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Machine learning techniques have opened new avenues for real-time quantum state tomography (QST). In this work, we demonstrate the deployment of machine learning-based QST onto edge devices, specifically utilizing field programmable gate arrays (FPGAs). This implementation is realized using the {\it Vitis AI Integrated Development Environment} provided by AMD\textsuperscript \textregistered~Inc. Compared to the Graphics Processing Unit (GPU)-based machine learning QST, our FPGA-based one reduces the average inference time by an order of magnitude, from 38 ms to 2.94 ms, but only sacrifices the average fidelity about $1\% $ reduction (from 0.99 to 0.98). The FPGA-based QST offers a highly efficient and precise tool for diagnosing quantum states, marking a significant advancement in the practical applications for quantum information processing and quantum sensing., Comment: 6 pages, 5 figures

The addition of a single photon to a light field can lead to exactly the same \emph{outcome} as the subtraction of a single photon. We prove that this \cterm is true for pure squeezed vacuum states of light, and in some sense only for those. We show that mixed states can show this \cterm for addition or subtraction of a photon if they are generated from incoherent sums of pure squeezed vacuum states with the same squeezing. We point out that our results give a reinterpretation to the fact that pure squeezed vacuum states, with squeezing $e^{-z}$, are formally annihilated by Bogoliubov-transformed annihilation operators: $\hat a_z = \hat a \cosh(z) - \hat a^\dagger \sinh(z) $., Comment: 7 pages, 3 figures

Even though heralded single-photon sources have been generated routinely through the spontaneous parametric down conversion, vacuum and multiple photon states are unavoidably involved. With machine-learning, we report the experimental implementation of single-photon quantum state tomography by directly estimating target parameters. Compared to the Hanbury Brown and Twiss (HBT) measurements only with clicked events recorded, our neural network enhanced quantum state tomography characterizes the photon number distribution for all possible photon number states from the balanced homodyne detectors. By using the histogram-based architecture, a direct parameter estimation on the negativity in Wigner's quasi-probability phase space is demonstrated. Such a fast, robust, and precise quantum state tomography provides us a crucial diagnostic toolbox for the applications with single-photon Fock states and other non-Gaussisan quantum states., Comment: 8 pages, 8 figures

Beam splitters allow us to superpose two continuous single mode quantum systems. To study the behaviour of their strongly mode mixing dynamics we consider variable beam splitters and their dynamics using Wigner's phase space distribution, W, the evolution of which is governed by the continuity-equation $ \frac{\partial}{\partial \tau} W = - {\nabla } \cdot {J}$. We derive the form of the corresponding Wigner current, J, of each outgoing mode after tracing out the other. The influence of the modes on each other is analyzed and visualized using their respective Wigner distributions and Wigner currents. This allows us to perform geometrical analyses of the mode interactions, casting new light on beam splitter behaviour. Several of the presented results should be immediately testable in experiments., Comment: 5 figures. arXiv admin note: text overlap with arXiv:2307.16510

For a simple quantum system weakly interacting with the environment Wigner's 1932 formulation of quantum physics can be used to derive coupling to the environment using simple algebra. We show that the correct expressions, using coupling terms of `Lindblad form', are forced upon us. This is remarkable given that it took several decades before Lindblad's result was found in 1976., Comment: 6 pages, 1 figure

Optical "Schr\"odinger cat" states, the non-classical superposition of two quasi-classical coherent states, serve as a basis for gedanken experiments testing quantum physics on mesoscopic scales and are increasingly recognized as a resource for quantum information processing. Here, we report the first experimental realization of optical "Schr\"odinger cats" by adding a photon to a squeezed vacuum state, so far only photon-subtraction protocols have been realized. Photon-addition gives us the advantage of using heralded signal photons as experimental triggers, and we can generate "Schr\"odinger cats" at rates exceeding $8.5 \times 10^4$ counts per second; at least one order of magnitude higher than all previously reported realizations. Wigner distributions with pronounced negative parts are demonstrated at down to -8.89 dB squeezing, even when the initial squeezed vacuum input state has low purity. Benchmarking against such a degraded squeezed input state we report a maximum fidelity of more than 80% with a maximum cat amplitude of $|\alpha| \approx 1.66$. Our experiment uses photon-addition from pairs, one of those photons is used for monitoring, giving us enhanced control; moreover the pair production rates are high and should allow for repeated application of photon-addition via repeat-stages., Comment: 5 pages, 2 figures, 1 table

We find that there exists a universal law of coiling not only for a long elastic strip contacting within a tube but also for a short one. Here the elastic strip we consider has the ratio of $2 < L/R \le 2\pi$ for its length $L$ to the tube radius $R$. By varying the ratio of $L/R$, we identify four types of deformation for such a short elastic strip, namely, two point-contact, three point-contact, continuous-contact, and self-contact. With theoretical formulas in closed forms and experimental demonstration, these four types are verified for any elastic strips contacting within a tube, irrespective of elastic properties, strip lengths, and tube radius. Our results on coiling can be readily applied to a variety of physical systems, including thin flexible electronic devices, van der Waals materials in scroll shape, and DNA packaging into viral capsids.

Quantum machine learning is a rapidly growing field at the intersection of quantum technology and artificial intelligence. This review provides a two-fold overview of several key approaches that can offer advancements in both the development of quantum technologies and the power of artificial intelligence. Among these approaches are quantum-enhanced algorithms, which apply quantum software engineering to classical information processing to improve keystone machine learning solutions. In this context, we explore the capability of hybrid quantum-classical neural networks to improve model generalization and increase accuracy while reducing computational resources. We also illustrate how machine learning can be used both to mitigate the effects of errors on presently available noisy intermediate-scale quantum devices, and to understand quantum advantage via an automatic study of quantum walk processes on graphs. In addition, we review how quantum hardware can be enhanced by applying machine learning to fundamental and applied physics problems as well as quantum tomography and photonics. We aim to demonstrate how concepts in physics can be translated into practical engineering of machine learning solutions using quantum software., Comment: 46 pages, 15 figures

With the capability to find the best fit to arbitrarily complicated data patterns, machine-learning (ML) enhanced quantum state tomography (QST) has demonstrated its advantages in extracting complete information about the quantum states. Instead of using the reconstruction model in training a truncated density matrix, we develop a high-performance, lightweight, and easy-to-install supervised characteristic model by generating the target parameters directly. Such a characteristic model-based ML-QST can avoid the problem of dealing with large Hilbert space, but keep feature extractions with high precision. With the experimentally measured data generated from the balanced homodyne detectors, we compare the degradation information about quantum noise squeezed states predicted by the reconstruction and characteristic models, both give agreement to the empirically fitting curves obtained from the covariance method. Such a ML-QST with direct parameter estimations illustrates a crucial diagnostic toolbox for applications with squeezed states, including advanced gravitational wave detectors, quantum metrology, macroscopic quantum state generation, and quantum information process., Comment: 3 figures

Frequency dependent squeezing is the main upgrade for achieving broadband quantum noise reduction in upcoming observation runs of gravitational wave detectors. The proper frequency dependence of the squeezed quadrature is obtained by reflecting squeezed vacuum from a Fabry-Perot filter cavity detuned by half of its linewidth. However, since the squeezed vacuum contains no classical amplitude, co-propagating auxiliary control beams are required to achieve the filter cavity's length, alignment, and incident beam pointing stability. In our frequency dependent squeezing experiment at the National Astronomical Observatory of Japan, we used a control beam at a harmonic of squeezed vacuum wavelength and found visible detuning variation related to the suspended mirrors angular drift. These variations can degrade interferometer quantum noise reduction. We investigated various mechanisms that can cause the filter cavity detuning variation. The detuning drift is found to be mitigated sufficiently by fixing the incident beam pointing and applying filter cavity automatic alignment. It was also found that there is an optimal position of the beam on the filter cavity mirror that helps to reduce the detuning fluctuations. Here we report a stabilized filter cavity detuning variation of less than 10$\,$Hz compared to the 113$\,$Hz cavity linewidth. Compared to previously published results [Phys. Rev. Lett. 124, 171101 (2020)], such detuning stability would be sufficient to make filter cavity detuning drift induced gravitational wave detector detection range fluctuation reduce from $11\%$ to within $2\%$., Comment: Accepted by PRD

We experimentally reconstruct Wigner's current of quantum phase space dynamics for the first time. We reveal the ``push-and-pull" associated with damping and diffusion due to the coupling of a squeezed vacuum state to its environment. In contrast to classical dynamics, where (at zero temperature) dissipation only ``pulls" the system toward the origin of phase space, we also observe an outward ``push" because our system has to obey Heisenberg's uncertainty relations. With squeezed vacuum states generated by an optical parametric oscillator at variable pumping levels, we identify the pure squeezing dynamics and its central stagnation point with a topological charge of `$-1$'. We experimentally verify that this charge is protected for weakly as well as strongly decohering conditions. This work demonstrates high resolving power and establishes an experimental paradigm for measuring quantumness and non-classicality of the dynamics of open quantum systems., Comment: 8 pages, 4 figures

According to von Neumann, the global Hamiltonian of whole universe must be Hermitian in order to keep the eigenvalues real and to construct a self-consistent quantum theory. In addition to the open system approach by introducing environmental degrees of freedom to a small system, a global Hermitian Hamiltonian can also be generated through the dilation from a small Hilbert space. For example, a local non-Hermitian $\cal PT$-symmetric system can be simulated with a global Hermitian one by the Naimark dilation. When shared by Alice and Bob, the internal nonlocality in such dilated Hermitian systems is revealed recently, but only with a two-fold structure. In this paper, we extend such a discussion to the generalized case when the two-fold structure breaks. The internal nonlocality is discussed with different correlation pictures and the corresponding correlation bounds. Our results provide a device-independent test on the reliability of the simulation in the global Hermiticity., Comment: 12 pages, close to the published version

We propose a straightforward and effective approach to design, by strain-engineering, photonic topological insulators supporting high quality factors edge states. Chiral strain-engineering creates opposite synthetic gauge fields in two domains resulting in Landau levels with the same energy spacing but different topological numbers. The boundary of the two topological domains hosts robust time-reversal and spin-momentum-locked edge states, exhibiting high quality factors due to continuous strain modulation. By shaping the synthetic gauge field, we obtain a remarkable field confinement and tunability, with the strain strongly affecting the degree of localization of the edge states. Notably the two-domain design stabilizes the strain-induced topological edge state. The large potential bandwidth of the strain-engineering and the opportunity to induce the mechanical stress at the fabrication stage enables large scalability for many potential applications in photonics, such as tunable microcavities, new lasers and information processing devices, including the quantum regime., Comment: 31 pages, 10 figures

The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. However, unavoidable lossy effect is commonly believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg (up to 1/N^3) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe, i.e, the entangled Fock (N00N-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible both for the linear and nonlinear metrologies with the SJJs, and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.

In order to leverage the full power of quantum noise squeezing with unavoidable decoherence, a complete understanding of the degradation in the purity of squeezed light is demanded. By implementing machine learning architecture with a convolutional neural network, we illustrate a fast, robust, and precise quantum state tomography for continuous variables, through the experimentally measured data generated from the balanced homodyne detectors. Compared with the maximum likelihood estimation method, which suffers from time-consuming and over-fitting problems, a well-trained machine fed with squeezed vacuum and squeezed thermal states can complete the task of reconstruction of the density matrix in less than one second. Moreover, the resulting fidelity remains as high as $0.99$ even when the anti-squeezing level is higher than $20$~dB. Compared with the phase noise and loss mechanisms coupled from the environment and surrounding vacuum, experimentally, the degradation information is unveiled with machine learning for low and high noisy scenarios, i.e., with the anti-squeezing levels at $12$~dB and $18$~dB, respectively. Our neural network enhanced quantum state tomography provides the metrics to give physical descriptions of every feature observed in the quantum state with a single-shot measurement and paves a way of exploring large-scale quantum systems in real-time., Comment: 15 pages, 6 figures

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent $\cal PT$-symmetric Hamiltonian. Our system is initially set in the unbroken $\cal PT$-symmetric phase and later goes across the so-called exceptional point and enters the broken $\cal PT$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\cal PT$-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system., Comment: 9 pages, 4 figures, close to the published version

Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic subroutine in many quantum algorithms and plays an important role in studying physical phenomena. Simulating quantum walk processes is computationally challenging for classical processors. With an increasing improvement in qubits fidelity and qubits number in a single register, there is a potential to improve quantum walks simulations substantially. However, efficient ways to simulate quantum walks in qubit registers still have to be explored. Here, we explore the relationship between quantum walk on graphs and quantum circuits. Firstly, we discuss ways to obtain graphs provided quantum circuit. We then explore techniques to represent quantum walk on a graph as a quantum circuit. Specifically, we study hypercube graphs and arbitrary graphs. Our approach to studying the relationship between graphs and quantum circuits paves way for the efficient implementation of quantum walks algorithms on quantum computers., Comment: 11 pages, 5 figures, 3 tables

By utilizing Bose-Einstein condensate solitons, optically manipulated and trapped in a double-well potential, coupled through nonlinear Josephson effect, we propose novel quantum metrology applications with two soliton qubit states. In addition to steady-state solutions in different scenarios, phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes. Schr\"odinger-cat states, maximally path-entangled ($N00N$) states, and macroscopic soliton qubits are predicted and exploited for the distinguishability of obtained macroscopic states in the framework of binary (non-orthogonal) state discrimination problem. For arbitrary phase estimation in the framework of linear quantum metrology approach, these macroscopic soliton states are revealed to have a scaling up to the Heisenberg limit (HL). The examples are illustrated for HL estimation of angular frequency between the ground and first excited macroscopic states of the condensate, which opens new perspectives for current frequency standards technologies., Comment: 21 pages, 9 figures

The Josephson junctions (JJs) are at the heart of modern quantum technologies and metrology. In this work we establish quantum features of an atomic soliton Josephson junction (SJJ) device, which consists of two weakly-coupled condensates with negative scattering length. The condensates are trapped in a double-well potential and elongated in one dimension. Starting with classical field theory we map for the first time a two-soliton problem onto the effective two-mode Hamiltonian and perform a second quantization procedure. Compared to the conventional Bosonic Josephson junction (BJJ) condensate system, we show that the SJJ-model in quantum domain exhibits unusual features due to its effective nonlinear strength proportional to the square of total particle number, $N^2$. A novel self-tuning effect for the effective tunneling parameter is also demonstrated in the SJJ-model, which depends on the particle number and rapidly vanishes as the JJ population imbalance increases. The formation of entangled Fock state superposition is predicted for the quantum SJJ-model, revealing dominant $N00N$-state components at the "edges" for $n=0, N$ particle number. We have shown that the obtained quantum state is more resistant to few particle losses from the condensates if tiny components of entangled Fock states are present in the vicinity of the major $N00N$-state component. This peculiarity of the quantum SJJ-model establishes an important difference from its semiclassical analogue obtained in the framework of Hartree approach., Comment: 36 pages, 8 figures

We study the formation of lines in phase space in Wigner's distribution $W.$ Whereas lines in phase space do not form in classical systems, unless special initial states are chosen, we find, for large classes of systems and initial states of quantum systems that $W$ tends to form straight line patterns crisscrossing phase space. These arise from the states' coherences. Some of those lines have astonishing extent, reaching across the entire state. We show that the formation of such straight line patterns is due to the formation of 'randomized grid states'. We establish their stability to perturbations, and that they are tied to interference phenomena in configuration space. We additionally identify generic higher-order `eye' patterns in phase space which occur less often since they require the formation of more specific regular grid states; and we show that the randomization of eye patterns tends to deform them into lines., Comment: 12 pages 17 figures. J. Phys. A: Math. Theor (2022)

To effectively realize a $\cal PT$-symmetric system, one can dilate a $\cal PT$-symmetric Hamiltonian to some global Hermitian one and simulate its evolution in the dilated Hermitian system. However, with only a global Hermitian Hamiltonian, how do we know whether it is a dilation and is useful for simulation? To answer this question, we consider the problem of how to extract the internal nonlocality in the Hermitian dilation. We unveil that the internal nonlocality brings nontrivial correlations between the subsystems. By evaluating the correlations with local measurements in three different pictures, the resulting different expectations of the Bell operator reveal the distinction of the internal nonlocality. When the simulated $\cal PT$-symmetric Hamiltonian approaches its exceptional point, such a distinction tends to be most significant. Our results clearly make a difference between the Hermitian dilation and other global Hamiltonians without internal nonlocality. They also provide the figure of merit to test the reliability of the simulation, as well as to verify a $\cal PT$-symmetric (sub)system.

In order to transport information with topological protection, we reveal and demonstrate experimentally the existence of a characteristic length $L_c$, coined as the transport length, in the bulk size for edge states in one-dimensional Su-Schrieffer-Heeger (SSH) chains. In spite of the corresponding wavefunction amplitude decays exponentially, characterized by the penetration depth $\xi$, the transport between two edge states remains possible even when the lattice size $L$ is much larger than the penetration depth, i.e., $\xi \ll L \le L_c$. Due to the non-zero coupling energy in a finite-size system, the supported SSH edge states are not completely isolated at the two ends, giving an abrupt change in the wave localization, manifested through the inverse participation ratio to the lattice size. To verify such a non-exponential scaling factor to the system size, we implement a chain of split-ring resonators and their complementary ones with controllable hopping strengths. By performing the measurements on the group velocity from the transmission spectroscopy of non-trivially topological edge states with pulse excitations, the transport velocity between two edge states is directly observed with the number of lattices up to $20$. Along the route to harness topology to protect optical information, our experimental demonstrations provide a crucial guideline for utilizing photonic topological devices., Comment: 6 pages, 5 figures

The astrophysical reach of current and future ground-based gravitational-wave detectors is mostly limited by quantum noise, induced by vacuum fluctuations entering the detector output port. The replacement of this ordinary vacuum field with a squeezed vacuum field has proven to be an effective strategy to mitigate such quantum noise and it is currently used in advanced detectors. However, current squeezing cannot improve the noise across the whole spectrum because of the Heisenberg uncertainty principle: when shot noise at high frequencies is reduced, radiation pressure at low frequencies is increased. A broadband quantum noise reduction is possible by using a more complex squeezing source, obtained by reflecting the squeezed vacuum off a Fabry-Perot cavity, known as filter cavity. Here we report the first demonstration of a frequency-dependent squeezed vacuum source able to reduce quantum noise of advanced gravitational-wave detectors in their whole observation bandwidth. The experiment uses a suspended 300-m-long filter cavity, similar to the one planned for KAGRA, Advanced Virgo and Advanced LIGO, and capable of inducing a rotation of the squeezing ellipse below 100 Hz.

We propose a universal strategy to realize a broadband control on arbitrary scatterers, through multiple coherent beams. By engineering the phases and amplitudes of incident beams, one can suppress the dominant scattering partial waves, making the obstacle lose its intrinsic responses in a broadband spectrum. The associated coherent beams generate a finite and static region, inside which the corresponding electric field intensity and Poynting vector vanish. As a solution to go beyond the sum-rule limit, our methodology is also irrespective of inherent system properties, as well as extrinsic operating wavelength, providing a non-invasive control on the wave-obstacles interaction for any kinds of shape.

Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, resulting a click. How much information can a photon carry? We study a bipartite asymmetric "two-way signaling" protocol as an extension of that proposed by Del Santo and Daki\'{c}. Suppose that Alice and Bob are distant from each other and each of them has an $n$-bit string. They are tasked to exchange the information of their local n-bit strings with each other, using only a single photon during the communication. It has been shown that the superposition of different spatial locations in a Mach-Zehnder (MZ) interferometer enables bipartite local encodings. We show that, after the travel of a photon through a cascade of $n$-level MZ interferometers in our protocol, the one of Alice or Bob whose detector clicks can access the other's full information of $n$-bit string, while the other can gain one-bit of information. That is, the wave-particle duality makes two-way signaling possible, and a single photon can carry arbitrarily large (but finite) information., Comment: 6 pages, 6 figures

By considering a cigar-shaped trapping potential elongated in a proper curvilinear coordinate, we discover a new form of wave localization which arises from the interplay of geometry and topological protection. The potential is modulated in its shape such that local curvature introduces a trapping potential. The curvature varies along the trap curvilinear axis encodes a topological Harper modulation. The varying geometry maps our system in a one-dimensional Andre-Aubry-Harper grating. We show that a mobility edge exists and topologically protected states arises. These states are extremely robust with respect to disorder in shape of the string. The results may be relevant for localization phenomena in Bose-Einstein condensates, optical fibers and waveguides, and new laser devices, but also for fundamental studies on string theory. Taking into account that the one-dimensional modulation mimic the existence of a additional dimensions, our system is the first example of physically realizable five-dimensional string., Comment: 10 pages, 6 figures

Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here we show that the process of finding these requirements can be automated by learning from simulated examples. The automation is done by using a convolutional neural network of a particular type that learns to understand with which network and under which coherence requirements quantum advantage is possible. Our machine learning approach is applied to study noisy quantum walks on cycle graphs of different sizes. We found that it is possible to predict the existence of quantum advantage for the entire decoherence parameter range, even for graphs outside of the training set. Our results are of importance for demonstration of advantage in quantum experiments and pave the way towards automating scientific research and discoveries., Comment: 6 pages, 4 figures

Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the corresponding phase diagram, exhibit one- and two-humped solitons with almost perfect agreement to numerical solutions. The results obtained in this work reveal a hitherto unexplored area of soliton physics associated with nonlinear corrections to wave dispersion., Comment: 10 pages, 4 figures

We study the eigen-energy and eigen-function of a quantum particle acquiring the probability density-dependent effective mass (DDEM) in harmonic oscillators. Instead of discrete eigen-energies, continuous energy spectra are revealed due to the introduction of a nonlinear effective mass. Analytically, we map this problem into an infinite discrete dynamical system and obtain the stationary solutions by perturbation theory, along with the proof on the monotonicity in the perturbed eigen-energies. Numerical results not only give agreement to the asymptotic solutions stemmed from the expansion of Hermite-Gaussian functions, but also unveil a family of peakon-like solutions without linear counterparts. As nonlinear Schr{\"o}dinger wave equation has served as an important model equation in various sub-fields in physics, our proposed generalized quantum harmonic oscillator opens an unexplored area for quantum particles with nonlinear effective masses., Comment: 10 pages, 3 figures

Realizing the topological bands of helical states poses a challenge in studying ultracold atomic gases. Motivated by the recent experimental success in realizing chiral optical ladders, here we present a scheme for synthesizing topological quantum matter, especially the quantum spin Hall phase, in the chiral optical ladders. More precisely, we first establish the synthetic pseudo-spin-orbit coupling and Zeeman splitting in the chiral ladders. We analyze the band structure of the ladders exposed to the bichromatic optical potentials and report the existence of quantum spin Hall phase. We further identify a rich phase diagram of the bichromatic chiral ladders, illustrating that our proposal features a large space of system parameters exhibiting a variety of quantum phase transitions. Our scheme can be readily implemented in the existing experimental systems and hence provides a new method to engineer the sophisticated topological bands for cold atomic gases., Comment: 6 pages, 4 figures

Space and time are crucial twins in physics. In quantum mechanics, spatial correlations already reveal nonclassical features, such as entanglement, and have bred many quantum technologies. However, the nature of quantum temporal correlations still remains in vague. In this Letter, based on the entangled-history formalism, we prove rigorously that temporal correlations are equivalent to spatial correlations. The effect of temporal correlations corresponds to a quantum channel. The resulting quantifications and classifications of quantum temporal correlations are illustrated in a natural way. Our proposed procedures also show how to determine temporal correlations completely.

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed because of the lack of control strategies. We introduce a new concept of nonlinear wave topological control, based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the nonlinear Schr\"odinger equation solutions by the Riemann theta function. We prove it experimentally by reporting the first observation of supervised transitions between extreme waves with different genera, like the continuous transition from dispersive shock to rogue waves. Specifically, we use a parametric time-dependent nonlinearity to shape the asymptotic wave genus. We consider the box problem in a focusing Kerr-like photorefractive medium and tailor time-dependent propagation coefficients, as nonlinearity and dispersion, to explore each region in the state-diagram and include all the dynamic phases in the nonlinear wave propagation. Our result is the first example of the topological control of integrable nonlinear waves. This new technique casts light on dispersive shock waves and rogue wave generation, and can be extended to other nonlinear phenomena, from classical to quantum ones. The outcome is not only important for fundamental studies and control of extreme nonlinear waves, but can be also applied to spatial beam shaping for microscopy, medicine and spectroscopy, and to the broadband coherent light generation., Comment: 11 pages, 5 figures

Time evolution is an indivisible part in any physics theory. Usually, people are accustomed to think that the universe is a fixed background and the system itself evolves step by step in time. However, Yakir Aharonov challenges this view using his two-vector formalism. In this paper, using the entangled history formalism, we attain three achievements., Comment: 6 pages

Quantum entanglement is an essential ingredient for the absolute security of quantum communication. Generation of continuous-variable entanglement or two-mode squeezing between light fields based on the effect of electromagnetically induced transparency (EIT) has been systematically investigated in this work. Here, we propose a new scheme to enhance the degree of entanglement between probe and coupling fields of coherent-state light by introducing a two-photon detuning in the EIT system. This proposed scheme is more efficient than the conventional one, utilizing the dephasing rate of ground-state coherence, i.e., the decoherence rate to produce entanglement or two-mode squeezing which adds far more excess fluctuation or noise to the system. In addition, maximum degree of entanglement at a given optical depth can be achieved with a wide range of the coupling Rabi frequency and the two-photon detuning, showing our scheme is robust and flexible. It is also interesting to note that while EIT is the effect in the perturbation limit, i.e. the probe field being much weaker than the coupling field and treated as a perturbation, there exists an optimum ratio of the probe to coupling intensities to achieve the maximum entanglement. Our proposed scheme can advance the continuous-variable-based quantum technology and may lead to applications in quantum communication utilizing squeezed light., Comment: 10 pages, 6 figures

With the wave interferometric approach, we study how extrinsically multiple coherent waves excitation can dramatically alter the overall scattering states, resulting in tailoring the energy assignment among radiation and dissipation. To explore the concept, we derive the corresponding formulas for dissipation and scattering powers for cylindrical passive systems encountered by general configurations of incident waves with various illuminating directions, phases, and intensities. We demonstrate that a linear superposition of incident waves extrinsically interferes the target channels in a desirable way. Moreover, the interferometric results can be irrespective to the inherent system configurations like size, materials, and structures. The extrinsic interfering waves pave a non-invasive solution to manipulate light and matter interaction, with potential applications in metasurfaces, nanophotonics, and metadevices.

By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $\cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $\cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system., Comment: 4 pages; with Supplemental Material

With theoretical analyses and numerical calculations, we show that a passive scatterer at the sub-wavelength scale can simultaneously exhibit both nearly zero forward scattering (NZFS) and nearly zero backward scattering (NZBF). It is related to the interference of dipolar quadrupole modes of different origin, leading to coexistence of Kerker's first and second conditions at the same time. For optical frequencies, we propose two different sets of composited materials in multi-layered nano-structures, i.e., CdTe/Si/TiO2 and TiO2/Au/Si, for the experimental realization.

Through the $\eta$-inner product, we investigate $\cal PT$-symmetric quantum mechanics from the viewpoint of superposition and coherence theory. It is argued that $\cal PT$-symmetric quantum systems are endowed with stationary superposition or superposition-free properties. A physical interpretation of $\eta$-inner product in $\mathbb C^2$ is given through the Stokes parameters, showing the difference between broken and unbroken $\cal PT$-symmetric quantum systems., Comment: Add an author Ray-Kuang Lee

By considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schr\"odinger-cat superposition states and maximally path entangled $N00N$-states. With these macroscopic states, we examine Mach-Zehnder interferometer in the context of parity measurements, in order to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio between two-body scattering length and intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons., Comment: 7 pages, 4 figures

To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals. With a temporally periodic modulation in the external bias voltage, corresponding to a modulation in the nonlinear strength, an enhancement in the visibility of MI at resonant frequency is reported through spontaneous optical pattern formations. Modeled by such temporally periodic nonlinear driving force to the system, theoretical curves obtained from a nonlinear non-instantaneous Schr\"{o}dinger equation give good agreement to experimental data. As MI is a universal signature of symmetry-breaking phenomena, our observation on the resonance in MI may provide a control on chaotic, solitary, and turbulence waves., Comment: 5 pages, 4 figures

For matter wave scattering from passive quantum obstacles, we propose a phase diagram in terms of phase and modulus of scattering coefficients to explore all possible directional scattering patterns. In the phase diagram, we can not only have the physical bounds on scattering coefficients for all channels, but also indicate the competitions among absorption, extinction, and scattering cross sessions. With help of this phase diagram, we discuss different scenarios to steer scattering probability distribution, through the interference between $s$- and $p$-channels. In particular, we reveal the required conditions to implement a quantum scatterer, i.e., a quantum dot in semiconductor matrix, with a minimum (or zero) value in the scattering probability toward any direction. Our results provide a guideline in designing quantum scatterers with controlling and sensing matter waves., Comment: 6 pages, 3 figures

In the framework of the Gross-Pitaevskii equation, we study the formation and stability of effectively two-dimensional solitons in dipolar Bose-Einstein condensates (BECs), with dipole moments polarized at an arbitrary angle $\theta$ relative to the direction normal to the system's plane. Using numerical methods and the variational approximation, we demonstrate that unstable Townes solitons, created by the contact attractive interaction, may be completely stabilized (with an anisotropic shape) by the dipole-dipole interaction (DDI), in interval $\theta ^{\text{cr}}<\theta \leq \pi /2$. The stability boundary, $\theta ^{\text{cr}}$, weakly depends on the relative strength of DDI, remaining close to the "magic angle", $\theta_{m}=\arccos \left( 1/\sqrt{3}\right) $. The results suggest that DDIs provide a generic mechanism for the creation of stable BEC\ solitons in higher dimensions., Comment: 9 pages, 7 figures; Phys. Rev. A, in press

For a bipartite state with equal local dimension d, we prove that one can obtain work gain under Landauer's erasure process on one party in identically and independently distributed (iid) limit when the corresponding fully entangled fraction is larger than 1/d. By processing a given state to the maximally mixed state, we give an approximation for the largest extractable work with an error in the energy scale, which becomes negligible in the large system limit. As a step to link quantum thermodynamics and quantum nonlocality, we also provide a simple picture to approximate the optimal work extraction and suggest a potential thermodynamic interpretation of fully entangled fraction for isotropic states., Comment: 5+4 pages, 2 figures

For passive electromagnetic scatterers, we explore a variety of extreme limits on directional scattering patterns in phase diagram, regardless of details on the geometric configurations and material properties. By demonstrating the extinction cross-sections with the power conservation intrinsically embedded in phase diagram, we give an alternative interpretation for Kerker first and second conditions, associated with zero backward scattering (ZBS) and nearly zero forward scattering (NZFS). The physical boundary and limitation for these directional radiations are illustrated, along with a generalized Kerker condition with implicit parameters. By taking the dispersion relations of gold-silicon core-shell nanoparticles into account, based on the of phase diagram, we reveal the realistic parameters to experimentally implement ZBS and NZFS at optical frequencies., Comment: 8 pages, 4 figures

The use of geometrical constraints opens many new perspectives in photonics and in fundamental studies of nonlinear waves. By implementing surface structures in vertical cavity surface emitting lasers as manifolds for curved space, we experimentally study the impacts of geometrical constraints on nonlinear wave localization. We observe localized waves pinned to the maximal curvature in an elliptical-ring, and confirm the reduction in the localization length of waves by measuring near and far field patterns, as well as the corresponding dispersion relation. Theoretically, analyses based on a dissipative model with a parabola curve give good agreement remarkably to experimental measurement on the transition from delocalized to localized waves. The introduction of curved geometry allows to control and design lasing modes in the nonlinear regime., Comment: 6 pages, 6 figures

To achieve high degree of quantum noise squeezing, an optical cavity is often employed to enhance the interaction time between light and matter. Here, we propose to utilize the effect of coherent population trapping (CPT) to directly generate squeezed light without any optical cavity. Combined with the slow propagation speed of light in a CPT medium, a coherent state passing through an atomic ensemble with a high optical density (OD) can evolve into a highly squeezed state even in a single passage. Our study reveals that noise squeezing of more than $10$ dB can be achieved with an OD of 1,000, which is currently available in experiments. A larger OD can further increase the degree of squeezing. As the light intensity and two-photon detuning are key factors in the CPT interaction, we also demonstrate that the minimum variance at a given OD can be reached for a wide range of these two factors, showing the proposed scheme is flexible and robust. Furthermore, there is no need to consider the phase-matching condition in the CPT scheme. Our introduction of high OD in atomic media not only brings a long light-matter interaction time comparable to optical cavities, but also opens new avenue in the generation of squeezed light for quantum interface., Comment: PRA (in press)

Quantum steering, also called Einstein-Podolsky-Rosen steering, is the intriguing phenomenon associated with the ability of spatially separated observers to steer---by means of local measurements---the set of conditional quantum states accessible by a distant party. In the light of quantum information, all steerable quantum states are known to be resources for quantum information processing tasks. Here, via a quantity dubbed steering fraction, we derive a simple, but general criterion that allows one to identify quantum states that can exhibit quantum steering, thus making an important step towards the characterization of steerable quantum states. The criterion, in turn, also provides upper bounds on the largest steering-inequality violation achievable by arbitrary finite-dimensional maximally entangled states. For the quantification of steerability, we prove that a strengthened version of the steering fraction is a convex steering monotone and demonstrate how it is related to two others, namely, steerable weight and steering robustness. Using these tools, we further demonstrate the superactivation of steerability, i.e., we show how the steerability of certain entangled, but unsteerable quantum states can be recovered by allowing joint measurements on multiple copies of the same state. In particular, our approach allows one to explicitly construct a steering inequality to manifest this phenomenon. Finally, we prove that there exist quantum states (including some unsteerable under projective measurements) whose steering-inequality violation can be arbitrarily amplified by allowing joint measurements on three copies of the same state. For completeness, we also demonstrate how the largest steering-inequality violation can be used to bound the largest Bell-inequality violation and derive, analogously, a simple sufficient condition for Bell-nonlocality from the latter., Comment: v3: published version; v2: 10+5 pages, 1 figure; results in Sec III, Sec V and Appendix B expanded, references updated; see also related work by Quintino et al.at arXiv:1610.01037

The interaction of hot atoms with laser fields experiences a Doppler shift which can severely affect the precise spatial measurement of an atom. We suggest an experimentally realizable scheme to address this issue in three-dimension position measurement of a single atom in vapors of rubidium atoms. Three-level lambda type atom-field configuration is considered where a moving atom interacts with three orthogonal standing-wave laser fields and spatial information of the atom in 3D space is obtained via upper-level population using a weak probe laser field. The atom moves with a velocity along the probe laser field and due to the Doppler broadening the precision in the spatial information deteriorates significantly. It is reported that via a microwave field the precision in the position measurement of the single atom can be obtained in the hot rubidium atom overcoming the limitation posed by the Doppler shift., Comment: 5 Pages, 4 figures