A general method of the Foldy-Wouthuysen transformation is developed. This method is applicable to relativistic particles with any spin in arbitrarily strong external fields. It can be used when the de Broglie wavelength is much smaller than the characteristic distance. Contrary to previously developed relativistic methods, the present method satisfies the condition of the exact Foldy-Wouthuysen transformation and is well substantiated. The derived relativistic Foldy-Wouthuysen Hamiltonian is expanded in powers of the Planck constant. In this expansion, terms proportional to the zero and first powers are determined exactly in accordance with the above condition, and terms proportional to higher powers are not specified. The obtained result agrees with the corresponding formula for the Foldy-Wouthuysen Hamiltonian previously deduced by an iterative relativistic method and proves the validity of results obtained with this formula.

Recently it has been demonstrated that the finite difference Hartree-Fock method can be used to deliver highly accurate values of electric multipole moments together with polarizabilities ${\alpha }_{zz},A_{z,zz}$, and hyperpolarizabilities ${\beta }_{zzz}$, ${\gamma }_{zzz},B_{zz,zz}$, for the ground states of various atomic and diatomic systems. Since these results can be regarded as de facto Hartree-Fock limit values their quality is of the utmost importance. This paper reexamines the use of the finite field method to calculate these electric properties, discusses its accuracy, and presents an updated list of the properties for the following atoms and diatomic molecules: ${\mathrm{H}}^{-}$, He, Li, ${\mathrm{Li}}^{+},{\mathrm{Li}}^{2+},{\mathrm{Li}}^{-},{\mathrm{Be}}^{2+}$, Be, ${\mathrm{B}}^{+},{\mathrm{C}}^{2+}$, Ne, ${\mathrm{Mg}}^{2+}$, Mg, ${\mathrm{Al}}^{+},{\mathrm{Si}}^{2+}$, Ar, ${\mathrm{K}}^{+},{\mathrm{Ca}}^{2+},{\mathrm{Rb}}^{+},{\mathrm{Sr}}^{2+},{\mathrm{Zr}}^{4+},{\mathrm{He}}_2$, ${\mathrm{Be}}_2,{\mathrm{N}}_2,{\mathrm{F}}_2,{\mathrm{O}}_2$, HeNe, ${\mathrm{LiH}}^{2+}$, LiCl, LiBr, BH, CO, FH, NaCl, and KF. The potential energy curves and the dependence of the electric properties on the internuclear distance is also studied for ${\mathrm{He}}_2,{\mathrm{LiH}}^{+},{\mathrm{Be}}_2$, and HeNe systems.

We present results of ab initio numerical calculations for low-order-harmonic generation as well as calculations of the higher-order terms in the respective perturbative power-series expansions of the susceptibilities for third- and fifth-order-harmonic generation. We find that the transition from perturbative to nonperturbative interaction in these low-order nonlinear processes occurs at about ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. Our findings confirm previous results that any deviation from the predictions of lowest-order perturbation theory indicates that the perturbative series expansion is not applicable and, if required, needs to be replaced by a nonperturbative treatment of the interaction between the atom and the field. In particular, the results also show that the observation of low-order-harmonic yields cannot be considered as a test of higher-order Kerr effects.

We present a detailed theoretical study on the photoionization from the bound excited ${}^{1}P$ state of He to continua dominated by multiple doubly excited resonance series embedded in multiple single-ionization channels between the $N=2$ and $N=3$ thresholds. In addition to identifying the individual resonance series, our investigation has also demonstrated unambiguously the level crossing between overlapping resonance series and how the closely spaced pairs of resonances migrate as energy increases.

We study the interplay between the dynamics of a Bose-Einstein condensate in a double-well potential and that of an optical cavity mode. The cavity field is superimposed to the double-well potential and affects the atomic tunneling processes. The cavity field is driven by a laser red detuned from the bare cavity resonance; the dynamically changing spatial distribution of the atoms can shift the cavity in and out of resonance. At resonance the photon number is hugely enhanced and the atomic tunneling becomes amplified. The Josephson-junction equations are revisited and the phase diagram is calculated. We find solutions with finite imbalance and at the same time find a lack of self-trapping solutions due to the emergence of a new separatrix resulting from enhanced tunneling.

The Josephson sum rule relates the superfluid density to the condensate order parameter via the infrared residue of the single-particle Green's function. We establish an effective Josephson relation for disordered condensates valid upon ensemble averaging. This relation has the merit of showing explicitly how superfluidity links to the coherent density, i.e., the density of condensed particles with zero momentum. Detailed agreement is reached with perturbation theory for weak disorder.

We study the condensed phase of a Bose-Fermi mixture with a tunable pairing interaction between bosons and fermions with many-body diagrammatic methods and fixed-node diffusion quantum Monte Carlo simulations. A universal behavior of the condensate fraction and bosonic momentum distribution with respect to the boson concentration is found to hold in an extended range of boson-fermion couplings and concentrations. For vanishing boson density, we prove that the bosonic condensate fraction reduces to the quasiparticle weight Z of the Fermi polaron studied in the context of polarized Fermi gases, unifying in this way two apparently unrelated quantities.

Differential phase contrast (DPC) in a scanning transmission electron microscope is a widely employed technique for probing electromagnetic fields on the nanoscale. We show that the DPC signal corresponds to the averaged lateral probability current of the scattered electron probe. Based on this result we discuss the interpretation of DPC in terms of the projected electric and magnetic fields and the influence of experimental parameters thereon. We further show that DPC can be interpreted as a quantum weak measurement and that the reciprocal broad beam illumination technique is given by an astigmatic transport of intensity reconstruction.

The observation of the nonlocal properties of multipartite entangled states is of great importance for quantum information protocols. Such properties, however, are fragile and may not be observed in the presence of decoherence exhibited by practical physical systems. In this work we investigate the robustness of the nonlocality of symmetric states experiencing phase and amplitude damping, using suitable Bell inequalities based on an extended version of Hardy's paradox. We derive thresholds for observing nonlocality in terms of experimental noise parameters and demonstrate the importance of the choice of the measurement bases for optimizing the robustness. For $W$ states, in the phase damping case, we show that this choice can lead to a trade-off between obtaining a high violation of the nonlocal test and optimal robustness thresholds; we also show that in this setting the nonlocality of $W$ states is particularly robust for a large number of qubits. Furthermore, we apply our techniques to the discrimination of symmetric states belonging to different entanglement classes, thus illustrating their usefulness for a wide range of practical quantum information applications.

Quantum-speed-limit (QSL) time captures the intrinsic minimal time interval for a quantum system evolving from an initial state to a target state. In single qubit open systems, it was found that the memory (non-Markovian) effect of environment plays an essential role in shortening QSL time or, say, increasing the capacity for potential speedup. In this paper, we investigate the QSL time for multiqubit open systems. We find that for a certain class of states the memory effect still acts as the indispensable requirement for cutting the QSL time down, while for another class of states this takes place even when the environment is of no memory. In particular, when the initial state is in product state $|111\cdots 1\rangle$, there exists a sudden transition from no capacity for potential speedup to potential speedup in a memoryless environment. In addition, we also display evidence for the subtle connection between QSL time and entanglement that weak entanglement may shorten QSL time even more.

Based on our previous work of the classical over-barrier ionization model, the single- and double-ionization cross sections of positron-helium impact are calculated. The calculation results are consistent with the experimental data. The screened Coulomb potential is used to obtain the trajectory of the positron in single-ionization process. The positron is seemed to be scattered by the rest $\mathrm{H}{\mathrm{e}}^{+}$ core in double ionization. The strong Coulomb defection effect makes the double ionization to be significantly suppressed at low velocities.

A parameter-free spherical complex optical potential approach in the fixed-nuclei approximation is applied here to calculate elastic differential, integral, and momentum-transfer cross sections as well as total (elastic plus inelastic) cross sections for the scattering of electrons from $\mathrm{N}{\mathrm{H}}_3$ and $\mathrm{P}{\mathrm{H}}_3$ molecules (i.e., nonmetallic hydrides) in the electron energy range of 0.1–100 eV. The projectile-target interaction is represented by a sum of a real and an imaginary potential. Present calculated results are compared with the available calculations and the experimental measurements. The quantitative features of the scattering parameters (such as Ramsauer-Townsend minimum and shape resonance structure), as observed in experiments, are well reproduced in the present study.

We consider the interaction of Rydberg atoms with strong infrared laser pulses using an approach based on the Magnus expansion of the time evolution operator. First-order corrections beyond the electric dipole approximation are also included in the theory. We illustrate the dynamics of the interaction at the parameters of the experiment [Eichmann et al., Phys. Rev. Lett. 110, 203002 (2013)]. It emerges that the depletion of Rydberg atoms in this regime comes predominantly from the nondipole effects.

In this work, we develop a hybrid-order Poincaré sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincaré sphere and high-order Poincaré sphere to a more general form. Polarization evolution in inhomogeneous anisotropic media with special geometry can be conveniently described by state evolution along the longitude line on the hybrid-order Poincaré sphere. Similar to that in previously proposed Poincaré spheres, the Berry curvature can be regarded as an effective magnetic field with monopole centered at the origin of sphere and the Berry connection can be interpreted as the vector potential. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincaré sphere are demonstrated to be proportional to the variation of total angular momentum. Our scheme provides a convenient method to describe the spin-orbit interaction in inhomogeneous anisotropic media.

We consider adiabatic interaction of five-level atomic systems and their media with four short laser pulses under the condition of all two-photon detunings being zero. We derive analytical expressions for eigenvalues of the system's Hamiltonian and determine conditions of adiabaticity for both the atom and the medium. We analyze, in detail, the system's behavior when the eigenvalue with nonvanishing energy is realized. As distinct from the usual dark state of a five-level system (corresponding to zero eigenvalue), which is a superposition of three states, in our case the superposition of four states does work. We demonstrate that this seemingly unfavorable case nevertheless completely imitates a three-level system not only for a single atom but also in the medium, since the propagation equations are also split into those for three- and two-level media separately. We show that, under certain conditions, all the coherent effects observed in three-level media, such as population transfer, light slowing, light storage, and so on, may efficiently be realized in five-level media. This has an important advantage that the light storage can be performed twice in the same medium; i.e., the second pulse can be stored without retrieving the first one, and then the two pulses can be retrieved in any desired sequence.

We propose a scheme to realize stable propagation of linear and nonlinear surface polaritons (SPs) by placing a $N-\text{type}$ four-level quantum emitters at the interface between a dielectric and a negative-index metamaterial (NIMM). We show that in linear propagation regime SPs can acquire an active Raman gain (ARG) from a pump field and a gain doublet appears in the gain spectrum of a signal field induced by the quantum interference effect from a control field. The ARG can be used not only to completely compensate the Ohmic loss in the NIMM but also to acquire a superluminal group velocity for the SPs. We also show that in the nonlinear propagation regime a huge enhancement of the Kerr nonlinearity of the SPs can be obtained. As a result, ARG-assisted $(1 + 1)-$ and $(2 + 1)-$ dimensional superluminal surface polaritonic solitons with extremely low generation power may be produced based on the strong confinement of the electric field at the dielectric-NIMM interface.

Interlaced spin grating is a scheme for the preparation of spectrospatial periodic absorption gratings in an inhomogeneously broadened absorption profile. It relies on the optical pumping of atoms in a nearby long-lived ground state sublevel. The scheme takes advantage of the sublevel proximity to build large contrast gratings with unlimited bandwidth and preserved average optical depth. It is particularly suited to Tm-doped crystals in the context of classical and quantum signal processing. In this paper, we study the optical pumping dynamics at play in an interlaced spin grating and describe the corresponding absorption profile shape in an optically thick atomic ensemble. We show that, in Tm:YAG, the diffraction efficiency of such a grating can reach $18.3\%$ in the small-angle and $11.6\%$ in the large-angle configuration when the excitation is made of simple pulse pairs, considerably outperforming conventional gratings.

Information about the interaction of a many-electron quantum system with its environment, we show, is encoded within the one-electron density matrix (1-RDM). While the 1-RDM from an ensemble many-electron quantum system must obey the Pauli exclusion principle, the 1-RDM must obey additional constraints known as generalized Pauli conditions when it corresponds to a closed system describable by a single wave function. By examining the 1-RDM's violation of these generalized Pauli conditions, we obtain a sufficient condition at the level of a single electron for a many-electron quantum system's openness. In an application to exciton dynamics in photosynthetic light harvesting we show that the interaction of the system with the environment (quantum noise) relaxes significant constraints imposed on the exciton dynamics by the generalized Pauli conditions. This relaxation provides a geometric (kinematic) interpretation for the role of noise in enhancing exciton transport in quantum systems.

The generation of (Bell-)nonlocal correlations, i.e., correlations leading to the violation of a Bell-like inequality, requires the usage of a nonlocal resource, such as an entangled state. When given a correlation (a collection of conditional probability distributions) from an experiment or from a theory, it is desirable to determine the extent to which the participating parties would need to collaborate nonlocally for its (re)production. Here, we propose to achieve this via the minimal group size (MGS) of the resource, i.e., the smallest number of parties that need to share a given type of nonlocal resource for the above-mentioned purpose. In addition, we provide a general recipe—based on the lifting of Bell-like inequalities—to construct MGS witnesses for nonsignaling resources starting from any given ones. En route to illustrating the applicability of this recipe, we also show that when restricted to the space of full-correlation functions, nonsignaling resources are as powerful as unconstrained signaling resources. Explicit examples of correlations where their MGS can be determined using this recipe and other numerical techniques are provided.

An all-optical scheme for simulating non-Markovian evolution of a quantum system is proposed. It uses only linear optics elements and by controlling the system parameters allows one to control the presence or absence of information backflow from the environment. A sufficient and necessary condition for the non-Markovianity of our channel based on Gaussian inputs is proved. Various criteria for detecting non-Markovianity are also investigated by checking the dynamical evolution of the channel.