Entanglement detection is an important problem in quantum information theory because quantum entanglement is a key resource in quantum information processing. Realignment criterion is a powerful tool for the detection of entangled states in bipartite and multipartite quantum systems. It works well not only for negative-partial-transpose entangled states (NPTESs) but also for positive-partial-transpose entangled states (PPTESs). Since the matrix corresponding to the realignment map is indefinite, the experimental implementation of the map is an obscure task. In this work, first, we approximate the realignment map to a positive map using the method of structural physical approximation, and then we show that the structural physical approximation of the realignment map (SPA-R) is completely positive. Positivity of the constructed map is characterized using moments which can be physically measured. Next, we develop a separability criterion based on our SPA-R map in the form of an inequality and show that the developed criterion not only detect NPTESs but also PPTESs. Further, we show that for a special class of states called Schmidt-symmetric states, the SPA-R separability criteria reduce to the original form of the realignment criteria. We provide some examples to support the results obtained. Moreover, we analyze the error that may occur because of approximating the realignment map.

A random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an $n$-bit string, while only having limited information about the $n$-bit string. Quantum RACs usually utilize either communication of quantum bits or a shared-in-advance quantum state used in conjunction with classical communication. Here we consider the latter version of the quantum protocols under the constraint of single-bit communication and with a shared arbitrary state of two qubits. Taking the worst-case success probability as the figure of merit, we demonstrate that any state with an invertible correlation matrix can be used to outperform the best classical RAC for $n=3$. We derive an additional condition sufficient to beat the best classical performance in the case of $n=2$. In particular, separable states turn out to be a useful resource behind the quantum advantage for $n=2,3$. For $n\ge 4$, RACs assisted with a single copy of a quantum state do not outperform the classical RACs.

Quantum computers, using efficient Hamiltonian evolution routines, have the potential to simulate Green's functions of classically intractable quantum systems. However, the decoherence errors of near-term quantum processors prohibit large evolution times, posing limits to the spectrum resolution. In this paper, we show that atomic norm minimization, a well-known super-resolution technique, can significantly reduce the minimum circuit depth for accurate spectrum reconstruction. We demonstrate this technique by recovering the spectral function of an impurity model from measurements of its Green's function on an IBM quantum computer. The reconstruction error with the atomic norm minimization is one order of magnitude smaller than with more standard signal processing methods. Super-resolution methods can facilitate the simulation of large and previously unexplored quantum systems, and may constitute a useful nonvariational tool to establish a quantum advantage in the near future.

It is usually assumed that interaction potentials, in general, and atom-surface potential, in particular, can be expressed in terms of an expansion involving integer powers of the distance between the two interacting objects. Here, we show that, in the short-range expansion of the interaction potential of a neutral atom and a dielectric surface, logarithms of the atom-wall distance appear. These logarithms are accompanied with logarithmic sums over virtual excitations of the atom interacting with the surface in analogy to Bethe logarithms in quantum electrodynamics. We verify the presence of the logarithmic terms in the short-range expansion using a model problem with realistic parameters. By contrast, in the long-range expansion of the atom-surface potential, no logarithmic terms appear, and the interaction potential can be described by an expansion in inverse integer powers of the atom-wall distance. Several subleading terms in the large-distance expansion are obtained as a byproduct of our investigations. Our findings explain why the use of simple interpolating rational functions for the description of the atom-wall interaction in the intermediate regions leads to significant deviations from exact formulas.

By numerically solving the three-dimensional time-dependent Schrödinger equation, we have studied the energy- and angle-resolved time delay in $\mathrm{H}{{}_2}^{+}$ photoionization using the reconstruction of attosecond beating by the interference of two-photon transition (RABITT) technique. Around the electron energy of $E_c\sim 1.4$ a.u., the RABITT time delay varies significantly with the energy and emission angle. The time delay changes from positive values to negative values as the increasing energy and emission angle. We have applied the spheroidal wave analysis to reveal this interesting time delay. By analyzing the time-delay dependent modulation of the anisotropic parameters, the energy and angle dependence of the time delay is well interpreted from the perspective of spheroidal wave interference. It shows that the Cooper-like minimum of a $p$ spheroidal wave is responsible for this sign change of the RABITT time delay.

Caustics are singularities that occur naturally in optical, hydrodynamic, and quantum waves, giving rise to high-amplitude patterns that can be described using catastrophe theory. In this paper we study caustics in a statistical field theory setting in the form of the sine-Gordon model that describes a variety of physical systems including coupled one-dimensional (1D) superfluids. Specifically, we use classical field simulations to study the dynamics of two ultracold 1D Bose gases (quasicondensates) that are suddenly coupled to each other and find that the resulting nonequilibrium dynamics is dominated by caustics. Thermal noise is included by sampling the initial states from a Boltzmann distribution for phononic excitations. We find that caustics pile up over time in both the number and phase difference observables, leading to a characteristic nonthermal circus-tent-shaped probability distribution at long times.

We study the temporal growth and spatial propagation of quantum correlations in a two-dimensional bilayer realizing a spin-1/2 quantum XXZ model with couplings mediated by long-range and anisotropic dipolar interactions. Starting with an initial state consisting of spins with opposite magnetization in each of the layers, we predict a dynamic instability that results, at short times, in the creation of correlated pairs of excitations at specific momenta at exponentially fast rates and entanglement between spatially separated modes. The momentum structure of the created pairs can be controlled via the dipolar orientation, the layer separation, or the dipolar couplings. The predicted behavior remains observable at very low filling fractions, making it accessible in state-of-the-art experiments with Rydberg atoms, magnetic atoms, and polar molecule arrays.

Motivated by recent experiments, we study the properties of large Bose-Hubbard chains with single-particle losses at one site using classical field methods. We construct and validate a compact effective model that reduces computations to only a few sites. We show that in the mean-field approach the description captures the stationary states of the dissipative mode very well. Not only is there good quantitative agreement in the hysteresis loop, but the dark soliton state can be reproduced as well due to the preservation of the $\text{U}\left(1\right)$ symmetry. Bimodality of the steady states, observed on longer timescales, is studied using the truncated Wigner method. We compare the switching statistics and derive the effective Liouvillian gap as a function of the tunneling, showing that the effective description underestimates fluctuations.

This paper proves the equality of the group velocity and the energy velocity of electromagnetic Bloch waves in bianisotropic nonabsorbing periodic superlattices of generic crystallographic symmetry.

We discuss a fundamental question regarding the Abraham-Minkowski debate about the momentum of light in a medium: If an atom in a gas absorbs a photon, what is the momentum transferred to it? We consider a classical model for the internal degrees of freedom of the absorbing atom, computing the absorbed energy and momentum using the Lorentz force law due to the microscopic electromagnetic fields. Each nonabsorbing atom from the gas is treated as a dielectric sphere, with the set of atoms forming a linear, dielectric, nonmagnetic, and nonabsorbing medium with a refractive index $n$ close to 1. Our numerical results indicate that, if the atoms are classically localized, the average absorbed momentum increases with $n$, but is smaller than Minkowski's momentum $n{p}_0, p_0$ being the photon momentum in vacuum. However, experiments performed with Bose-Einstein condensates [G. K. Campbell et al., Phys. Rev. Lett. 94, 170403 (2005)] are consistent with the atom absorbing Minkowski's momentum. We argue that there is no contradiction between these results since, in a Bose-Einstein condensate, the atoms are in a quantum state spatially superposed in a relatively large volume, forming a “continuous” medium. In this sense, the experimental verification of an atomic momentum recoil compatible with Minkowski's momentum would be a quantum signature of the medium state.

Characterizing multipartite quantum correlations beyond two parties is of utmost importance for building cutting edge quantum technologies, although the comprehensive picture is still missing. Here we investigate quantum correlations (QCs) present in a multipartite system by exploring connections between magentathree different frameworks, namely, the monogamy score (MS), localizable quantum correlations (LQC), and genuine multipartite entanglement (GME) content of the state. We find that the frequency distribution of GME for Dicke states with higher excitations resembles that of random states. We show that there is a critical value of GME beyond which all states become monogamous and it is investigated by considering different powers of MS which provides various layers of monogamy relations. Interestingly, such a relationship between LQC and MS as well as GME does not hold. States having a very low GME (low monogamy score, both positive and negative) can localize a high amount of QCs in two parties. We also provide an upper bound to the sum of bipartite QC measures including LQC for random states and establish a gap between the actual upper bound and the algebraic maximum.

Integrated optical quantum memories are a scalable solution to synchronize a large number of quantum nodes. Without compact quantum memories, some astonishing quantum applications such as distributed quantum computing and quantum sensor networks would not be possible. Rather than find a specific material that meets all the requirements of an on-chip quantum memory as other protocols usually do, we propose to assign the memory requirements on coherent storage and controllability to rare-earth ions and a lithium niobate crystal, respectively. Specifically, optical quantum states are stored in an erbium-doped lithium niobate microcavity by utilizing the electro-optic effect of lithium niobate. The cavity frequency can be shifted by an external electric field, thus modifying the resonance condition between the cavity and the collective atomic excitation. This effect is further used to suppress or enhance the emission of photon echoes. Our calculated results show that high efficiency and a low noise performance are achievable.

Adiabatic rapid passage (ARP) is a powerful technique for efficient transfer of population between quantum states. In the laboratory, the efficiency of ARP is often limited by noise on either the energies of the states or the frequency of the driving field. We study ARP in the simple setting of a two-level system subject to sinusoidal fluctuations on the energy level separation by numerically solving the optical Bloch equations in the absence of damping. We investigate the dependence of the efficiency of population transfer on the frequency and amplitude of the perturbation and find that it is predominantly affected by resonant coupling when the detuning matches the frequency of the noise. We present intuitive principles for when ARP becomes inefficient within this model, and provide a sufficient condition for the population transfer to be above an arbitrary threshold.

The dynamics of one-dimensional quantum many-body systems is often numerically simulated with matrix-product states (MPSs). The computational complexity of MPS methods is known to be related to the growth of entropies of reduced density matrices for bipartitions of the chain. While for closed systems the entropy relevant for the complexity is uniquely defined by the entanglement entropy, for open systems it depends on the choice of the representation. Here, we systematically compare the growth of different entropies relevant to the complexity of matrix-product representations in open-system simulations. We simulate an $XXZ$ spin-1/2 chain in the presence of spontaneous emission and absorption and dephasing. We compare simulations using a representation of the full density matrix as a matrix-product density operator (MPDO) with a quantum trajectory unraveling, where each trajectory is itself represented by an MPS (QT + MPS). We show that the bipartite entropy in the MPDO description (operator entanglement, OE) generally scales more favorably with time than the entropy in QT + MPS (trajectory entanglement, TE): (i) For spontaneous emission and absorption the OE vanishes while the TE grows and reaches a constant value for large dissipative rates and sufficiently long times; (ii) for dephasing the OE exhibits only logarithmic growth while the TE grows polynomially. Although QT + MPS requires a smaller local state space, the more favorable entropy growth can thus make MPDO simulations fundamentally more efficient than QT + MPS. Furthermore, MPDO simulations allow for easier exploitation of higher-order Trotter decompositions and translational invariance, allowing for larger time steps and system sizes.

We theoretically investigate the combined effects of the chirality and the finite total thickness of nematic cholesteric liquid crystals on the Casimir-Lifshitz torque. We find that the larger the thickness, the more sinusoidal the angular dependence of the torque becomes. We use a Fourier decomposition to quantify this result. The general direction of the torque depends on whether the configuration of two cholesterics is heterochiral or homochiral.

A near-infrared femtosecond laser pulse produces laserlike coherent radiation from singly ionized ${\mathrm{N}}_2{}^{+}$ molecules when it experiences filamentation in air or pure nitrogen, and the lasing radiation reaches maximal intensity when the driving pulse is slightly polarized elliptically. Based on a strong-field transient ionization model that considers ionization-induced quantum coherence, we reproduced the general feature of this counterintuitive dependence of the lasing intensity on pump laser ellipticity by numerically solving the Maxwell-Bloch equations of the lasing amplification process. The simulation results suggest that the competition effect between the increase of $B{}^2{\mathrm{\Sigma }}_u^{+}\leftarrow X{}^2{\mathrm{\Sigma }}_u^{+}$ inversion probability and the decrease of overall ${\mathrm{N}}_2{}^{+}$ ion production with the increasing ellipticity is mainly at the origin of observed ellipticity dependence. Additionally, the simulation predicts that ionization-induced quantum coherence also exhibits a nonzero ellipticity dependence and plays a nontrivial role in the weakly seeded and self-seeded scenarios. Our findings suggest that controlling the ionization-induced coherence could be a promising approach to improve the ${\mathrm{N}}_2{}^{+}$ lasing generation.

With the rapid development of topological circuits in recent years, it has been possible to explore the characteristics of various topological insulators as an independent platform. Here, we propose to use the circuit system to realize the Möbius insulators, whose algebraic structure can be enriched in a projective way. Through the circuit, we can observe the energy distribution of the whole model and the dispersion along the edge. In addition, we discuss the effect of different defects on the edge energy distribution. Our research not only gives people a deeper understanding of the topological physical phenomena caused by projective symmetry but also brings the application of circuits in the field of topological insulator research to a higher level.

We studied gap solitons and nonlinear Bloch waves in Kerr nonlinear systems under competition between quadratic and quartic dispersions. The results show that nonlinear Bloch waves can still be regarded as infinite fundamental gap solitons chains. We also revealed the properties of the gap solitons in the relevant band gaps by numerical analysis. Notably, for the two classical dipole modes in the first gap, the variation of the dispersion coefficient leads to the change of the soliton power relation due to the interaction between the two solitons composing them. We obtained the stable interval variation rule of gap waves without calculation by analyzing the interaction between fundamental gap solitons. This is consistent with our linear stability analysis and real-time numerical monitoring results. This finding provides an idea for further investigation of the physical properties of higher-order solitons under higher-order dispersion.

We use time-frequency continuous variables as the standard framework to describe states of light in the subspace of individual photons occupying distinguishable auxiliary modes. We adapt to this setting the interplay between metrological properties and the phase-space picture already extensively studied for quadrature variables. We also discuss in details the Hong-Ou-Mandel interferometer, which was previously shown to saturate precision limits, and provide a general formula for the coincidence probability of a generalized version of this experiment. From the obtained expression, we systematically analyze the optimality of this measurement setting for arbitrary unitary transformations applied to each one of the input photons. As concrete examples, we discuss transformations which can be represented as translations and rotations in time-frequency phase space for some specific states.

We study the emission of a single-photon by a two-level emitter inside an atomic cavity consisting of two atomic mirrors coupled to a one-dimensional waveguide. With proper atomic separations, we realize a frequency comb as well as spectrum narrowing in the waveguide with the symmetric setting, and also unidirectional spectrum narrowing with asymmetric parameters. Within a suitable range, we can control the central frequency of the narrowed spectra by modulating atomic separations. Due to the collective interaction among the emitters, entanglement sudden birth and revival are observed between the mirrors.