We present the results of an investigation of elastic electron scattering by ethylene ${\mathrm{C}}_2{\mathrm{H}}_4$ with incident electron energies ranging from 0.5 to 20 eV, using the complex Kohn variational method. These fully ab initio calculations accurately reproduce experimental angular differential cross sections at energies below 3 eV. Low-energy electron scattering by ethylene is sensitive to the inclusion of electronic correlation and target-distortion effects. We therefore report results that describe the dynamic polarization of the target by the incident electron and involve calculations over a range of different geometries, including the effects of nuclear motion in the resonant ${}^2{B}_{2g}$ symmetry with an adiabatic nuclei treatment of the C-C stretch mode. The inclusion of dynamic polarization and the effect of nuclear motion are equally critical in obtaining accurate results. The calculated cross sections are compared with recent experimental measurements.

Experimental and theoretical electron-excitation cross sections are reported for the ${2s}^{2}2p{}^2{P}^o\to {2s2p}^2{}^{4}P$ and $\to {2s2p}^2{}^{2}D$ transitions in ${\mathrm{O}}^{3+}.$ The transition energies are centered at 8.85 and 15.7 eV, respectively. Measurements are made using the energy-loss merged-beams method. The center-of-mass energy range covered is 6.1 (below threshold) to 19.3 eV. Comparison is made with results of new calculations in a 25-state R-matrix theory and with results in a previous eight-state R-matrix calculation. The presence of rich resonance structure is confirmed in both experiment and theory. In most cases there is good agreement in the magnitude of cross section, and energy location of the resonances.

This paper introduces a correlation-polarization potential for vibrational excitation in electron-molecule scattering. This potential generalizes a recently proposed model for elastic scattering [Bouferguene et al., Phys. Rev. A 59, 2712 (1999)]. Our potential contains no adjustable parameters and reflects known qualitative dependencies of correlation and polarization effects on the internuclear separation of the target molecule and on the position coordinate of the scattering electron. We test our potential on vibrationally elastic and inelastic scattering from ${\mathrm{N}}_2$ in an energy range that includes the ${}^2{\Pi }_g$ shape resonance. This resonance gives rise to intricate oscillatory structures in integral and differential cross sections; these structures are very sensitive to the correlation effects this potential is designed to model. Our $e-{\mathrm{N}}_2$ cross sections agree well with experimental and other theoretical cross sections except at energies above the resonance, where experimental differential cross sections show a pronounced dip at scattering angles below about 60°. This dip is not present in the theoretical cross sections.

A time-dependent variational Lagrangian analysis based on the Gross-Pitaevskii energy functional serves to study the dynamics of a metastable macroscopic central hole in a rapidly rotating Bose-Einstein condensate. The resulting oscillation frequencies of the core radius reproduce the trends seen in recent experiments [Engels et al., Phys. Rev. Lett. 90, 170405 (2003)], but the theoretical values are smaller by a factor $\approx 0.6–\mathrm{0.8.}$

A unified description of multitime correlation functions, nonlinear response functions, and quantum measurements is developed using a common generating function which allows a direct comparison of their information content. A general formal expression for photon counting statistics from single quantum objects is derived in terms of Liouville-space correlation functions of the material system by making a single assumption that a spontaneous emission is described by a master equation.

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.

We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally entangled states with fixed marginal mixednesses, and determine an analytical upper bound relating the entanglement of formation to the marginal linear entropies. This result partially generalizes to mixed states the quantification of entanglement with marginal mixednesses holding for pure states. We identify a class of entangled states that, for fixed marginals, are globally more mixed than product states when measured by the linear entropy. Such states cannot be discriminated by the majorization criterion.

We investigate dynamical behavior of fragmentation of a spinor Bose-Einstein condensate in both the semiclassical and quantum regimes. We show that an unfragmented condensate can become fragmented at later times due to the inherent interactions of elastic atomic collisions, when a certain phase relationship exists among the state amplitudes in different components initially. A close relationship between the fragmentation and population dynamics of atomic distributions within different spin components is found for certain initial states with zero magnetization. The type of fragmentation regime is characterized via atom-number fluctuations. We also address complications of our study when the condensate spatial mode function is different for each spin component.

The filamentation of a focused femtosecond pulse in fused silica was systemically investigated both experimentally and numerically. We observed the different filamentation of a laser pulse under different external focusing conditions and input energy experimentally. For instance, a focused femtosecond laser pulse with an energy of 3.3 μJ induced a long electron plasma filament for an effective numerical aperture (NA) of 0.01 of focusing objective, an electron plasma filament with two-foci structure for 0.04 effective NA, and a short filament for effective NA of 0.09. In theory, the numerical results of the extended nonlinear Schrödinger (NLS) equation agreed with experimental results under different focusing conditions and energy. Moreover, under different focusing conditions we found the filamentation is connected with different temporal reshaping behaviors, and the temporal compression of the reshaped laser pulse in propagation is responsible for the two-foci structure of an electron plasma filament.

We report on the superstrong field ionization of complex rare gases (xenon, krypton, and argon) by 800-nm, 10-Hz laser pulses of 25-fs duration with a peak intensity greater than ${10}^{19}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ whose electric field well exceeds the Coulombic binding field in strength. We observed charge states as high as ${\mathrm{Xe}}^{26+},$ ${\mathrm{Kr}}^{19+},$ and ${\mathrm{Ar}}^{16+},$ which correspond to Ni-like Xe, Cl-like Kr and He-like Ar, respectively. We compared integral ionic charge state yields of these atoms with those results from the Ammosov-Delone-Krainov model. We found that ionization at a given intensity depends on the atomic species in the fully relativistic field for the first time to our knowledge.

We propose an implementation of the parametric amplification of an arbitrary radiation-field state previously prepared in a high-Q cavity. This nonlinear process is accomplished through the dispersive interactions of a single three-level atom (fundamental |g〉, intermediate |i〉, and excited |e〉 levels) simultaneously with (i) a classical driving field and (ii) a previously prepared cavity mode whose state we wish to squeeze. We show that, in the adiabatic approximantion, the preparation of the initial atomic state in the intermediate level |i〉 becomes crucial for obtaining the degenerated parametric amplification process.

We put bounds on the minimum detection efficiency necessary to violate local realism in Bell experiments. These bounds depend on simple parameters like the number of measurement settings or the dimensionality of the entangled quantum state. We derive them by constructing explicit local hidden variable models which reproduce the quantum correlations for sufficiently small detectors efficiency.

We study an isolated, perfectly reflecting, mirror illuminated by an intense laser pulse. We show that the resulting radiation pressure efficiently entangles a mirror vibrational mode with the two reflected optical sideband modes of the incident carrier beam. The entanglement of the resulting three-mode state is studied in detail and it is shown to be robust against the mirror mode temperature. We then show how this continuous-variable entanglement can be profitably used to teleport an unknown quantum state of an optical mode onto the vibrational mode of the mirror.

Energies of ${5l}_j(l=s,p,d,f,g)$ and ${4f}_j$ states in neutral Ag and Ag-like ions with nuclear charges $Z=48\mathrm{}–100$ are calculated using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are calculated for the 17 possible ${5l}_j-{5l}_{j^{\prime }}^{\prime }$ and ${4f}_j-{5l}_{j^{\prime }}$ electric-dipole transitions. Third-order corrections to energies and dipole matrix elements are included for neutral Ag and for ions with $Z<~60.$ Second-order corrections are included for $Z>\mathrm{}60.\mathrm{}$ Comparisons are made with available experimental data for transition energies and lifetimes. Correlation energies and transition rates are shown graphically as functions of nuclear charge Z for selected cases. These calculations provide a theoretical benchmark for comparison with experiment and theory.

A time-dependent method is used to study the photoionization of the simplest one-electron molecule, ${\mathrm{H}}_2^{+}.$ We use the variational principle to solve the time-dependent Schrödinger equation for ${\mathrm{H}}_2^{+}$ in spherical coordinates $(r,\theta )$ centered on the center of mass of the ${\mathrm{H}}_2^{+}$ system in a time-varying electromagnetic field, in the fixed-nuclei approximation. Bound and continuum states of ${\mathrm{H}}_2^{+}$ are obtained by diagonalizing the two-dimensional Hamiltonian for ${\mathrm{H}}_2^{+}$ on a uniform lattice. Two different algorithms for the time propagation of the Schrödinger equation are described, the first an explicit time propagator involving matrix multiplication and the second an implicit time propagator involving matrix inversion. Single-photoionization cross sections for ${\mathrm{H}}_2^{+}$ are presented for the cases where the laser field is oriented both parallel and perpendicular to the internuclear axis. Excellent agreement is found between the present calculations and previous work. Two- and three-photon ionization cross sections are also presented for the cases where the laser field is oriented both parallel and perpendicular to the internuclear axis. Comparison with previous work is available only for the parallel orientation case where good agreement is found with a previous time-independent calculation.

We present a steady-state analysis of a quantum-mechanical model of an atom laser. A single-mode atomic trap coupled to a continuum of external modes is driven by a saturable pumping mechanism. In the dilute flux regime, where atom-atom interactions are negligible in the output, we find an analytic form for the linewidth and frequency shift of the laser. This result does not make the Born-Markov approximation, but is based on the far less restrictive “self-consistent Markov approximation.” The more exact treatment has a different effective damping rate and occupation of the lasing mode, as well as a shifted frequency and linewidth of the output. We examine gravitational damping numerically, finding linewidths and frequency shifts for a range of pumping rates. We treat mean-field damping analytically, finding a memory function for the Thomas-Fermi regime. The occupation and linewidth are found to have a nonlinear scaling behavior which has implications for the stability of atom lasers.

Recently it has been predicted that if a gas of spin-1/2 bosonic atoms is cooled down while conserving its total spin, it can form a Bose-Einstein condensate in a new type of fragmented state. In that fragmented state two orbital wave functions are macroscopically occupied. We derive a set of Gross-Pitaevskii equations that describe the two occupied wave functions, taking into account the effects of interatomic interactions. We then analyze the solutions of those equations in some special cases. In particular, we find that if the fragmented state is realized in a toroidal trap, under certain conditions the system will spontaneously acquire macroscopic orbital angular momentum. Finally, we discuss the nature of the phase transition from an uncondensed gas to a fragmented-state condensate.

We present the results of an exact numeric simulation of N one-dimensional bosons with attractive δ-functional interaction in a rotating ring. We prove that even at intermediate values of N, the system can be described by conventional methods of weakly interacting gas, the dimensionless parameter of weak interaction being just $1/N.$ When the strength of interaction is less than a certain threshold value, the dependence of angular momentum on the rotation frequency features plateaus characteristic of the irrotational fluid.

We investigate energetic stability of vortices near the surface of a Bose-Einstein condensate. From an energy functional of a rotating Bose-Einstein condensate, written in terms of variables local to the surface, and a suitable trial wave function, we calculate the energy of a moving vortex. The energetic stability of the vortex is investigated in terms of the rotation frequency of the confining potential. The critical frequency at which the vortices enter the condensate is calculated and compared with the experiment where a reasonable agreement is obtained.

As it was proposed and recently verified experimentally, the mechanism of Feshbach resonance in a condensate can create a second condensate component of molecules that coexists with the atomic condensate. In this work we investigate signatures of the presence of the molecular condensate through the equilibrium properties and collective excitations of the hybrid system of atoms and molecules, subjected to a trap, employing a time-dependent variational ansatz. We show that the shape of the condensate changes significantly by the presence of the molecules and that modes unique to this hybrid system appear at observable frequencies.