Quantum gas systems are ideal analog quantum simulation platforms for tackling some of the most challenging problems in strongly correlated quantum matter. However, they also expose the urgent need for new theoretical frameworks. Simple models in one dimension, well studied with conventional methods, have received considerable recent attention as test cases for new approaches. Ladder models provide the logical next step, where established numerical methods are still reliable, but complications of higher dimensional effects like gauge fields can be introduced. In this paper, we investigate the application of the recently developed neural-network quantum states in the two-leg Bose-Hubbard ladder under strong synthetic magnetic fields. Based on the restricted Boltzmann machine and feedforward neural network, we show that variational neural networks can reliably predict the superfluid-Mott insulator phase diagram in the strong coupling limit comparable with the accuracy of the density-matrix renormalization group. In the weak coupling limit, neural networks also diagnose other many-body phenomena such as the vortex, chiral, and biased-ladder phases. Our work demonstrates that the two-leg Bose-Hubbard model with magnetic flux is an ideal test ground for future developments of neural-network quantum states.

In this paper, we turn our attention to light propagation in three-dimensional electrodynamics. More specifically, we investigate the behavior of light rays in a continuous bidimensional hypothetical medium living in a three-dimensional ambient spacetime. Relying on a fully covariant approach, we assume that the medium is endowed with a local and linear-response tensor which maps field strengths into excitations. In the geometric optics limit, we then obtain the corresponding Fresnel equation and, using well-known results from algebraic geometry, we derive the effective optical metric and indicate possible applications of this formalism in the context of solid-state physics.

In this work, we revisit the tight focusing of a radially polarized partially coherent Gaussian Schell-model beam and examine the effect of spatial coherence of the incident beam on the focal-plane three-dimensional (3D) polarization characters, including the 3D degree of polarization, polarimetric dimensionality, and polarimetric structure. The polarimetric structure and the associated structure for the spin density vector of the tightly focused field are obtained via the 3D characteristic decomposition of the $3\times 3$ polarization matrix. We demonstrate that the generated focused field shows the genuine 3D polarization state and a sophisticated spin structure due to the reduced spatial coherence in the incident beam. We find the contributions to whole 3D polarization state of the focused field from the pure state, middle-term state, and 3D unpolarized state in the characteristic decomposition, as well as the contributions to the total spin density vector from the spins of pure state and middle-term state can be controlled by the transverse spatial coherence width of the incident Gaussian Schell-model beam. In addition, the genuine 3D polarization and the spin structure are analyzed in the connection of the recently introduced concept of polarimetric nonregularity.

We propose an approach for achieving a two-photon process in which a single two-level atom can simultaneously absorb or emit two photons separately distributed in two cavities. This two-photon process is realized by a two-level atom dispersively coupled to a classical pulse and two cavities. The main advantage of this proposal lies in the fact that because only two levels of the atom are used, i.e., no auxiliary atomic levels are utilized, decoherence from the higher energy levels of the atom is avoided. In addition, we find that the two-photon process can enable the synthesis of a hybrid atom-cavity-cavity Greenberger-Horne-Zeilinger (GHZ) entangled state. As an example, we further discuss the experimental feasibility of creating the proposed hybrid GHZ state in a circuit QED system. This proposal is quite general and can be implemented in a wide range of physical systems, such as a natural or artificial atom coupled to two optical or microwave cavities.

Quantum metrology enhances measurement precision by utilizing the properties of quantum physics. In interferometry, this is typically achieved by evolving highly entangled quantum states before performing single-shot measurements to reveal information about an unknown parameter. While this is often the optimum approach, implementation with all but the smallest states is still extremely challenging. An alternative approach is quantum jump metrology [L. A. Clark et al., Phys. Rev. A 99, 022102 (2019)], which deduces information by continuously monitoring an open quantum system while inducing phase-dependent temporal correlations with the help of quantum feedback. Taking this approach here, we analyze measurements of a relative phase in an optical network of two cavities with quantum feedback in the form of laser pulses. It is shown that the proposed approach can exceed the standard quantum limit without the need for complex quantum states while being scalable and more practical than previous related schemes.

We study steady-state phases of a one-dimensional array of Rydberg atoms coupled by a microwave (MW) field where the higher-energy Rydberg state decays to the lower-energy one via single-body and collective (superradiant) decay. Using mean-field approaches, we examine the interplay among the MW coupling, intrastate van der Waals (vdW) interaction, and single-body and collective dissipation between Rydberg states. A linear stability analysis reveals that a series of phases, including uniform, antiferromagnetic, oscillatory, and bistable and multistable phases can be obtained. Without the vdW interaction, only uniform phases are found. In the presence of the vdW interaction, multistable solutions are enhanced when increasing the strength of the superradiant decay rate. Our numerical simulations show that the bistable and multistable phases are stabilized by superradiance in a long chain. The critical point between the uniform and multistable phases and its scaling with the atom number is obtained. Through numerically solving the master equation of a finite chain, we show that the mean-field multistable phase could be characterized by expectation values of Rydberg populations and two-body correlations between Rydberg atoms in different sites.

We consider two closely spaced slits of subwavelength width, pierced in a metal screen, that are illuminated by short, arbitrarily polarized, plane-wave pulses. The $p$-polarized component generates plasmonic pulses propagating on the metal surface between the slits. In addition to the primary transmitted pulses, scattering of the plasmonic pulses by the opposite slit is found to produce secondary (echo) radiation pulses, which causes splitting, shaping, and time-dependent polarization modulation of the radiated pulses in the far field. We study these effects in the linear regime. A previously explored phenomenological model is extended to the time domain and is validated by rigorous numerical calculations. Our analytical and numerical results have implications for the transmission of pulsed light through arrangements of nanoscale apertures with plasmonic coupling.

The generation of vortices in the focusing of circularly polarized light beams results from the spin-orbit interaction (SOI), which is very similar to the generation of vortices when a light beam normally passes through an optically thin slab. However, its physical origin and the intrinsic relationship between both systems are still not well elucidated. Here, we establish a unified full-wave theory to revisit this problem. It is revealed that the origin of vortex generation in the transverse fields of the focusing system is the momentum-dependent Pancharatnam-Berry (PB) phase, which shares the same physics as the vortex generation in the slab case. In particular, we find that, under normal incidence, the beam transmitted through an optically thin slab has a longitudinal field and also exhibits a vortex with a topological charge of $\pm 1$ owing to the Berry-phase mechanism, akin to the focusing case. These findings not only unify the SOI-induced vortex generation in the optically thin slab and focusing systems within a single framework, uncovering the physical origin behind the SOI-induced vortex generation in optics, but also may shed light on understanding the SOIs in other fields.

$\mathcal{N}$ emitters collectively coupled to a quantized cavity mode are described by the Tavis-Cummings model. We present a complete analytical solution of the model in the presence of inhomogeneous couplings and energetic disorder. We derive the exact expressions for the bright and the dark sectors that decouple the disordered model and find that, in the thermodynamic limit, the energetic disorder transforms the bright sector to Fano's model that can be easily solved. We thoroughly explore the effects of energetic disorder assuming a Gaussian distribution of emitter transition energies. We compare the Fano resonances in optical absorption and inelastic electron scattering in both the weak and the strong coupling regimes. We study the evolution of the optical absorption with an increase in the disorder strength and find that it changes the lower and upper polaritons to their broadened resonances that finally transform to a single resonance at the bare cavity photon energy, thus taking the system from the strong to the weak coupling regime. Interestingly, we learn that Rabi splitting can exist even in the weak coupling regime, while the polaritonic peaks in the strong coupling regime can represent almost excitonic states at intermediate disorder strengths. We also calculate the photon Green's function to see the effect of cavity leakage and nonradiative emitter losses and find that the polariton line width exhibits a minimum as a function of detuning when the cavity leakage is comparable to the Fano broadening.

We analyze the application of the history state formalism to quantum walks. The formalism allows one to describe the whole walk through a pure quantum history state, which can be derived from a timeless eigenvalue equation. It naturally leads to the notion of system-time entanglement of the walk, which can be considered as a measure of the number of orthogonal states visited in the walk. We then focus on one-dimensional discrete quantum walks, where it is shown that such entanglement is independent of the initial spin orientation for real Hadamard-type coin operators and real initial states (in the standard basis) with definite site parity. Moreover, in the case of an initially localized particle it can be identified with the entanglement of the unitary global operator that generates the whole history state, which is related to its entangling power and can be analytically evaluated. Besides, it is shown that the evolution of the spin subsystem can also be described through a spin history state with an extended clock. A connection between its average entanglement (over all initial states) and that of the operator generating this state is also derived. A quantum circuit for generating the quantum walk history state is provided as well.

In studies of one-dimensional Bethe ansatz solvable models, a Fredholm integral equation of the second kind with a difference kernel on a finite interval often appears. This equation does not generally admit a closed-form solution and hence its analysis is quite complicated. Here we study a family of such equations, concentrating on their moments. We find exact relations between the moments in the form of difference-differential equations. The latter results significantly advance the analysis, enabling one to practically determine all the moments from the explicit knowledge of the lowest one. As applications, several examples are considered. First, we study the moments of the quasimomentum distribution in the Lieb-Liniger model and find explicit analytical results. The latter moments determine several basic quantities, e.g., the $N$-body local correlation functions. We prove the equivalence between different expressions found in the literature for the three-body local correlation functions and find an exact result for the four-body local correlation function in terms of the moments of the quasimomentum distributions. We eventually find the analytical results for the three- and four-body correlation functions in the form of asymptotic series in the regimes of weak and strong interactions. Next, we study the exact form of the low-energy spectrum of a magnon (a polaron) excitation in the two-component Bose gas described by the Yang-Gaudin model. We find its explicit form, which depends on the moments of the quasimomentum distributions of the Lieb-Liniger model. Then, we address a seemingly unrelated problem of capacitance of a circular capacitor and express the exact result for the capacitance in the parametric form. In the most interesting case of short plate separations, the parametric form has a single logarithmic term. This should be contrasted with the explicit result that has a complicated structure of logarithms.

There is increasing interest in quantum algorithms (QAs) that are based on the imaginary time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy postprocessing computational steps on a classical computer, such as solving linear equations. Here we provide an alternative approach to implement ITE. A key feature in our approach is the use of an orthogonal basis set: the propagated state is efficiently expressed in terms of orthogonal basis states at every step of the evolution. We argue that the number of basis states needed at those steps to achieve an accurate solution can be kept on the order of $n$, the number of qubits, by controlling the precision (number of significant digits) and the imaginary time increment. The number of quantum gates per imaginary time step is estimated to be polynomial in $n$. Additionally, while in many QAs the locality of the Hamiltonian is a key assumption, in our algorithm this restriction is not required. This characteristic of our algorithm renders it useful for studying highly nonlocal systems, such as the occupation-representation nuclear shell model. We illustrate our algorithm through numerical implementation on an IBM quantum simulator.

Quantum error mitigation is a key concept for the development of practical applications based on current noisy intermediate-scale quantum devices. One of the most promising methods is Richardson extrapolation to the zero noise limit. While its main idea is rather simple, the full potential of Richardson extrapolation has not been completely uncovered yet. We give an in-depth analysis of the relevant parameters of Richardson extrapolation and propose an optimized protocol for its implementation. This protocol allows for a precise control of the increase in statistical uncertainty and lays the foundation for a significant improvement of the mitigation performance achieved by increasing the number of nodes. Furthermore, we present a set of nodes that, on average, outperforms the linear, exponential, or Chebyshev nodes frequently used for Richardson extrapolation without requiring any additional resources.

Quantum entanglement is a key resource, which grants quantum systems the ability to accomplish tasks that are classically impossible. Here, we apply Feynman's sum-over-histories formalism to interacting bipartite quantum systems and introduce entanglement measures for bipartite quantum histories. Based on the Schmidt decomposition of the matrix comprised of the Feynman propagator complex coefficients, we prove that bipartite quantum histories are entangled if and only if the Schmidt rank of this matrix is larger than 1. The proposed approach highlights the utility of using a separable basis for constructing the bipartite quantum histories and allows for quantification of their entanglement from the complete set of experimentally measured sequential weak values. We then illustrate the nonclassical nature of entangled histories with the use of Hardy's overlapping interferometers and explain why local hidden variable theories are unable to correctly reproduce all observable quantum outcomes. Our theoretical results elucidate how the composite tensor product structure of multipartite quantum systems is naturally extended across time and clarify the difference between quantum histories viewed as projection operators in the history Hilbert space and those viewed as chain operators and propagators in the standard Hilbert space.

A model-operator approach to fully relativistic calculations of the nuclear recoil effect on energy levels in many-electron atomic systems is worked out. The one-electron part of the model operator for treating the normal mass shift beyond the Breit approximation is represented by a sum of semilocal and nonlocal potentials. The latter ones are constructed by employing the diagonal and off-diagonal matrix elements rigorously evaluated for hydrogenlike ions to first order in the electron-to-nucleus mass ratio. The specific mass shift beyond the lowest-order relativistic approximation has a form which can be directly employed in calculations. The capabilities of the method are probed by comparison of its predictions with the results of ab initio QED calculations. The proposed operator can be easily incorporated into any relativistic calculation based on the Dirac-Coulomb-Breit Hamiltonian.

Casimir forces between charge-neutral bodies originate from quantum vacuum fluctuations of electromagnetic fields, which exhibit a critical dependence on material's electromagnetic properties. Over the years, in situ modulation of a material's optical properties has been enabled through various means and has been widely exploited in a plethora of applications such as electro-optical modulation, transient color generation, bio- or chemical sensing, etc. Yet Casimir force modulation has been hindered by difficulty in achieving high modulation signals due to the broadband nature of the Casimir interaction. Here we propose and investigate two configurations that allow for in situ modulation of Casimir forces through electrical gating of a metal-insulator-semiconductor junction comprised of transparent conductive oxide (TCO) materials. By switching the gate voltage on and off, a force modulation of >400 pN is predicted due to substantive charge carrier accumulation in the TCO layer, which can be easily measured using state-of-the-art force measurement techniques in an atomic force microscope. We further examine the influence of the oxide layer thickness on the force modulation, suggesting the importance of the fine control of the oxide layer deposition. Our work provides a promising pathway for modulating the Casimir effect in situ with experimentally measurable force contrast.