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Noiseless quantum amplifiers are probabilistic quantum devices that enhance amplitude of coherent states without adding any noise, which has far reaching applications in quantum optics and quantum information processing. Here, we report on experimental implementation of an advanced noiseless quantum amplifier for coherent states of light that is based on conditional addition of two photons followed by conditional subtraction of two photons. We comprehensively characterize the noiselessly amplified coherent states via quantum state tomography and analyze the amplification gain and noise properties of the amplifier. We observe very good agreement between the experiment and theoretical predictions. Our work reveals that sequences of multiple photon additions and subtractions represent an efficient and experimentally feasible alternative to multiplexing that was originally proposed to boost the performance of noiseless quantum amplifiers. Beyond noiseless quantum amplification, our experiment represents a significant step forward towards engineering complex quantum operations on traveling light beams by coherent combinations of various sequences of multiphoton additions and subtractions., Comment: 7 pages, 7 figures, REVTeX 4

Probabilistic heralded Gaussification of quantum states of light is an important ingredient of protocols for distillation of continuous variable entanglement and squeezing. An elementary step of heralded Gaussification protocol consists of interference of two copies of the state at a balanced beam splitter, followed by conditioning on outcome of a suitable Gaussian quantum measurement on one output mode. When iterated, the protocol either converges to a Gaussian state, or diverges. Here we report on experimental investigation of the convergence properties of iterative heralded Gaussification. We experimentally implement two iterations of the protocol, which requires simultaneous processing of four copies of the input state. We utilize the phase-randomized coherent states as the input states, which greatly facilitates the experiment, because these states can be generated deterministically and their mean photon number can easily be tuned. We comprehensively characterize the input and partially Gaussified states by balanced homodyne detection and quantum state tomography. Our experimental results are in good agreement with theoretical predictions and they provide new insights into the convergence properties of heralded quantum Gaussification., Comment: 18 pages, 12 figures

Energy extraction from a measured quantum system is a cornerstone of information thermodynamics as illustrated by Maxwell's demon. The nonequilibrium physics of many-particle systems is additionally strongly influenced by quantum statistics. We here report the first experimental realization of a quantum demon in a many-particle photonic setup made of two identical thermal light beams. We show that single-photon measurements combined with feedforward operation may deterministically increase the mean energy of one beam faster than energy fluctuations, thus improving the thermodynamic stability of the device. We moreover demonstrate that bosonic statistics can enhance the energy output above the classical limit, and further analyze the counterintuitive thermodynamics of the demon using an information-theoretic approach. Our results underscore the pivotal role of many-particle statistics for enhanced energy extraction in quantum thermodynamics., Comment: 10 pages, 7 figures

Characterization of quantum states and devices is paramount to quantum science and technology. The characterization consists of individual measurements, which are required to be precisely known. A mismatch between actual and assumed constituent measurements limits the accuracy of this characterization. Here, we show that such a mismatch introduces reconstruction artifacts in quantum state tomography. We use these artifacts to detect and quantify the mismatch and gain information about the actual measurement operators. It consequently allows the mitigation of systematic errors in quantum measurement and state preparation., Comment: 6 pages, 2 figures

Conditional addition of photons represents a crucial tool for optical quantum state engineering and it forms a fundamental building block of advanced quantum photonic devices. Here we report on experimental implementation of the conditional addition of several photons. We demonstrate the addition of one, two, and three photons to input coherent states with various amplitudes. The resulting highly nonclassical photon-added states are completely characterized with time-domain homodyne tomography, and the nonclassicality of the prepared states is witnessed by the negativity of their Wigner functions. We experimentally demonstrate that the conditional addition of photons realizes approximate noiseless quantum amplification of coherent states with sufficiently large amplitude. We also investigate certification of the stellar rank of the generated multiphoton-added coherent states, which quantifies the non-Gaussian resources required for their preparation. Our results pave the way towards the experimental realization of complex optical quantum operations based on combination of multiple photon additions and subtractions.

We analyze the pinning of vortices for a stationary rotating dipolar supersolid along the low-density paths between droplets as a function of the rotation frequency. We restrict ourselves to the stationary configurations of vortices with the same symmetry as that of the array of droplets. In particular, such an analysis clearly reveals that vortices are not only pinned at local density minima, but instead their coordinates are smooth functions of the rotation frequency. Our approach to explaining such a behavior exploits the fact that the wave function of each rotating droplet acquires a linear phase on the coordinates. Hence, the relative phases between the nearest neighboring droplets allow us to predict the position of the vortices in the intermediate low-density region. Here, we show that for a droplet distribution forming a triangular lattice, the phases of three neighboring droplets are needed for the correct description of the vortex location. In particular, for our confined system, we demonstrate that the estimate accurately reproduces the extended Gross-Pitaevskii results in the spatial regions where the neighboring droplets are well-defined.

The polarization of light conveys crucial information about the spatial ordering and optical properties of a specimen. However, precise polarization measurement in challenging conditions, including constrained spaces, low light levels, and high-speed scenarios, remains a severe challenge. Addressing this problem, we introduce a real-time polarization measurement method that is accurate down to a single-photon level and provides complete information about the polarization state. Free of moving components, the polarization sensor utilizes a short rigid piece of few-mode fiber followed by a fiber array and a detector array. The calibration of the sensor relies on a neural network yielding unprecedented accuracy across all polarization states, including partially polarized light. We validate the approach by visualizing the polarization structure of biological specimens and the liquid crystal polymer sample (birefringent USAF test). Our method offers an efficient and reliable solution for real-time polarization sensing and microendoscopy under low-light conditions., Comment: 17 pages, 6 figures, data & code: https://github.com/VasinkaD/Polarization-Deep-Sense

We study the nucleation and dynamics of vortices in rotating lattice potentials where weakly linked condensates are formed with each condensate exhibiting an almost axial symmetry. Due to such a symmetry, the on-site phases acquire a linear dependence on the coordinates as a result of the rotation, which allows us to predict the position of vortices along the low density paths that separate the sites. We first show that, for a system of atoms loaded in a four-site square lattice potential, subject to a constant rotation frequency, the analytical expression that we obtain for the positions of vortices of the stationary arrays accurately reproduces the full three-dimensional Gross-Pitaevskii results. We then study the time-dependent vortex nucleation process when a linear ramp of the rotation frequency is applied to a lattice with sixteen sites. We develop a formula for the number of nucleated vortices which turns to have a linear dependence on the rotation frequency with a smaller slope than that of the standard estimate which is valid in absence of the lattice. From time-dependent Gross-Pitaevskii simulations we further find that the on-site populations remain almost constant during the time evolution instead of spreading outwards, as expected from the action of the centrifugal force. Therefore, the time-dependent phase difference between neighboring sites acquires a running behavior typical of a self-trapping regime. We finally show that, in accordance with our predictions, this fast phase-difference evolution provokes a rapid vortex motion inside the lattice. Our analytical expressions may be useful for describing other vortex processes in systems with the same on-site axial symmetry.

The increasing complexity of the recent photonic experiments challenges developing efficient multi-channel coincidence counting systems with high-level functionality. Here, we report a coincidence unit able to count detection events ranging from singles to 16-fold coincidences with full channel-number resolution. The device operates within sub-100~ps coincidence time windows, with a maximum input frequency of 1.5~GHz and an overall jitter of less than 10~ps. The unit high-level timing performance renders it suitable for quantum photonic experiments employing low-timing-jitter single-photon detectors. Additionally, the unit can be used in complex photonic systems to drive feed-forward loops. We have demonstrated the developed coincidence counting unit in photon-number-resolving detection to directly quantify the statistical properties of light, specifically coherent and thermal states, with a fidelity exceeding 0.999 up to 60~photons., Comment: 7 pages, 8 figures, 1 table

Methods for controlling the motion of single particles, optically levitated in vacuum, have developed rapidly in recent years. The technique of cold damping makes use of feedback-controlled, electrostatic forces to increase dissipation without introducing additional thermal fluctuations. This process has been instrumental in the ground-state cooling of individual electrically charged nanoparticles. Here we show that the same method can be applied to a pair of nanoparticles, coupled by optical binding forces. These optical binding forces are about three orders of magnitude stronger than typical Coulombic inter-particle force and result in a coupled motion of both nanoparticles characterized by a pair of normal modes. We demonstrate cold damping of these normal modes, either independently or simultaneously, to sub-Kelvin temperatures at pressures of 5x10^{-3} mbar. Experimental observations are captured by a theoretical model which we use to survey the parameter space more widely and to quantify the limits imposed by measurement noise and time delays. Our work paves the way for the study of quantum interactions between meso-scale particles and the exploration of multiparticle entanglement in levitated optomechanical systems.

We explore, experimentally and theoretically, the emergence of coherent coupled oscillations and synchronization between a pair of non-Hermitian, stochastic, opto-mechanical oscillators, levitated in vacuum. Each oscillator consists of a polystyrene microsphere trapped in a circularly polarized, counter-propagating Gaussian laser beam. Non-conservative, azimuthal forces, deriving from inhomogeneous optical spin, push the micro-particles out of thermodynamic equilibrium. For modest optical powers each particle shows a tendency towards orbital circulation. Initially, their stochastic motion is weakly correlated. As the power is increased, the tendency towards orbital circulation strengthens and the motion of the particles becomes highly correlated. Eventually, centripetal forces overcome optical gradient forces and the oscillators undergo a collective Hopf bifurcation. For laser powers exceeding this threshold, a pair of limit cycles appear, which synchronize due to weak optical and hydrodynamic interactions. In principle, arrays of such Non-Hermitian elements can be arranged, paving the way for opto-mechanical topological materials or, possibly, classical time crystals. In addition, the preparation of synchronized states in levitated optomechanics could lead to new and robust sensors or alternative routes to the entanglement of macroscopic objects.

A quantum-light source that delivers photons with a high brightness and a high degree of entanglement is fundamental for the development of efficient entanglement-based quantum-key distribution systems. Among all possible candidates, epitaxial quantum dots are currently emerging as one of the brightest sources of highly entangled photons. However, the optimization of both brightness and entanglement currently requires different technologies that are difficult to combine in a scalable manner. In this work, we overcome this challenge by developing a novel device consisting of a quantum dot embedded in a circular Bragg resonator, in turn, integrated onto a micromachined piezoelectric actuator. The resonator engineers the light-matter interaction to empower extraction efficiencies up to 0.69(4). Simultaneously, the actuator manipulates strain fields that tune the quantum dot for the generation of entangled photons with corrected fidelities to a maximally entangled state up to 0.96(1). This hybrid technology has the potential to overcome the limitations of the key rates that plague QD-based entangled sources for entanglement-based quantum key distribution and entanglement-based quantum networks.

We report a single-photon Mach-Zehnder interferometer stabilized to a phase precision of 0.05 degrees over 15 hours. To lock the phase, we employ an auxiliary reference light at a different wavelength than the quantum signal. The developed phase locking operates continuously, with negligible crosstalk, and for an arbitrary phase of the quantum signal. Moreover, its performance is independent of intensity fluctuations of the reference. Since the presented method can be used in a vast majority of quantum interferometric networks it can significantly improve phase-sensitive applications in quantum communication and quantum metrology.

We report on direct experimental certification of the quantum non-Gaussian character of a photon-number resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements $\hat{\Pi}_m$ associated with the $m$-fold coincidence counts, up to $m=7$. The experimental ability to certify from the first principles the quantum non-Gaussian character of $\hat{\Pi}_m$ is for large $m$ limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors., Comment: 15 pages, 8 figures

The quantification of the entanglement present in a physical system is of para\-mount importance for fundamental research and many cutting-edge applications. Currently, achieving this goal requires either a priori knowledge on the system or very demanding experimental procedures such as full state tomography or collective measurements. Here, we demonstrate that by employing neural networks we can quantify the degree of entanglement without needing to know the full description of the quantum state. Our method allows for direct quantification of the quantum correlations using an incomplete set of local measurements. Despite using undersampled measurements, we achieve a quantification error of up to an order of magnitude lower than the state-of-the-art quantum tomography. Furthermore, we achieve this result employing networks trained using exclusively simulated data. Finally, we derive a method based on a convolutional network input that can accept data from various measurement scenarios and perform, to some extent, independently of the measurement device., Comment: 10 pages, 5 figures, 1 table

The generation of photon pairs in single quantum dots is based on a process that is, in its nature, deterministic. However, an efficient extraction of these photon pairs from a high-index semiconductor host material requires engineering of the photonic environment. We report on a micropillar-based device featuring an extraction efficiency of 69.4(10)$\%$ that is achieved by harnessing a broadband operation suitable for extraction of photon pairs emitted from a single quantum dot. Opposing the approaches that rely solely on Purcell enhancement to realize the enhancement of the extraction efficiency, our solution exploits a suppression of the emission into the modes other than the cavity mode. Our technological implementation requires modest fabrication effort enabling higher device yields that can be scaled up to meet the growing needs of quantum technologies. Furthermore, the design of the device can be further optimized to allow for an extraction efficiency of 85$\%$.

By means of a two-mode model, we show that transitions to different arrays of coexistent regimes in the phase space can be attained by rotating a double-well system, which consists of a toroidal condensate with two diametrically placed barriers. Such a configuration corresponds to the atomtronic counterpart of the well-known direct-current superconducting quantum interference device. Due to the phase gradient experimented by the on-site localized functions when the system is subject to rotation, a phase difference appears on each junction in order to satisfy the quantization of the velocity field around the torus. We demonstrate that such a phase can produce a significant change on the relative values of different types of hopping parameters. In particular, we show that within a determined rotation frequency interval, a hopping parameter, usually disregarded in nonrotating systems, turns out to rule the dynamics. At the limits of such a frequency interval, bifurcations of the stationary points occur, which substantially change the phase space portrait that describes the orbits of the macroscopic canonical conjugate variables. We analyze the emerging dynamics that combines the $0$ and $\pi$ Josephson modes, and evaluate the small-oscillation time-periods of such orbits at the frequency range where each mode survives. All the findings predicted by the model are confirmed by Gross-Pitaevskii simulations., Comment: 13 pages, 8 figures. Accepted in PRA

Accurate control of light polarization represents a core building block in polarization metrology, imaging, and optical and quantum communications. Voltage-controlled liquid crystals offer an efficient way of polarization transformation. However, common twisted nematic liquid crystals are notorious for lacking an accurate theoretical model linking control voltages and output polarization. An inverse model, which would predict control voltages required to prepare a target polarization, is even more challenging. Here we report both the direct and inverse models based on deep neural networks, radial basis functions, and linear interpolation. We present an inverse-direct compound model solving the problem of control voltages ambiguity. We demonstrate one order of magnitude improvement in accuracy using deep learning compared to the radial basis function method and two orders of magnitude improvement compared to the linear interpolation. Errors of the deep neural network model also decrease faster than the other methods with an increasing number of training data. The best direct and inverse models reach the average infidelities of $4 \times 10^{-4}$ and $2 \times 10^{-4}$, respectively, which is the accuracy level not reported yet. Furthermore, we demonstrate local and remote preparation of an arbitrary single-photon polarization state using the deep learning models. The results will impact the application of twisted-nematic liquid crystals, increasing their control accuracy across the board. The presented bidirectional learning can be used for optimal classical control of complex photonic devices and quantum circuits beyond interpolation., Comment: 8 pages, 5 figures, 1 table, data & code: https://github.com/VasinkaD/NeuralLC

We demonstrate a direct single-source measurement of absolute nonlinearity of single-photon detectors with unprecedented accuracy. We discover a surprising supralinear behavior of single-photon avalanche diodes and show that it cannot be explained using known theoretical models. We also fully characterize sub- and supra-linear operation regimes of superconducting nanowire single-photon detectors and uncover the supralinearity under faint continuous illumination. The results identify new detector anomalies that supersede existing knowledge of nonlinear effects at the single-photon level., Comment: 19 pages, 16 figures, 4 tables

Ethereum platform operates with rich spectrum of data structures and hashing and coding functions. The main source describing them is the Yellow paper, complemented by a lot of informal blogs. These sources are somehow limited. In particular, the Yellow paper does not ideally balance brevity and detail, in some parts it is very detail, while too shallow elsewhere. The blogs on the other hand are often too vague and in certain cases contain incorrect information. As a solution, we provide this document, which summarises data structures used in Ethereum. The goal is to provide sufficient detail while keeping brevity. Sufficiently detailed formal view is enriched with examples to extend on clarity.

We apply the quotient graph theory described by Band, Berkolaiko, Joyner and Liu to particular graphs symmetric with respect to $S_3$ and $C_3$ symmetry groups. We find the quotient graphs for the three-edge star quantum graph with Neumann boundary conditions at the loose ends and three types of coupling conditions at the central vertex (standard, $\delta$ and preferred-orientation coupling). These quotient graphs are smaller than the original graph and the direct sum of quotient graph Hamiltonians is unitarily equivalent to the original Hamiltonian., Comment: 18 pages, 1 figure, submitted to the proceedings of 10th Workshop on Quantum Chaos and Localisation Phenomena, 27-28 May 2021, Warsaw, Poland

We report a non-blocking high-resolution digital delay line based on an asynchronous circuit design. Field programmable gate array logic primitives were used as a source of delay and optimally arranged using combinatorial optimization. This approach allows for an efficient trade-off of the resolution and a delay range together with minimized dead time operation. We demonstrate the method by implementing the delay line adjustable from 23 ns up to 1635 ns with a resolution of 10 ps. We present a detailed experimental characterization of the device focusing on thermal instability, timing jitter, and pulse spreading, which represent three main issues of the asynchronous design. We found a linear dependence of the delay on the temperature with the slope of 0.2 ps/K per a logic primitive. We measured the timing jitter of the delay to be in the range of 7 ps - 165 ps, linearly increasing over the dynamic range of the delay. We reduced the effect of pulse spreading by introducing pulse shrinking circuits, and reached the overall dead time of 4 ns - 22.5 ns within the dynamic range of the delay. The presented non-blocking delay line finds usage in applications where the dead time minimization is crucial, and tens of picoseconds excess jitter is acceptable, such as in many advanced photonic networks.

Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.

We propose a method of arbitrarily shaping and scaling the temporal intensity correlations of an optical signal locally, avoiding periodic correlations. We demonstrate our approach experimentally using stochastic intensity modulation. We also analyze and simulate shaping both temporal correlations and photon statistics that are fully specified by the user. We show that within the confines of monotony and convexity, the temporal correlations are independent of photon statistics and can take any shape., Comment: 11 pages, 6 figures, 3 tables

A workflow for evaluation of entanglement source quality is proposed. Based on quantum state density matrices obtained from theoretical models and experimental data, we make an estimate of a potential performance of a quantum entanglement source in quantum key distribution protocols. This workflow is showcased for continuously pumped spontaneous parametric down-conversion (SPDC) source, where it highlights the trade-off between entangled pair generation rate and entanglement quality caused by multiphoton nature of the generated quantum states. We employ this characterization technique to show that secure key rate of down-converted photon pairs is limited to 0.029 bits per detection window due to intrinsic multiphoton contributions. We also report that there exists one optimum gain for continuous-wave down-conversion sources. We find a bound for secure key rate extracted from SPDC sources and make a comparison with perfectly single-pair quantum states, such as those produced by quantum dots., Comment: 13 pages, 5 figures

We study a special dynamical regime of a Bose-Einstein condensate in a ring-shaped lattice where the populations in each site remain constant during the time evolution. The states in this regime are characterized by equal occupation numbers in alternate wells and non-trivial phases, while the phase differences between neighboring sites evolve in time yielding persistent currents that oscillate around the lattice. We show that the velocity circulation around the ring lattice alternates between two values determined by the number of wells and with a specific time period that is only driven by the onsite interaction energy parameter. In contrast to the self-trapping regime present in optical lattices, the occupation number at each site does not show any oscillation and the particle imbalance does not possess a lower bound for the phenomenon to occur. These findings are predicted with a multimode model and confirmed by full three-dimensional Gross-Pitaevskii simulations using an effective onsite interaction energy parameter.

We develop a multimode model that describes the dynamics on a rotating Bose-Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross-Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross-Pitaevskii simulations finding a perfect agreement.

Coherent interaction of a quantum system with environment usually induces quantum decoherence. However, remarkably, in certain configurations the coherent system-environment coupling can be simultaneously explored to engineer a specific dark state of the environment that eliminates the decoherence. Here we report on experimental demonstration of such protocol for suppression of quantum decoherence by quantum decoherence itself. The protocol is based on indirect control of the environment via quantum measurements on quantum probes interacting with the environment prior to the system that should be protected. No direct manipulation with the environment is required to suppress the decoherence. In our proof-of-principle experiment, we demonstrate protection of a single qubit coupled to another single qubit. We implement the required quantum circuits with linear optics and single photons, which allows us to maintain very high degree of control and flexibility in the experiment. Our results clearly confirm the decoherence suppression achieved by the protocol and pave the way to its application to other physical platforms., Comment: 10 pages, 7 figures

Engineering quantum states of light represents a crucial task in the vast majority of photonic quantum technology applications. Direct manipulation of the number of photons in the light signal, such as single-photon subtraction and addition, proved to be an efficient strategy for the task. Here we propose an adaptive multi-photon subtraction scheme where a particular subtraction task is conditioned by all previous subtraction events in order to maximize the probability of successful subtraction. We theoretically illustrate this technique on the model example of conversion of Fock states via photon subtraction. We also experimentally demonstrate the core building block of the proposal by implementing a feedforward-assisted conversion of two-photon state to a single-photon state. Our experiment combines two elementary photon subtraction blocks where the splitting ratio of the second subtraction beam splitter is affected by the measurement result from the first subtraction block in real time using an ultra-fast feedforward loop. The reported optimized photon subtraction scheme applies to a broad range of photonic states, including highly nonclassical Fock states and squeezed light, advancing the photonic quantum toolbox., Comment: 11 pages, 5 figures

This work presents stochastic approaches to model the counting behavior of actively quenched single-photon avalanche diodes (SPADs) subjected to continuous-wave constant illumination. We present both analytical expressions and simulation algorithms predicting the distribution of the number of detections in a finite time window. We also present formulas for the mean detection rate. The approaches cover recovery time, afterpulsing, and twilight pulsing. We experimentally compare the theoretical predictions to measured data using commercially available silicon SPADs. Their total variation distances range from $10^{-5}$ to $10^{-2}$., Comment: 11 pages, 5 figures, 1 table

Generation of particular polarization states of light, encoding information in polarization degree of freedom, and efficient measurement of unknown polarization are the key tasks in optical metrology, optical communications, polarization-sensitive imaging, and photonic information processing. Liquid crystal devices have proved to be indispensable for these tasks, though their limited precision and the requirement of a custom design impose a limit of practical applicability. Here we report fast preparation and detection of polarization states with unprecedented accuracy using liquid-crystal cells extracted from common twisted nematic liquid-crystal displays. To verify the performance of the device we use it to prepare dozens of polarization states with average fidelity 0.999(1) and average angle deviation 0.5(3) deg. Using four-projection minimum tomography as well as six-projection Pauli measurement, we measure polarization states employing the reported device with the average fidelity of 0.999(1). Polarization measurement data are processed by the maximum likelihood method to reach a valid estimate of the polarization state. In addition to the application in classical polarimetry, we also employ the reported liquid-crystal device for full tomographic characterization of a three-mode Greenberger--Horne--Zeilinger entangled state produced by a photonic quantum processor., Comment: data&code: https://github.com/BielakM/polarimeter

Photonic routing is a key building block of many optical applications challenging its development. We report a 2$\times$2 photonic coupler with splitting ratio switchable by a low-voltage electronic signal with 10~GHz bandwidth and tens of nanoseconds latency. The coupler can operate at any splitting ratio ranging from 0:100 to 100:0 with the extinction ratio of 26 dB in optical bandwidth of 1.3 THz. We show sub-nanosecond switching between arbitrary coupling regimes including balanced 50:50 beam splitter, 0:100 switch, and a photonic tap. The core of the device is based on Mach-Zehnder interferometer in a dual-wavelength configuration allowing real-time phase lock with long-term sub-degree stability at single-photon level. Using the reported coupler, we demonstrate for the first time the perfectly balanced time-multiplexed device for photon-number-resolving detectors and also the active preparation of a photonic temporal qudit state up to four time bins. Verified long-term stable operation of the coupler at the single photon level makes it suitable for wide application range in quantum information processing and quantum optics in general.

We study the collisional dynamics of multiple dark solitons in a Bose-Einstein condensate confined by a toroidal trap. We assume a tight enough confinement in the radial direction to prevent possible dissipative effects due to the presence of solitonic vortices. Analytical expressions for the initial order parameters with imprinted phases are utilized to generate different initial arrays of solitons, for which the time-dependent Gross-Pitaevskii equation is numerically solved. Given that the soliton velocity is conserved due to the lack of dissipation, we are able to apply a simple quasiparticle description of the soliton dynamics. In fact, the trajectory equations are written in terms of the velocities and the angular shifts produced at each collision, in analogy to the infinite one-dimensional system. To calculate the angular shifts, we directly extract them from the trajectories given by the Gross-Pitaevskii simulations and, on the other hand, we show that accurate values can be analytically obtained by adapting a formula valid for the infinite one-dimensional system that involves the healing length, which in our inhomogeneous system must be evaluated in terms of the sound velocity along the azimuthal direction. We further show that very good estimates of such a sound velocity can be directly determined by using the ground state density profile and the values of the imprinted phases. We discuss the possible implementation of the system here proposed using the current experimental techniques., Comment: 13 pages, 8 figures