of communication and sensing. Here, we aim at summarizing the state of the art in the development of quantum technologies which have an impact in the field of space applications. Our goal is to outline a complete framework for the design, development, implementation, and exploitation of quantum technology in space.

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.

Agile and versatile quantum communication: Signatures and secrets

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

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

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.

Binary homodyne detection for observing quadrature squeezing in satellite links

Christian R. Müller, Kaushik P. Seshadreesan, C. Peuntinger, C. Marquardt

Optical satellite links open up new prospects for realizing quantum physical experiments over unprecedented length scales. We analyze and affirm the feasibility of detecting quantum squeezing in an optical mode with homodyne detection of only one bit resolution, as is found in satellites already in orbit. We show experimentally that, in combination with a coherent displacement, a binary homodyne detector can still detect quantum squeezing efficiently even under high loss. The sample overhead in comparison to nondiscretized homodyne detection is merely a factor of 3.3.

Binary Homodyne Detection for Observing Quadrature Squeezing in Satellite Links

Christian R. Mueller, Kaushik P Seshadreesan, Christian Peuntinger, Christoph Marquardt

Optical satellite links open up new prospects for realizing quantum physical experiments over unprecedented length scales. We analyze and affirm the feasibility of detecting quantum squeezing in an optical mode with homodyne detection of only one bit resolution, as is found in satellites already in orbit. We show experimentally that, in combination with a coherent displacement, a binary homodyne detector can still detect quantum squeezing efficiently even under high loss. The sample overhead in comparison to non-discretized homodyne detection is merely a factor of 3.3.

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.

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.

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.

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

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

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

R&D advances for quantum communication systems

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

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

Squeezed vacuum states from a whispering gallery mode resonator

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

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

The standard quantum limit of coherent beam combining

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

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

Resonant electro-optic frequency comb

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

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

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.

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.

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.

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.

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.

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).

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.

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'.

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.

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

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

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.

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.

Polarization-Selective Out-Coupling of Whispering-Gallery Modes

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

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

Temporal shaping of single photons enabled by entanglement

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

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

Free-Space Quantum Signatures Using Heterodyne Measurements

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

Detecting the spatial quantum uncertainty of bosonic systems

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

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

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

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

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

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

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

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

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

Evading Vacuum Noise: Wigner Projections or Husimi Samples?

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

Experimental generation of amplitude squeezed vector beams

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

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

Parsing polarization squeezing into Fock layers

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

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

30 years of squeezed light generation

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

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

Single-mode squeezing in arbitrary spatial modes

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

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

Nonlinear and quantum optics with whispering gallery resonators

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

Classically entangled optical beams for high-speed kinematic sensing

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

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

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

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

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

Quantum-like nonseparable structures in optical beams

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

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

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

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

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

A robust quantum receiver for phase shift keyed signals

C. R. Mueller, Ch Marquardt

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

Entangling the Whole by Beam Splitting a Part

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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.

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

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

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

Trojan-horse attacks threaten the security of practical quantum cryptography

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

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

All-optical phase-preserving multilevel amplitude regeneration

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

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

Observation of the Geometric Spin Hall Effect of Light

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

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

Cascaded phase-preserving multilevel amplitude regeneration

Tobias Roethlingshoefer, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

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

Atmospheric continuous-variable quantum communication

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

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

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

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

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

All-Optical Simultaneous Multilevel Amplitude and Phase Regeneration

Tobias Roethlingshoefer, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

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

Atomic mercury vapor inside a hollow-core photonic crystal fiber

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

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

Distribution of Squeezed States through an Atmospheric Channel

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

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

A versatile source of single photons for quantum information processing

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

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

Optimal working points for continuous-variable quantum channels

Imran Khan, Christoffer Wittmann, Nitin Jain, Nathan Killoran, Norbert Luetkenhaus, Christoph Marquardt, Gerd Leuchs

The most important ability of a quantum channel is to preserve the quantum properties of transmitted quantum states. We experimentally demonstrate a continuous-variable system for efficient benchmarking of quantum channels. We probe the tested quantum channels for a wide range of experimental parameters such as amplitude, phase noise, and channel lengths up to 40 km. The data is analyzed using the framework of effective entanglement. We subsequently are able to deduce an optimal point of operation for each quantum channel with respect to the rate of distributed entanglement. This procedure is a promising candidate for benchmarking quantum nodes and individual links in large quantum networks of different physical implementations.

An optimized photon pair source for quantum circuits

Georg Harder, Vahid Ansari, Benjamin Brecht, Thomas Dirmeier, Christoph Marquardt, Christine Silberhorn

We implement an ultrafast pulsed type-II parametric down conversion source in a periodically poled KTP waveguide at telecommunication wavelengths with almost identical properties between signal and idler. As such, our source resembles closely a pure, genuine single mode photon pair source with indistinguishable modes. We measure the joint spectral intensity distribution and second order correlation functions of the marginal beams and find with both methods very low effective mode numbers corresponding to a Schmidt number below 1.16. We further demonstrate the indistinguishability as well as the purity of signal and idler photons by Hong-Ou-Mandel interferences between signal and idler and between signal/idler and a coherent field, respectively. Without using narrowband spectral filtering, we achieve a visibility for the interference between signal and idler of 94.8% and determine a purity of more than 80% for the heralded single photon states. Moreover, we measure raw heralding efficiencies of 20.5% and 15.5% for the signal and idler beams corresponding to detector-loss corrected values of 80% and 70%. (C) 2013 Optical Society of America

The polarization properties of a tilted polarizer

Jan Korger, Tobias Kolb, Peter Banzer, Andrea Aiello, Christoffer Wittmann, Christoph Marquardt, Gerd Leuchs

Polarizers are key components in optical science and technology. Thus, understanding the action of a polarizer beyond oversimplifying approximations is crucial. In this work, we study the interaction of a polarizing interface with an obliquely incident wave experimentally. To this end, a set of Mueller matrices is acquired employing a novel procedure robust against experimental imperfections. We connect our observation to a geometric model, useful to predict the effect of polarizers on complex light fields. (C) 2013 Optical Society of America

Multipolar hierarchy of efficient quantum polarization measures

P. de la Hoz, A. B. Klimov, G. Bjork, Y. -H. Kim, C. Mueller, Ch. Marquardt, G. Leuchs, L. L. Sanchez-Soto

We advocate a simple multipole expansion of the polarization density matrix. The resulting multipoles appear as successive moments of the Stokes variables and can be obtained from feasible measurements. In terms of these multipoles we construct a whole hierarchy of measures that accurately assess higher-order polarization fluctuations.

Distributing Entanglement with Separable States

Christian Peuntinger, Vanessa Chille, Ladislav Mista Jr., Natalia Korolkova, Michael Foertsch, Jan Korger, Christoph Marquardt, Gerd Leuchs

We experimentally demonstrate a protocol for entanglement distribution by a separable quantum system. In our experiment, two spatially separated modes of an electromagnetic field get entangled by local operations, classical communication, and transmission of a correlated but separable mode between them. This highlights the utility of quantum correlations beyond entanglement for the establishment of a fundamental quantum information resource and verifies that its distribution by a dual classical and separable quantum communication is possible.

The photonic wheel - demonstration of a state of light with purely transverse angular momentum

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, G. Leuchs

In classical mechanics, a system may possess angular momentum which can be either transverse (e.g. in a spinning wheel) or longitudinal (e.g. for a spiraling seed falling from a tree) with respect to the direction of motion. However, for light, a typical massless wave system, the situation is less versatile. Photons are well-known to exhibit intrinsic angular momentum which is longitudinal only: the spin angular momentum defining the polarization and the orbital angular momentum associated with a spiraling phase front. Here we show that it is possible to generate a novel state of the light field that contains purely transverse angular momentum, the analogue of a spinning mechanical wheel. We realize this state by tight focusing of a polarization tailored light beam and measure it using an optical nano-probing technique. Such a novel state of the light field can find applications in optical tweezers and spanners where it allows for additional rotational degree of freedom not achievable in single-beam configurations so far.

Entanglement of Gaussian states and the applicability to quantum key distribution over fading channels

Vladyslav C. Usenko, Bettina Heim, Christian Peuntinger, Christoffer Wittmann, Christoph Marquardt, Gerd Leuchs, Radim Filip

Entanglement properties of Gaussian states of light as well as the security of continuous variable quantum key distribution with Gaussian states in free-space fading channels are studied. These qualities are shown to be sensitive to the statistical properties of the transmittance distribution in the cases when entanglement is strong or when channel excess noise is present. Fading, i.e. transmission fluctuations, caused by beam wandering due to atmospheric turbulence, is a frequent challenge in free-space communication. We introduce a method of fading discrimination and subsequent post-selection of the corresponding sub-states and show that it can improve the entanglement resource and restore the security of the key distribution over a realistic fading link. Furthermore, the optimal post-selection strategy in combination with an optimized entangled resource is shown to drastically increase the protocol's robustness to excess noise, which is confirmed for experimentally measured fading channel characteristics. The stability of the result against finite data ensemble size and imperfect channel estimation is also addressed.

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.

Quadrature phase shift keying coherent state discrimination via a hybrid receiver

C. R. Mueller, M. A. Usuga, C. Wittmann, M. Takeoka, Ch Marquardt, U. L. Andersen, G. Leuchs

We propose and experimentally demonstrate a near-optimal discrimination scheme for the quadrature phase shift keying (QPSK) protocol. We show in theory that the performance of our hybrid scheme is superior to the standard scheme-heterodyne detection-for all signal amplitudes and underpin the predictions with our experimental results. Furthermore, our scheme provides hitherto the best performance in the domain of highly attenuated signals. The discrimination is composed of a quadrature measurement, a conditional displacement and a threshold detector.

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.

Probabilistic cloning of coherent states without a phase reference

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

We present a probabilistic cloning scheme operating independently of any phase reference. The scheme is based solely on a phase-randomized displacement and photon counting, omitting the need for nonclassical resources and nonlinear materials. In an experimental implementation, we employ the scheme to clone coherent states from a phase covariant alphabet and demonstrate that the cloner is capable of outperforming the hitherto best-performing deterministic scheme. An analysis of the covariances between the output states shows that uncorrelated clones can be approached asymptotically. This simultaneously demonstrates how the effect of loss on coherent states can be compensated via noiseless preamplification.

Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Foertsch, D. Elser, U. L. Andersen, et al.

Quantum systems such as, for example, photons, atoms, or Bose-Einstein condensates, prepared in complex states where entanglement between distinct degrees of freedom is present, may display several intriguing features. In this Letter we introduce the concept of such complex quantum states for intense beams of light by exploiting the properties of cylindrically polarized modes. We show that already in a classical picture the spatial and polarization field variables of these modes cannot be factorized. Theoretically it is proven that by quadrature squeezing cylindrically polarized modes one generates entanglement between these two different degrees of freedom. Experimentally we demonstrate amplitude squeezing of an azimuthally polarized mode by exploiting the nonlinear Kerr effect in a specially tailored photonic crystal fiber. These results display that such novel continuous-variable entangled systems can, in principle, be realized.

Birefringence and dispersion of cylindrically polarized modes in nanobore photonic crystal fiber

T. G. Euser, M. A. Schmidt, N. Y. Joly, C. Gabriel, C. Marquardt, L. Y. Zang, M. Foertsch, P. Banzer, A. Brenn, et al.

We demonstrate experimentally and theoretically that a nanoscale hollow channel placed centrally in the solid-glass core of a photonic crystal fiber strongly enhances the cylindrical birefringence (the modal index difference between radially and azimuthally polarized modes). Furthermore, it causes a large split in group velocity and group velocity dispersion. We show analytically that all three parameters can be varied over a wide range by tuning the diameters of the nanobore and the core. (C) 2010 Optical Society of America

After-gate attack on a quantum cryptosystem

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, Ch Marquardt, V. Makarov, G. Leuchs

We present a method to control the detection events in quantum key distribution systems that use gated single-photon detectors. We employ bright pulses as faked states, timed to arrive at the avalanche photodiodes outside the activation time. The attack can remain unnoticed, since the faked states do not increase the error rate per se. This allows for an intercept-resend attack, where an eavesdropper transfers her detection events to the legitimate receiver without causing any errors. As a side effect, afterpulses, originating from accumulated charge carriers in the detectors, increase the error rate. We have experimentally tested detectors of the system id3110 (Clavis2) from ID Quantique. We identify the parameter regime in which the attack is feasible despite the side effect. Furthermore, we outline how simple modifications in the implementation can make the device immune to this attack.

Superlinear threshold detectors in quantum cryptography

Lars Lydersen, Nitin Jain, Christoffer Wittmann, Oystein Maroy, Johannes Skaar, Christoph Marquardt, Vadim Makarov, Gerd Leuchs

We introduce the concept of a superlinear threshold detector, a detector that has a higher probability to detect multiple photons if it receives them simultaneously rather than at separate times. Highly superlinear threshold detectors in quantum key distribution systems allow eavesdropping the full secret key without being revealed. Here, we generalize the detector control attack, and analyze how it performs against quantum key distribution systems with moderately superlinear detectors. We quantify the superlinearity in superconducting single-photon detectors based on earlier published data, and gated avalanche photodiode detectors based on our own measurements. The analysis shows that quantum key distribution systems using detector(s) of either type can be vulnerable to eavesdropping. The avalanche photodiode detector becomes superlinear toward the end of the gate. For systems expecting substantial loss, or for systems not monitoring loss, this would allow eavesdropping using trigger pulses containing less than 120 photons per pulse. Such an attack would be virtually impossible to catch with an optical power meter at the receiver entrance.

Device Calibration Impacts Security of Quantum Key Distribution

Nitin Jain, Christoffer Wittmann, Lars Lydersen, Carlos Wiechers, Dominique Elser, Christoph Marquardt, Vadim Makarov, Gerd Leuchs

Characterizing the physical channel and calibrating the cryptosystem hardware are prerequisites for establishing a quantum channel for quantum key distribution (QKD). Moreover, an inappropriately implemented calibration routine can open a fatal security loophole. We propose and experimentally demonstrate a method to induce a large temporal detector efficiency mismatch in a commercial QKD system by deceiving a channel length calibration routine. We then devise an optimal and realistic strategy using faked states to break the security of the cryptosystem. A fix for this loophole is also suggested.

Quantum Light from a Whispering-Gallery-Mode Disk Resonator

J. U. Fuerst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch Marquardt, G. Leuchs

Optical parametric down-conversion has proven to be a valuable source of nonclassical light. The process is inherently able to produce twin-beam correlations along with individual intensity squeezing of either parametric beam, when pumped far above threshold. Here, we present for the first time the direct observation of intensity squeezing of -1.2 dB of each of the individual parametric beams in parametric down-conversion by use of a high quality whispering-gallery-mode disk resonator. In addition, we observed twin-beam quantum correlations of -2.7 dB with this cavity. Such resonators feature strong optical confinement and offer tunable coupling to an external optical field. This work exemplifies the potential of crystalline whispering-gallery-mode resonators for the generation of quantum light. The simplicity of this device makes the application of quantum light in various fields highly feasible.

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

Geometric Spin Hall Effect of Light at polarizing interfaces

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, G. Leuchs

The geometric Spin Hall Effect of Light (geometric SHEL) amounts to a polarization-dependent positional shift when a light beam is observed from a reference frame tilted with respect to its direction of propagation. Motivated by this intriguing phenomenon, the energy density of the light beam is decomposed into its Cartesian components in the tilted reference frame. This illustrates the occurrence of the characteristic shift and the significance of the effective response function of the detector. We introduce the concept of a tilted polarizing interface and provide a scheme for its experimental implementation. A light beam passing through such an interface undergoes a shift resembling the original geometric SHEL in a tilted reference frame. This displacement is generated at the polarizer and its occurrence does not depend on the properties of the detection system. We give explicit results for this novel type of geometric SHEL and show that at grazing incidence this effect amounts to a displacement of multiple wavelengths, a shift larger than the one introduced by Goos-Hanchen and Imbert-Fedorov effects.

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.

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.

Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator

J. U. Fuerst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, G. Leuchs

We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering-gallery-mode resonator made of lithium niobate. A conversion efficiency of 9% is achieved at 30 mu W in-coupled continuous wave pump power. The observed saturation pump power of 3.2 mW is almost 2 orders of magnitude lower than the state-of-the-art value. This suggests an application of our frequency doubler as a source of nonclassical light requiring only a low-power pump, which easily can be quantum noise limited. Our theoretical analysis of the three-wave mixing in a whispering-gallery-mode resonator provides the relative conversion efficiencies for frequency doubling in various modes.

Assessing the Polarization of a Quantum Field from Stokes Fluctuations

A. B. Klimov, G. Bjoerk, J. Soederholm, L. S. Madsen, M. Lassen, U. L. Andersen, J. Heersink, R. Dong, Ch. Marquardt, et al.

We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincare sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.

Transverse angular momentum of photons

Andrea Aiello, Christoph Marquardt, Gerd Leuchs

We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasiparaxial photon beams in vacuum and reproduces the known results for classical beams when applied to coherent states of the field. Both the Poynting vector, alias the linear momentum, and the angular-momentum quantum operators of a light beam are calculated including contributions from first-order transverse derivatives. This permits a correct description of the energy flow in the beam and the natural emergence of both the spin and the angular momentum of the photons. We show that for collimated beams of light, orbital angular-momentum operators do not satisfy the standard commutation rules. Finally, we discuss the application of our theory to some concrete cases.

A generator for unique quantum random numbers based on vacuum states

Christian Gabriel, Christoffer Wittmann, Denis Sych, Ruifang Dong, Wolfgang Mauerer, Ulrik L. Andersen, Christoph Marquardt, Gerd Leuchs

Random numbers are a valuable component in diverse applications that range from simulations(1) over gambling to cryptography(2,3). The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics(4-11). However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique(12-15). Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators.

Atmospheric channel characteristics for quantum communication with continuous polarization variables

B. Heim, D. Elser, T. Bartley, M. Sabuncu, C. Wittmann, D. Sych, C. Marquardt, G. Leuchs

We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100 m length on the flat roof of our institute's building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are auto-compensated. The LO also acts as a spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.

Low-Threshold Optical Parametric Oscillations in a Whispering Gallery Mode Resonator

J. U. Fuerst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, G. Leuchs

In whispering gallery mode (WGM) resonator light is guided by continuous total internal reflection along a curved surface. Fabricating such resonators from an optically nonlinear material one takes advantage of their exceptionally high quality factors and small mode volumes to achieve extremely efficient optical frequency conversion. Our analysis of the phase-matching conditions for optical parametric down-conversion (PDC) in a spherical WGM resonator shows their direct relation to the sum rules for photons' angular momenta and predicts a very low parametric oscillation threshold. We realized such an optical parametric oscillator (OPO) based on naturally phase-matched PDC in lithium niobate. We demonstrated a single-mode, strongly nondegenerate OPO with a threshold of 6: 7 mu W and linewidth under 10 MHz. This work demonstrates the remarkable capabilities of WGM-based OPOs.

Nonparaxial polarizers

Andrea Aiello, Christoph Marquardt, Gerd Leuchs

We develop a theoretical description for polarizers that goes beyond the paraxial approximation. By combining existing theories for fields with nonplanar wavefronts, we are able to derive a simple power series expansion expressing the electric field of a light beam after a polarizer as a linear function of the field and its spatial derivatives evaluated before the polarizer. The first few terms of such expansion are explicitly given, and their physical meaning is discussed. (C) 2009 Optical Society of America

Transverse Angular Momentum and Geometric Spin Hall Effect of Light

Andrea Aiello, Norbert Lindlein, Christoph Marquardt, Gerd Leuchs

We present a novel fundamental phenomenon occurring when a polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam. This effect has a purely geometric nature and amounts to a polarization-dependent shift or split of the beam intensity distribution evaluated as the time-averaged flux of the Poynting vector across the plane of observation. We demonstrate that such a shift is unavoidable whenever the beam possesses a nonzero transverse angular momentum. This latter result has general validity and applies to arbitrary systems such as, e.g., electronic and atomic beams.

Experimental entanglement distillation of mesoscopic quantum states

Ruifang Dong, Mikael Lassen, Joel Heersink, Christoph Marquardt, Radim Filip, Gerd Leuchs, Ulrik L. Andersen

The distribution of entangled states between distant parties in an optical network is crucial for the successful implementation of various quantum communication protocols such as quantum cryptography, teleportation and dense coding(1-3). However, owing to the unavoidable loss in any real optical channel, the distribution of loss-intolerant entangled states is inevitably afflicted by decoherence, which causes a degradation of the transmitted entanglement. To combat the decoherence, entanglement distillation, a process of extracting a small set of highly entangled states from a large set of less entangled states, can be used(4-14). Here we report on the distillation of deterministically prepared light pulses entangled in continuous variables that have undergone non-Gaussian noise. The entangled light pulses(15-17) are sent through a lossy channel, where the transmission is varying in time similarly to light propagation in the atmosphere. By using linear optical components and global classical communication, the entanglement is probabilistically increased.

Experimental demonstration of macroscopic quantum coherence in Gaussian states

Christoph Marquardt, Ulrik L. Andersen, Gerd Leuchs, Yuishi Takeno, Mitsuyoshi Yukawa, Hidehiro Yonezawa, Akira Furusawa

We witness experimentally the presence of macroscopic coherence in Gaussian quantum states using a recently proposed criterion [E. G. Cavalcanti and M. D. Reid, Phys. Rev. Lett. 97 170405 (2006)]. The macroscopic coherence stems from interference between macroscopically distinct states in phase space, and we prove experimentally that a coherent state contains these features with a distance in phase space of 0.51 +/- 0.02 shot noise units. This is surprising because coherent states are generally considered being at the border between classical and quantum states, not yet displaying any nonclassical effect. For squeezed and entangled states the effect may be larger but depends critically on the state purity.

Quantum reconstruction of an intense polarization squeezed optical state

Ch. Marquardt, J. Heersink, R. Dong, M. V. Chekhova, A. B. Klimov, L. L. Sanchez-Soto, U. L. Andersen, G. Leuchs

We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the Poincare space, providing a full quantum mechanical characterization of the measured polarization state.

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.

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.

Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state

O Glockl, S Lorenz, Christoph Marquardt, J Heersink, M Brownnutt, Christine Silberhorn, Q Pan, P van Loock, N Korolkova, et al.

We present a protocol for performing entanglement swapping with intense<br> pulsed beams. In a first step, the generation of amplitude correlations<br> between two systems that have never interacted directly is demonstrated.<br> This is verified in direct detection with electronic modulation of the<br> detected photocurrents. The measured correlations are better than<br> expected from a classical reconstruction scheme. In an entanglement<br> swapping process, a four-partite entangled state is generated. We prove<br> experimentally that the amplitudes of the four optical modes are quantum<br> correlated 3 dB below shot noise, which is consistent with the presence<br> of genuine four-party entanglement.

Quantum interferometry with intense optical pulses

Gerd Leuchs, Christine Silberhorn, O Glockl, Christoph Marquardt, N Korolkova

For intense optical pulses the optical Kerr interaction in matter such<br> as an optical fiber is large enough to generate quantum states of light<br> with significant non-classical properties. On this basis pairs of<br> entangled light pulses have been generated. This entanglement can be<br> used for novel schemes in high precision interferometry and for quantum<br> communication protocols such as quantum dense coding.

Direct experimental test of non-separability and other quantum techniques using continuous variables of light

N Korolkova, Christine Silberhorn, O Glockl, S Lorenz, Christoph Marquardt, Gerd Leuchs

We present schemes for the generation and evaluation of continuous<br> variable entanglement of bright optical beams and give a brief overview<br> of a variety of optical techniques and quantum communication<br> applications on this basis. A new entanglement-based quantum<br> interferometry scheme with bright beams is suggested. The performance of<br> the presented schemes is independent of the relative interference phase<br> which is advantageous for quantum communication applications.