We consider a finite one-dimensional Heisenberg $\mathit{XYZ}$ spin chain under the influence of a dissipative Lindblad environment obeying the Born-Markovian constraint in presence of an external magnetic field with closed and open boundary conditions. We present an exact numerical solution for the Lindblad master equation of the system in the Liouville space. The dynamics and asymptotic behavior of the nearest-neighbor and beyond-nearest-neighbor pairwise entanglements in the system are investigated under the effect of spatial anisotropy, temperature, system size, and different initial states. The entanglements in the free spin system exhibit nonuniform oscillatory behavior that varies significantly depending on the system size, anisotropy, and initial state. The $xy$ spatial anisotropy dictates the asymptotic behavior of the different entanglements in the system under the influence of the environment regardless of the initial state. Higher anisotropy yields higher steady-state value of the nearest-neighbor entanglement whereas a complete isotropy wipes it out. The longer range entanglements respond differently to the anisotropy variation. The anisotropy in the $z$ direction may enhance the entanglements depending on the interplay with the magnetic field applied in the same direction. As the temperature is raised, the steady state of the short-range entanglements is found to be robust within very small nonzero temperature range that depends critically on the spatial anisotropy. Moreover, the end to end entanglement transfer time and speed through the open boundary chain vary considerably based on the degree of anisotropy and temperature of the environment.

The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary $k$-body interactions, their use is limited to small $k$ because the strength of interaction is $k\mathrm{th}$ order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective $k$-body interactions using Hamiltonians consisting of at most $l$-body interactions with $l<k$. The idea is to first apply a unitary transformation on the system plus ancilla qubits (possibly using a gate-based device), then evolve with a new Hamiltonian which is more local than the original one (using an analog device), and finally reverse the unitary transformation. The net effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each $k$-body interaction irrespective of the value of $k$. It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.

The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the $\zeta$-function regularization approach with zero-point energies summation. As a prototype material, each plane is represented by a graphene sheet, an atomically thin layer of carbon atoms organized in a hexagonal lattice, whose optical response is described by a constant conductivity or Drude-Lorentz model conductivity. Asymptotic expressions for various separations are derived and compared to numerical calculations. We distinguish between large atom-plane distance limit, where retardation effects are prominent, and small atom-plane distance limit, where the typical van der Waals coefficient is found to be dependent on the number of graphenes and characteristic separations. The calculated energies for different atoms and graphene conductivity models brings forward the basic science of the Casimir-Polder effect and suggests ways to manipulate this interaction experimentally.

We present a detailed analysis of the propagation dynamics of short and intense circularly polarized pulses in an aligned diatomic gas. Compared to linearly polarized intense pulses, high harmonic generation (HHG) and the coherent generation of attosecond pulses in the intense-circular-polarization case are a new research area. More specifically, we numerically study the propagation of intense and short circularly polarized pulses in the one-electron ${\mathrm{H}}_2{}^{+}$ molecular gas, using a micro-macro Maxwell–Schrödinger model. In this model, the macroscopic polarization is computed from the solution of a large number of time-dependent Schrödinger equations, the source of dipole moments, and using a trace operator. We focus on the intensity and the phase of harmonics generated in the ${\mathrm{H}}_2{}^{+}$ gas as a function of the pulse-propagation distance. We show that short coherent circularly polarized pulses of same helicity can be generated in the molecular gas as a result of cooperative phase-matching effects.

We theoretically investigate the electron interference dynamics of ${{\mathrm{H}}_2}^{+}$ in an intense infrared laser field. At intermediate internuclear distances, an interference fringe appears in the electron momentum distribution. By tracing the time evolution of the electron density, we identify an internal scattering channel of the electrons. The observed fringe is attributed to the interference between the internal scattered and direct photoelectrons. Our results reveal that the electron behaviors inside a molecule can be mapped onto the experimentally accessible photoelectron momentum spectra, suggesting a time-resolved way of probing the complex laser-driven electron dynamics on an attosecond time scale.

Angular dependence of photoemission time delay for the valence $n{p}_{3/2}$ and $n{p}_{1/2}$ subshells of Ar, Kr, and Xe is studied in the dipole relativistic random phase approximation. Strong angular anisotropy of the time delay is reproduced near respective Cooper minima while the spin-orbit splitting affects the time delay near threshold.

We further examine a theory of phase contrast imaging (PCI) of cold atomic gases, first introduced by us in Phys. Rev. Lett. 112, 233602 (2014). We model the PCI measurement by directly calculating the entangled state between the light and the atoms due to the ac Stark shift, which induces a conditional phase shift on the light depending upon the atomic state. By interfering the light that passes through the BEC with the original light, one can obtain information of the atomic state at a single-shot level. We derive an exact expression for a measurement operator that embodies the information obtained from PCI, as well as the backaction on the atomic state. By the use of exact expressions for the measurement process, we go beyond the continuous variables approximation such that the non-Gaussian regime can be accessed for both the measured state and the postmeasurement state. Features such as the photon probability density, signal, signal variance, Fisher information, error of the measurement, and the backaction are calculated by applying the measurement operator to an atomic two-spin-state system. For an atomic state that is initially in a spin-coherent state, we obtain analytical expression for these quantities. There is an optimal atom-light interaction time that scales inversely proportional to the number of atoms, which maximizes the information readout.

We study numerically the evolution of Bose-Einstein condensate in the Sinai-oscillator trap described by the Gross-Pitaevskii equation in two dimensions. In the absence of interactions, this trap mimics the properties of Sinai billiards where the classical dynamics is chaotic and the quantum evolution is described by generic properties of quantum chaos and random matrix theory. We show that, above a certain border, the nonlinear interactions between atoms lead to the emergence of dynamical thermalization which generates the statistical Bose-Einstein distribution over eigenmodes of the system without interactions. Below the thermalization border, the evolution remains quasi-integrable. Such a Sinai-oscillator trap, formed by the oscillator potential and a repulsive disk located in the vicinity of the center, had been already realized in first experiments with the Bose-Einstein condensate formation by Ketterle group in 1995 and we argue that it can form a convenient test bed for experimental investigations of dynamical of thermalization. Possible links and implications for Kolmogorov turbulence in absence of noise are also discussed.

We propose using a nonlinear Mach-Zehnder interferometer (NMZI) to efficiently prepare photonic quantum states from a classical input. We first analytically investigate the simple NMZI that can filtrate a single-photon state from weak coherent state by preferentially blocking a two-photon component. As a generalization, we show that the cascaded NMZI can deterministically extract an arbitrary quantum state from a strong coherent state. Finally, we numerically demonstrate that the cascaded NMZI can be very efficient in both the input power and the level of cascade. The protocol of quantum state preparation with the NMZI can be extended to various systems of bosonic modes.

A scheme of high-precision two- and three-dimensional (3D) atom localization is proposed and analyzed by using a density matrix method for a five-level atom-light coupling scheme. In this system four strong laser components (which could be standing waves) couple a pair of atomic internal states to another pair of states in all possible ways to form a closed-loop diamond-shape configuration of the atom-light interaction. By systematically solving the density matrix equations of the motion, we show that the imaginary part of the susceptibility for the weak probe field is position dependent. As a result, one can obtain information about the position of the atom by measuring the resulting absorption spectra. Focusing on the signatures of the relative phase of the applied fields stemming from the closed- loop structure of the diamond- shape subsystem, we find out that there exists a significant phase dependence of the eigenvalues required to have a maximum in the probe absorption spectra. It is found that by properly selecting the controlling parameters of the system, a nearly perfect 2D atom localization can be obtained. Finally, we numerically explore the phase control of 3D atom localization for the present scheme and show the possibility to obtain 1/2 detecting probability of finding the atom at a particular volume in 3D space within one period of standing waves.

We describe an experiment demonstrating the possibility to generate collinear indistinguishable x-ray photon pairs with a highly suppressed background. By choosing angles near 90 degrees between the detectors and the pump beam, where the pump polarization is in the scattering plane, we improve the signal-to-noise ratio by 2 orders of magnitude. We measure the pure coincidence spectrum without any energy discrimination with a bandwidth of 1.5 keV at the full width at half maximum.

We analyze the radiation-pressure-induced interaction of mirror motion and light fields in Michelson-type interferometers used for the detection of gravitational waves and for fundamental research in tabletop quantum optomechanical experiments, focusing on the asymmetric regime with a (slightly) unbalanced beam splitter and a (small) offset from the dark port. This regime, as it was shown recently, provides new interesting features, in particular a stable optical spring and optical cooling on cavity resonance. We show that, generally, the nature of optomechanical coupling in Michelson-type interferometers does not fit into the standard dispersive-dissipative dichotomy. In particular, a symmetric Michelson interferometer with signal-recycling but without power-recycling cavity is characterized by a purely dissipative optomechanical coupling; only in the presence of asymmetry, additional dispersive coupling arises. In gravitational waves detectors possessing signal- and power-recycling cavities, yet another coherent type of optomechanical coupling takes place. We develop here a generalized framework for the analysis of asymmetric Michelson-type interferometers, which also covers the possibility of the injection of carrier light into both ports of the interferometer. Using this framework, we analyze in depth the anomalous features of the Michelson-Sagnac interferometer, which have been discussed and observed experimentally previously [A. Xuereb et al., Phys. Rev. Lett. 107, 213604 (2011); S. P. Tarabrin et al., Phys. Rev. A 88, 023809 (2013); A. Sawadsky et al., Phys. Rev. Lett. 114, 043601 (2015)].

Here we show that noisy coupling can lead to diffusive lossless energy transfer between individual quantum systems retaining a quantum character leading to entangled stationary states. Coherence may flow diffusively while being summarily preserved even when energy exchange is absent. Diffusive dynamics persists even in the case where additional noise suppresses all unitary excitation exchange: arbitrarily strong local dephasing, while destroying quantum correlations, does not affect energy transfer.

A single-step Eriksen transformation of $1S_{1/2},2P_{1/2}$, and $2P_{3/2}$ states of the relativistic hydrogenlike atom is performed exactly by expressing each transformed function (TF) as a linear combination of eigenstates of the Dirac Hamiltonian. The TFs, which are four-component spinors with vanishing two lower components, are calculated numerically and have the same symmetries as the initial states. For all nuclear charges $Z\in [1...92]$ a contribution of the initial state to TFs exceeds 86% of the total probability density. Next a large contribution to TFs comes from continuum states with negative energies close to $-m_0{c}^2-E_b$, where $E_b$ is the binding energy of the initial state. The contribution of other states to TFs is less than $0.1\%$ of the total probability density. Other components of TFs are nearly 0, which confirms both the validity of the Eriksen transformation and the accuracy of the numerical calculations. The TFs of the $1S_{1/2}$ and $2P_{1/2}$ states are close to the $1s$ and $2p$ states of the nonrelativistic hydrogenlike atom, respectively, but the TF of the $2P_{3/2}$ state differs qualitatively from the $2p$ state. Functions calculated with the use of a linearized Eriksen transformation, being equivalent to the second-order Foldy-Wouthuysen transformation, are compared with corresponding functions obtained by Eriksen transformation. Very good agreement between the two results is obtained.

Quantum systems allow one to sense physical parameters beyond the reach of classical statistics—with resolutions greater than $1/N$, where $N$ is the number of constituent particles independently probing a parameter. In the canonical phase-sensing scenario the Heisenberg limit $1/N^2$ may be reached, which requires, as we show, both the relative size of the largest entangled block and the geometric measure of entanglement to be nonvanishing as $N\to \infty$. Yet, we also demonstrate that in the asymptotic $N$ limit any precision scaling arbitrarily close to the Heisenberg limit ($1/N^{2-\varepsilon }$ with any $\varepsilon >0$) may be attained, even though the system gradually becomes noisier and separable, so that both the above entanglement quantifiers asymptotically vanish. Our work shows that sufficiently large quantum systems achieve nearly optimal resolutions despite their relative amount of entanglement being arbitrarily small. In deriving our results, we establish the continuity relation of the quantum Fisher information evaluated for a phaselike parameter, which lets us link it directly to the geometry of quantum states, and hence naturally to the geometric measure of entanglement.

We construct a theory for Bose-Einstein condensation of light in nanofabricated semiconductor microcavities. We model the semiconductor by one conduction and one valence band which consist of electrons and holes that interact via a Coulomb interaction. Moreover, we incorporate screening effects by using a contact interaction with the scattering length for a Yukawa potential and describe in this manner the crossover from exciton gas to electron-hole plasma as we increase the excitation level of the semiconductor. We then show that the dynamics of the light in the microcavities is damped due to the coupling to the semiconductor. Furthermore, we demonstrate that on the electron-hole plasma side of the crossover, which is relevant for the Bose-Einstein condensation of light, this damping can be described by a single dimensionless damping parameter that depends on the external pumping. Hereafter, we propose to probe the superfluidity of light in these nanofabricated semiconductor microcavities by making use of the differences in the response in the normal or superfluid phase to a sudden rotation of the trap. In particular, we determine frequencies and damping of the scissors modes that are excited in this manner. Moreover, we show that a distinct signature of the dynamical Casimir effect can be observed in the density-density correlations of the excited light fluid.

We apply the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) to systems of bosons or fermions in lattices described by Hubbard-type Hamiltonians with long-range or short-range interparticle interactions. The wave function is expanded in a variationally optimized time-dependent many-body basis generated by a set of effective creation operators that are related to the original particle creation operators by a time-dependent unitary transform. We use the time-dependent variational principle for the coefficients of this transform and the expansion coefficients of the wave function expressed in the time-dependent many-body basis as variational parameters to derive equations of motion. The convergence of MCTDH-X is shown by comparing its results to the exact diagonalization of one-, two-, and three-dimensional lattices filled with bosons with contact interactions. We use MCTDH-X to study the buildup of correlations in the long-time splitting dynamics of a Bose-Einstein condensate loaded into a large two-dimensional lattice subject to a barrier that is ramped up in the center. We find that the system is split into two parts with emergent time-dependent correlations that depend on the ramping time—for most barrier-raising times the system becomes twofold fragmented, but for some of the very fast ramps, the system shows revivals of coherence.

The present work is devoted to the theoretical study of the nonreciprocal optical properties in hybrid (isotropic and anisotropic) periodic multilayers for photon energy values chosen close to the electronic energy gaps of semiconductors (excitons). The optical properties of these resonant nonmagnetic photonic crystals, where linear and quadratic spatial dispersion effects are both present, will be studied in the framework of exciton-polariton self-consistent solutions of the Maxwell and Schrödinger equations in the effective-mass approximation. The main interesting optical properties, namely, giant transmission, absorption suppression, and optical unidirectional propagation, will be computed by implementing a two-layer “minimum model.”

We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.