Analytic formulas describing high-order-harmonic generation (HHG) by atoms in an intense laser field with small ellipticity are obtained quantum mechanically in the tunneling limit. The results show that factorization of the HHG yield in terms of an electron wave packet and the photorecombination cross section (PRCS) is valid only for $s$ states of a bound atomic electron, whereas the HHG yield for $p$ states involves two different atomic parameters. For the latter case, elliptic HHG spectroscopy enables one to retrieve both the energy and angular dependence of the PRCS of the target atom, as we illustrate for the case of HHG by Xe in a midinfrared laser field.

Motivated by a recent experiment in a tunable graphene analog [Tarruell et al., Nature 483, 302 (2012)], we consider a generalization of the Landau-Zener problem to the case of a quadratic crossing between two bands in the vicinity of the merging transition of Dirac cones. The latter is described by the so-called universal Hamiltonian. In this framework, the interband tunneling problem depends on two dimensionless parameters: one measures the proximity to the merging transition and the other the adiabaticity of the motion. Under the influence of a constant force, the probability for a particle to tunnel from the lower to the upper band is computed numerically in the whole range of these two parameters and analytically in different limits using (i) the Stückelberg theory for two successive linear band crossings, (ii) diabatic perturbation theory, (iii) adiabatic perturbation theory, and (iv) a modified Stückelberg formula. We obtain a complete phase diagram and explain the presence of probability oscillations in terms of interferences between two poles in the complex time plane. We also compare our results to the above-mentioned experiment.

We establish a complete set of hydrodynamic equations for a spin-1 Bose-Einstein condensate, which are equivalent to the multicomponent Gross-Pitaevskii equations and expressed in terms of only observable physical quantities: the spin and the nematic (or quadrupolar) tensor in addition to the density of particles and the mass current that appear in the hydrodynamic description of a scalar condensate. The obtained hydrodynamic equations involve a generalized Mermin-Ho relation that is valid regardless of the spatiotemporal dependence of the spin polarization. Low-lying collective modes for phonons and magnons are reproduced by linearizing the hydrodynamic equations. We also apply the single-mode approximation to the hydrodynamic equations and find a complete set of analytic solutions.

We study the affinities between the shape of the bright soliton of the one-dimensional nonlinear Schroedinger equation and the shape of the disorder-induced localization with a Gaussian random potential. For the most localized state, we derive expressions for the nonlinear eigenvalue and for the localization length. We investigate the stability and superlocalizations.

Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from this solution to the Zitterbewegung behavior in a Dirac-like system, where we show that it is crucial to include the first-order term in our solution to correctly describe a Dirac packet.

We introduce a monogamy inequality for quantum correlations, which implies that the sum of pairwise quantum correlations is upper limited by the amount of multipartite quantum correlations as measured by the global quantum discord. This monogamy bound holds either for pure or mixed quantum states provided that bipartite quantum discord does not increase under discard of subsystems. We illustrate the monogamy behavior for multipartite pure states with Schmidt decomposition as well as for $W$-GHZ mixed states. As a by-product, we apply the monogamy bound to investigate residual multipartite correlations.

Generating a unitary transformation in the shortest possible time is of practical importance to quantum information processing because it helps to reduce decoherence effects and improve robustness to additive control field noise. Many analytical and numerical studies have identified the minimum time necessary to implement a variety of quantum gates on coupled-spin qubit systems. This work focuses on exploring the Pareto front that quantifies the tradeoff between the competitive objectives of maximizing the gate fidelity $\mathcal{F}$ and minimizing the control time $T$. In order to identify the critical time $T^{*}$ below which the target transformation is not reachable, as well as to determine the associated Pareto front, we introduce a numerical method of Pareto front tracking (PFT). We consider closed two- and multiqubit systems with constant interqubit coupling strengths and each individual qubit controlled by a separate time-dependent external field. Our analysis demonstrates that unit fidelity (to a desired numerical accuracy) can be achieved at any $T\ge T^{*}$ in most cases. However, the optimization search effort rises superexponentially as $T$ decreases and approaches $T^{*}$. Furthermore, a small decrease in control time incurs a significant penalty in fidelity for $T<T^{*}$, indicating that it is generally undesirable to operate below the critical time. We investigate the dependence of the critical time $T^{*}$ on the coupling strength between qubits and the target gate transformation. Practical consequences of these findings for laboratory implementation of quantum gates are discussed.

We derive a stochastic process that describes the kinetics of a one-dimensional Bose gas in a regime where three-body collisions are important. In this situation the system becomes nonintegrable, offering the possibility of investigating dissipative phenomena more simply than in higher-dimensional gases. Unlike the quantum Boltzmann equation describing the average momentum distribution, the stochastic approach allows a description of higher-order correlation functions in a canonical ensemble. As will be shown, this ensemble differs drastically from the grand-canonical one. We illustrate the use of this method by determining the time evolution of the momentum-mode particle-number distribution and the static structure factor during the evaporative cooling process.

The constraints imposed by the initial system-environment correlation can lead to nonpositive dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map. Any initial system-environment correlations make the assignment map nonpositive, while the positivity of the dynamical map depends on the interplay between the assignment map and the system-environment coupling. We show how this interplay can reveal or hide the nonpositivity of the assignment map. We discuss the role of this interplay in Markovian models.

We study the geometric phase acquired by an inertial atom whose trajectories are parallel to a reflecting boundary due its coupling to vacuum fluctuations of electromagnetic fields, by treating the atom as an open quantum system in a bath of the fluctuating vacuum fields, and show that the phase is position dependent as a result of the presence of the boundary which modifies the field quantum fluctuations. Our result therefore suggests a possible way of detecting vacuum fluctuations in experiments involving geometric phase.

Inner-shell resonant absorption (IRA) effects were investigated on evolution dynamics of charge state distribution (CSD) in the interaction of ultraintense x-ray pulses with a neon atom. IRA is the physical origin of the large discrepancies found between theory and experiment at a photon energy of 1050 eV [L. Young et al., Nature (London) 466, 56 (2010)], where the rates of $K$-shell resonant absorption $1s\to 4p$ of Ne${}^{6+}$ and $1s\to 3p$ of Ne${}^{7+}$ are larger than the direct single-photon ionization rates by more than one order of magnitude, and hence IRA becomes the dominant absorption mechanism. Only when the IRA effects are properly taken into account can we correctly explain the observed CSD.

Gyroscopes find wide applications in everyday life from navigation and inertial sensing to rotation sensors in hand-held devices and automobiles. Current devices, based on either atomic or solid-state systems, impose a choice between long-time stability and high sensitivity in a miniaturized system. Here, we introduce a quantum sensor that overcomes these limitations by providing a sensitive and stable three-axis gyroscope in the solid state. We achieve high sensitivity by exploiting the long coherence time of the ${}^{14}$N nuclear spin associated with the nitrogen-vacancy center in diamond, combined with the efficient polarization and measurement of its electronic spin. Although the gyroscope is based on a simple Ramsey interferometry scheme, we use coherent control of the quantum sensor to improve its coherence time and robustness against long-time drifts. Such a sensor can achieve a sensitivity of $\eta \sim 0.5\left(\mathrm{mdeg}{\mathrm{s}}^{-1}\right)/\sqrt{\mathrm{Hz}{\mathrm{mm}}^3}$ while offering enhanced stability in a small footprint. In addition, we exploit the four axes of delocalization of the nitrogen-vacancy center to measure not only the rate of rotation, but also its direction, thus obtaining a compact three-axis gyroscope.

The absolute differential oscillator strengths (DOSs) for the photoabsorption of the Ne, Ar, and Xe atoms encapsulated in the C${}_{60}$ have been evaluated using the time-dependent density-functional theory, which solves the quantum Liouvillian equation with the Lanczos chain method. The calculations are performed in the energy regions both inside and outside the C${}_{60}$ giant resonance. The photoabsorption spectra of the atoms encaged in the C${}_{60}$ demonstrate strong oscillations inside the energy range of the C${}_{60}$ giant resonance. This type of oscillation cannot be explained by the confinement resonance, but is due to the energy transfer from the C${}_{60}$ valence electrons to the photoelectron through the intershell coupling.

We study the static properties of disk-shaped binary dipolar Bose-Einstein condensates of ${}^{168}$Er-${}^{164}$Dy and ${}^{52}$Cr-${}^{164}$Dy mixtures under the action of interspecies and intraspecies contact and dipolar interactions and demonstrate the effect of dipolar interaction using the mean-field approach. Throughout this study we use realistic values of interspecis and intraspecies dipolar interactions and the intraspecies scattering lengths and consider the interspecies scattering length as a parameter. The stability of the binary mixture is illustrated through phase plots involving a number of atoms of the species. The binary system always becomes unstable as the number of atoms increases beyond a certain limit. As the interspecies scattering length increases corresponding to more repulsion, an overlapping mixed state of the two species changes to a separated demixed configuration. During the transition from a mixed to a demixed configuration as the interspecies scattering length is increased for parameters near the stability line, the binary condensate shows special transient structures in density in the form of red-blood-cell-like biconcave and Saturn-ring-like shapes, which are direct manifestations of the dipolar interaction.

We envisage the possibility of producing and tuning electronic orbital currents in atoms by weak, spatially inhomogeneous laser pulses with optical vortices. As already known, when interacting with such pulses an electronic system attains a definite amount of angular momentum. Here we explore this effect in the case when the system size is atomically small, i.e., much smaller than the scale of the inhomogeneity of the light pulses. We show that, nonetheless, angular momentum is transferred to the atomic system. The amount of the attained angular momentum depends on the position of the atom inside the field. Our numerical calculations and analytical analysis show that, indeed, light-induced orbital magnetism emerges in a dilute atomic gas when it is exposed to resonant or broadband optical vortices. This effect can be assessed, for instance, in a Faraday rotation experiment.

Electrons carrying orbital angular momentum (OAM) have recently been discovered theoretically and obtained experimentally, which opens up possibilities for using them in high-energy physics. We consider such a twisted electron moving in the external field of a plane electromagnetic wave and study how this field influences the electron's OAM. Being motivated by the development of high-power lasers, we focus our attention on a classically strong-field regime for which $-e^2\overline{A^2}/\left(m_e^2{c}^4\right)\gtrsim 1$. It is shown that, along with the well-known “plane-wave” Volkov solution, the Dirac equation also has the “non-plane-wave” solutions, which possess OAM and spin-orbit coupling and generalize the free-electron's Bessel states. Motion of an electron with OAM in a circularly polarized laser wave reveals a twofold character: the wave-packet center moves along a classical helical trajectory with some quantum transverse broadening (due to OAM) existing even for a free electron. Using the twisted states, we calculate the electron's total angular momentum and predict its shift in the strong-field regime, which is analogous to the well-known shifts of the electron's momentum and mass (and to a less-known shift of its spin) in intense fields. Since the electron's effective angular momentum is conserved in a plane wave, as well as in some more general field configurations, we discuss several possibilities for accelerating nonrelativistic twisted electrons by using focused and combined electromagnetic fields.

Inspired by the recent works of Foster et al. [Phys. Rev. Lett. 102, 120401 (2009)] and Brunner et al. [Phys. Rev. Lett. 102, 160403 (2009)], we present a nonlocality distillation protocol for two three-level (qutrit) systems in the framework of generalized nonsignaling theories. Our protocol is based on a three-setting Bell inequality. It works efficiently for a specific class of three-input–three-output nonlocal boxes. In the asymptotic limit, all these nonlocal boxes can be distilled to the maximally nonlocal box defined by the inequality and nonsignaling constraints. Then we introduce a contracting protocol that reduces these boxes to the so-called “correlated nonlocal boxes.” As a result, our three-input–three-output nonlocal boxes also make communication complexity trivial and appear very unlikely to exist in nature.

The congruent transformation of the electronic Hamiltonian is developed to address the electron correlation problem in many-electron systems. The central strategy presented in this method is to perform transformation on the electronic Hamiltonian for the approximate removal of the Coulomb singularity. The principle difference between the present method and the transcorrelated method of Handy and Boys [Proc. R. Soc. London, Ser. A 310, 43 (1969)] is that the congruent transformation preserves the Hermitian property of the Hamiltonian. The congruent transformation is carried out using explicitly correlated functions and the optimum correlated transform Hamiltonian is obtained by performing a search over a set of transformation functions. The ansatz of the transformation function is selected to facilitate analytical evaluation of all the resulting integrals. The ground-state energy is obtained variationally by performing a full-configuration-interaction (FCI) calculation on the congruently transformed Hamiltonian. Computed results on well-studied benchmark systems show that for identical basis functions, the energy from the congruently transformed Hamiltonian is significantly lower than that from the conventional FCI calculation. Since the number of configuration state functions in the FCI calculation increases rapidly with the size of the one-particle basis set, the results indicate that the congruently transformed Hamiltonian provides a viable alternative to obtain FCI quality energy using a smaller underlying one-particle basis set.

We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuring the anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contact interaction. Within the realm of the Bogoliubov–de Gennes theory, we consider static properties and low-lying excitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system, the condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed in detail. Making use of the local density approximation, we extend these results in order to study the properties of a dipolar Bose gas in a harmonic trap and in the regime of large particle numbers. After deriving the equations of motion for the general case of a triaxial trap, we analyze the influence of quantum fluctuations on important properties of the gas, such as the equilibrium configuration and the low-lying excitations in the case of a cylinder-symmetric trap. In addition to the monopole and quadrupole oscillation modes, we also discuss the radial quadrupole mode. We find that the latter acquires a quantum correction exclusively due to the dipole-dipole interaction. As a result, we identify the radial quadrupole as a reasonably accessible source for the signature of dipolar many-body effects and stress the enhancing character that dipolar interactions have for quantum fluctuations in the other oscillation modes.

We theoretically investigate the momentum-resolved radio-frequency spectroscopy of a harmonically trapped atomic Fermi gas near a Feshbach resonance in the presence of equal Rashba and Dresselhaus spin-orbit coupling. The system is qualitatively modeled as an ideal gas mixture of atoms and molecules, in which the properties of molecules, such as the wave function, binding energy, and effective mass, are determined from the two-particle solution of two interacting atoms. We calculate separately the radio-frequency response from atoms and molecules at finite temperatures by using the standard Fermi golden rule and take into account the effect of harmonic traps within local density approximation. The total radio-frequency spectroscopy is discussed as functions of temperature and spin-orbit coupling strength. Our results give a qualitative picture of radio-frequency spectroscopy of a resonantly interacting spin-orbit-coupled Fermi gas and can be directly tested in atomic Fermi gases of ${}^{40}$K atoms at Shanxi University and ${}^6$Li atoms at the Massachusetts Institute of Technology.