We consider the dissipative dynamics of a qubit coupled to a nonlinear oscillator (NO) embedded in an Ohmic environment. By treating the nonlinearity up to first order and applying Van Vleck perturbation theory up to second order in the qubit-NO coupling, we derive an analytical expression for the eigenstates and eigenfunctions of the coupled qubit-NO system beyond the rotating wave approximation. In the regime of weak coupling to the thermal bath, analytical expressions for the time evolution of the qubit’s populations are derived: they describe a multiplicity of damped oscillations superposed to a complex relaxation part toward thermal equilibrium. The long-time dynamics is characterized by a single relaxation rate, which is maximal when the qubit is tuned to one of the resonances with the nonlinear oscillator.

In this paper we investigate the von Neumann entropy in the ground state of one-dimensional anyonic systems with the repulsive interaction. Based on the Bethe-ansatz solutions, the entanglement properties for the arbitrary statistical parameter $\left(0\le \kappa \le 1\right)$ are obtained from the one-particle reduced density matrix in the full interacting regime. It is shown that the entanglement entropy increases with the increase in the interaction strength and statistical parameter. The statistic parameter affects the entanglement properties from two aspects: renormalizing the effective interaction strength and introducing an additional anyonic phase. We also evaluate the entanglement entropy of hard-core anyons for different statistical parameters in order to clarify the effect solely induced by the anyonic phase.

Equilibrium mean charge states have been measured for 3–7 MeV lithium, boron, and carbon ions passing through thin carbon foils. The data are compared to the predictions of several semiempirical models of charge equilibrium in the $\le 1\text{MeV}/\text{u}$ regime. The current work underscores the general problem of extrapolating models developed for high-$Z$ projectiles to ions of low $Z$. A compilation of experimental data for low-$Z$ ions in the low-energy regime has been used to reparametrize a few of the charge equilibrium models. Experimental techniques, comments and suggestions on the nature of the equilibrium charge states of low-$Z$ ions are presented.

The dipole-dipole interaction among ultracold Rydberg atoms is simulated. We examine a general interaction scheme in which two atoms excited to the $x$ and $x^{\prime }$ states are converted to $y$ and $y^{\prime }$ states via a Förster resonance. The atoms are arranged in two spatially separated groups, each consisting of only one species of atom. We monitor the state mixing by recording the fraction of atoms excited to the $y^{\prime }$ state as the distance between the two groups is varied. With zero detuning a many-body effect that relies on always resonant interactions causes the state mixing to have a finite range. When the detuning is greater than zero, another many-body effect causes a peak in the state mixing when the two groups of atoms are some distance away from each other. To obtain these results it is necessary to include multiple atoms and solve the full many-body wave function. These simulation results are supported by recent experimental evidence. These many-body effects, combined with appropriate spatial arrangement of the atoms, could be useful in controlling the energy exchange among the atoms.

Laser-assisted photoemission by a chirped subfemtosecond extreme ultraviolet (xuv) pulse is considered within an exactly solvable quantum-mechanical model. Special emphasis is given to the energy dependence of photoexcitation cross section. The streaked spectra are analyzed within the classical picture of initial time-momentum distribution $r_{\text{ini}}\left(p,t\right)$ of photoelectrons mapped to the final energy scale. The actual time-momentum distribution in the absence of the probe laser field is shown to be a poor choice for $r_{\text{ini}}$, and a more adequate ansatz is suggested. The semiclassical theory offers a simple practically useful approximation for streaked spectra. Its limitations for sufficiently long chirped xuv pulses are established.

A theoretical study of the intense-field single ionization of molecular hydrogen or deuterium oriented either parallel or perpendicular to a linear-polarized laser pulse (400 nm) is performed for different internuclear separations and pulse lengths in an intensity range of $\left(2–13\right)\times {10}^{13}\text{W}{\text{cm}}^{-2}$. The investigation is based on a nonperturbative treatment that solves the full time-dependent Schrödinger equation of both correlated electrons within the fixed-nuclei and the dipole approximations. The results for various internuclear separations are used to obtain the ionization yields of molecular hydrogen and deuterium in their ground vibrational states. An atomic model is used to identify the influence of the intrinsic diatomic two-center character of the problem.

We theoretically investigate high-order harmonic generation from the diatomic molecules in an orthogonally polarized two-color few-cycle optical field by controlling the incident angle of the recolliding electron. We show that the combination of molecules and two-color polarization gating allows us to significantly suppress undesirable satellite pulses owing to the orientation dependence of high-order harmonic generation in molecules, giving rise to the generation of single attosecond pulses.

We address the properties of nonlinear multipole modes supported by an interface between two distinct optical lattices imprinted in two-dimensional nonlinear quadratic media. Such multipole-mode solitons feature out of phase between neighboring lobes, which may be located in two different sides of the lattices. We analyze the impact of guiding parameters of lattices on the existence and stability of multipole-mode interface solitons in different phase mismatching conditions. Remarkably, our results show that multipole-mode interface solitons have the highly asymmetric shape and they are stable in the broad range of system parameters.

We study the ability of beams with complex phase dislocations to guide and steer signal beams in self-focusing nonlinear media. In particular, we report on the experimental demonstration of signal deflection by beams carrying step-screw phase dislocation in the form of a fractional vortex dipole. We show how the beam deflection can be ruled by the geometry and orientation of the dipole.

A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This opens up some interesting classical Monte Carlo algorithms for approximating quantum circuits.

We report our experimental observations of spatial shift and splitting of four-wave mixing (FWM) signal beams induced by additional dressing laser beams. These effects are caused by the enhanced cross-Kerr nonlinearity due to atomic coherence in a two-level atomic system. The spatial separation and number of the split FWM beams can both be controlled by the intensity of the dressing beam, the Kerr nonlinearity, and atomic density. Theoretical results agree quite well with the observations. Studies of such controlled beam splitting can be very useful in understanding spatial soliton formation and interactions, and in applications for spatial signal processing.

The Auger transitions to different repulsive doubly charged molecular ion states are separated by measuring the angular resolved photoelectrons and Auger electrons in coincidence in the molecular fixed frame. The separation is achieved by comparing the experimental Auger-electron angular distributions at different kinetic-energy release values with theoretical curves calculated for different final dicationic states.

We find the existence of sub-Planck scale structures in the Pöschl-Teller potential, which is an exactly solvable potential with both symmetric and asymmetric features. We analyze these structures in both cases by looking at the Wigner distribution of the state evolved from an initial coherent state up to various fractional revival times. We also investigate the sensitivity to perturbations of the Pöschl-Teller potential and we verify that, similar to the harmonic oscillator, the presence of sub-Planck structure in phase space is responsible for a high sensitivity to phase-space displacements.

We consider continuous-time quantum walks on a finite graph to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The $S$ matrix for such graphs is defined. Its unitarity is proved as well as some other of its properties such as its transformation under time reversal. A spectral decomposition of the identity for the Hamiltonian of the graph is derived using its eigenvectors. We derive formulas for the $S$ matrix of a graph under certain operation such as cutting a tail, attaching a tail or connecting two tails to form an edge.

With the help of light-emitting diodes at the center wavelength of 470 nm, we demonstrate that light-induced atom desorption (LIAD) can be used for flexibly controlling the loading of magneto-optical traps (MOT) of cesium atoms. Under an ultralow background pressure in a quartz cell without any wall coating, we show that low intensity blue light can be used to control the loading rates (from 200 to 4000 atoms/s) and the number of cesium atoms (on the order of ${10}^4$ in our experiment) in a MOT without the use of dispensers or any secondary atom source. A theoretical model based on an atom loading rate equation is built which can simulate the magneto-optical trap loading process with LIAD. The theoretical results are in agreement with experimental data. Some important parameters of the vacuum system are determined accordingly. The decay time of the vacuum pressure is about 70 ms, which is much shorter than the usual vacuum system for experiments on atomic ensembles. It is very difficult to measure such short times by the traditional fluorescence detection of cold atoms due to the slow loading process. The change of desorption rate (on the order of ${10}^{13}\text{atoms}/\text{s}$) for the different desorption intensities is also determined based on the background pressure caused by noncesium atoms in the cell. According to the experimental data and theoretical calculations, we obtain a partial pressure of about $1.4\times {10}^{-10}\text{Torr}$ for the untrapped cesium atoms and about $6.4\times {10}^{-10}\text{Torr}$ for the noncesium atoms at the moment the desorption light is turned off. The system is almost an ideal vacuum system for transferring atoms into another region for further experiments.

We consider a Bose-Einstein condensate, which is characterized by long-range and anisotropic dipole-dipole interactions and vanishing $s$-wave scattering length, in a double-well potential. The properties of this system are investigated as functions of the height of the barrier that splits the harmonic trap into two halves, the number of particles (or dipole-dipole strength) and the aspect ratio $\lambda$, which is defined as the ratio between the axial and longitudinal trapping frequencies ${\omega }_z$ and ${\omega }_{\rho }$. The phase diagram is determined by analyzing the stationary mean-field solutions. Three distinct regions are found: a region where the energetically lowest lying stationary solution is symmetric, a region where the energetically lowest lying stationary solution is located asymmetrically in one of the wells, and a region where the system is mechanically unstable. For sufficiently large aspect ratio $\lambda$ and sufficiently high barrier height, the system consists of two connected quasi-two-dimensional sheets with density profiles whose maxima are located either at $\rho =0$ or away from $\rho =0$. The stability of the stationary solutions is investigated by analyzing the Bogoliubov–de Gennes excitation spectrum and the dynamical response to small perturbations. These studies reveal unique oscillation frequencies and distinct collapse mechanisms. The results derived within the mean-field framework are complemented by an analysis based on a two-mode model.

We theoretically analyze Fermi-Bose mixtures consisting of light fermions and heavy bosons that are loaded into optical lattices (ignoring the trapping potential). To describe such mixtures, we consider the Fermi-Bose version of the Falicov-Kimball model on a periodic lattice. This model can be exactly mapped onto the spinless Fermi-Fermi Falicov-Kimball model at zero temperature for all parameter space as long as the mixture is thermodynamically stable. We employ dynamical mean-field theory to investigate the evolution of the Fermi-Bose Falicov-Kimball model at higher temperatures. We calculate spectral moment sum rules for the retarded Green’s function and self-energy, and use them to benchmark the accuracy of our numerical calculations, as well as to reduce the computational cost by exactly including the tails of infinite summations or products. We show how the occupancy of the bosons, single-particle many-body density of states for the fermions, momentum distribution, and the average kinetic energy evolve with temperature. We end by briefly discussing how to experimentally realize the Fermi-Bose Falicov-Kimball model in ultracold atomic systems.

We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation, when constrained to a finite conserved angular momentum. In an isotropic trapping potential, the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodology to identify the condensate and the Goldstone mode associated with the broken rotational symmetry in the classical-field model. We also examine the variation in vortex trajectories and thermodynamic parameters of the field as the energy of the microcanonical field simulation is varied.