We present detailed discussions of cooling and trapping mechanisms for an atom in an optical trap inside an optical cavity, as relevant to recent experiments. The interference pattern of cavity QED and trapping fields in space makes the trapping wells, in principle, distinguishable from one another. This adds considerable flexibility to creating effective trapping and cooling conditions and to detection possibilities. Friction and diffusion coefficients are calculated in and beyond the low excitation limit and full three-dimensional simulations of the quasiclassical motion of a Cs atom are performed.

We investigate the behavior of a three-level atomic system with Λ structure of levels in the field of a sequence of short frequency-chirped bichromatic laser pulses (BLP’s) in the adiabatic passage regime of interaction. We show that the efficiency of the population transfer in this atomic system is sensitive to the relative phase of the pulses forming the BLP when the atom is prepared in a coherent superposition of its two ground states initially. We propose to use this sensitivity for coherent fast and robust writing and reading of optical phase information. The initial preparation of the atom in the “dark” superposition state is suggested through the action of a sequence of a few frequency-chirped BLP’s with duration longer than the atomic relaxation time.

We obtain a simple closed-form analytical expression for ionization rate as a function of instantaneous laser phase $\phi \mathrm{}\left(t\right),$ for arbitrary values of the Keldysh parameter $\gamma ,$ within the usual strong-field approximation. Our analysis allows us to explicitly distinguish multiphoton and tunneling contributions to the total ionization probability. The range of intermediate $\gamma \sim 1,$ which is typical for most current intense field experiments, is the regime of nonadiabatic tunneling. In this regime, the instantaneous laser phase dependence differs dramatically from both quasistatic tunneling and multiphoton limits. For cycle-averaged rates, our results reproduce standard Keldysh-like expressions.

We present a scheme for determining if the quantum state of a small trapped atomic Bose-Einstein condensate is a state with a well-defined number of atoms, a Fock state, or a state with a broken U(1) gauge symmetry, a coherent state. The proposal is based on the observation of Ramsey fringes. The population difference measured by a Ramsey fringe experiment will exhibit collapse and revivals due to the mean-field interactions. The collapse and revival times depend on the relative strengths of the mean-field interactions for the two components and the initial quantum state of the condensate.

This is a study of quasidiscrete Bogoliubov quasiparticles in a spherically symmetric harmonic trap. We first evaluate analytically the aymptotic energy shifts of the high-energy modes and find them to have $1/\sqrt{n}$ dependence on the number of radial nodes n, consistent with earlier semiclassical discussions. To address the question of the widths or decay rates $\gamma ,$ we attempt to clarify previous discussions by deriving an implicit equation for $\gamma$ from an assumption of exponential decay. Numerically, we study the trends in the behavior of the widths as a function of temperature, energy, particle number, and scattering lengths. In particular, we find that the width due to Landau decay rises rapidly at low n and then declines, while the Beliaev decay rate rises slowly with n. As temperature $\to 0,$ Beliaev decay reaches a constant (greater than 0 for $n>\mathrm{}0),$ while the Landau decay rate goes to zero. The decay rate $\gamma$ is approximately linear in the s-wave scattering length.

We consider one single copy of a mixed state of two qubits and investigate how its entanglement changes under local quantum operations and classical communications (LQCC) of the type ${\rho }^{\prime }\sim (A\otimes B)\rho (A\otimes {B)}^{†}.$ We consider a real matrix parametrization of the set of density matrices and show that these LQCC operations correspond to left and right multiplication by a Lorentz matrix, followed by normalization. A constructive way of bringing this matrix into a normal form is derived. This allows us to calculate explicitly the optimal local filtering operations for concentrating entanglement. Furthermore, we give a complete characterization of the mixed states that can be purified arbitrarily close to a Bell state. Finally, we obtain a new way of calculating the entanglement of formation.

We extend a procedure for the construction of photon position operators with transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)] to body rotations described by three Euler angles. The axial angle can be made a function of the two polar angles, and different choices of the functional dependence are analogous to different gauges of a magnetic field. Symmetries broken by a choice of gauge are reestablished by transformations within the gauge group. The approach allows several previous proposals to be related. Because of the coupling of the photon momentum and spin, our position operator, like that proposed by Pryce, is a matrix that does not commute with the spin operator. Unlike the Pryce operator, however, our operator has commuting components, but the commutators of these components with the total angular momentum require an extra term to rotate the matrices for each vector component around the momentum direction. Several proofs of the nonexistence of a photon position operator with commuting components are based on overly restrictive premises that do not apply here.

The natural widths of the Ar ${2p}^{-1},$ Kr ${3d}^{-1},$ Xe ${3d}^{-1},$ and Xe ${4d}^{-1}$ states have been determined from photoelectron spectra measured with very high resolution. Lifetime widths ${\Gamma }_L$ of $104\pm 3\mathrm{meV}$ and $111\pm 3\mathrm{meV}$ were obtained for the Xe ${4d}_{3/2}^{-1}$ and ${4d}_{5/2}^{-1}$ states, respectively. In contrast, no differences in the inherent lifetime width could be found for the spin-orbit split components of Ar $2p$ $({\Gamma }_L=118\mathrm{}\pm 4\mathrm{meV})$ and Kr $3d$ $({\Gamma }_L=88\mathrm{}\pm 4\mathrm{meV})$ ionized states. The lifetime widths of the Xe ${3d}_{3/2}^{-1}$ and ${3d}_{5/2}^{-1}$ states were found to be $490\pm 30\mathrm{meV}$ and $510\pm 30\mathrm{meV},$ respectively. The extracted lifetime widths are compared with the previously published experimental results.

Double differential and total cross sections (DDCS and TCS) for ionization of Li by fast bare ions, namely, ${\mathrm{H}}^{+},$ ${\mathrm{He}}^{2+},$ ${\mathrm{N}}^{7+},$ and ${\mathrm{Ar}}^{18+},$ are calculated within the continuum distorted wave eikonal-initial-state aproximation employing several static atomic potentials. Both the DDCS and the TCS cross sections, calculated using optimized potential method and $X_{\alpha }(\alpha =0.781)$ potentials, are nearly equivalent, but one pseudopotential tested, already successfully used in other branches of physics and chemistry, led to the wrong angular dependence and could present serious problems for fast ion-atom collision study.

We discuss binary atomic collisions in a Bose gas tightly confined in one (axial) direction and identify two regimes of scattering. In the quasi-two-dimensional (quasi-2D) regime, where the confinement frequency ${\omega }_0$ greatly exceeds the gas temperature $T,$ the scattering rates exhibit 2D features of the particle motion. At temperatures $T\sim ħ{\omega }_0$ one has a confinement-dominated 3D regime, where the confinement can change the momentum dependence of the scattering amplitudes. We describe the collision-induced energy exchange between the axial and radial degrees of freedom and analyze recent experiments on thermalization and spin-relaxation rates in a tightly (axially) confined gas of Cs atoms.

Dissociative attachment of low-energy electrons to the electronically excited and bent ${}^1{B}_2$ state of ${\mathrm{CS}}_2$ is studied. The measurements are carried out in a crossed three-beam geometry in which a laser beam is used to prepare the excited molecules. The absolute cross sections for the formation of ${\mathrm{S}}^{-}$ and ${\mathrm{CS}}^{-}$ by dissociative attachment to the ${}^1{B}_2$ excited state are determined by a measurement of the relative number density in the excited state. Based on the earlier observation of the formation of ${\mathrm{S}}_2^{-}$ from the linear symmetric ground state of ${\mathrm{CS}}_2,$ an increase in the ${\mathrm{S}}_2^{-}$ cross section was expected from the bent excited state. However, ${\mathrm{S}}_2^{-}$ is found to be absent from this state. Possible mechanisms are proposed to explain this counterintuitive result.

We discuss experiments on the ionization of atoms and molecules in intense laser fields, designed to facilitate a comparison of theory and experiment especially in the case of complex molecules. We concentrate on ionization in the regime where single ionization dominates. We describe an approach which allows a direct measurement of ionization efficiencies, absolute ionization rates, and well-defined saturation intensities. In addition, intensities where multiple ionization and Coulomb explosion set in are determined. We also analyze how ion yields are sensitive to any dependence of ionization rates on molecular alignment. Application of these procedures to molecular ionization is demonstrated in detail for the organic molecules benzene and cyclohexane.

We present a three-dimensional quantum study of high-order harmonic generation (HHG) of the Na atom in intense mid-ir laser fields. An accurate one-electron model potential is constructed for the description of the Na atom. The time-dependent Schrödinger equation is solved by means of the time-dependent generalized pseudospectral method, allowing nonuniform and optimal spatial grid discretization and accurate and efficient propagation of the wave function in space and time. Excellent agreement of the HHG spectrum in the length and acceleration forms is obtained from the lowest harmonics up to the cutoff. The HHG power spectrum shows fine structures and significant enhancement of the intensities of the lower harmonics due to the strong coupling of the $3s-\mathrm{np}$ states and the $3s-3p$ multiphoton resonance. We use a wavelet transform to present a detailed time-frequency analysis of the whole range of the HHG power spectrum. The results reveal striking details of the spectral and temporal fine structures of HHG, providing insights into different HHG mechanisms in different energy regimes of Na atoms at long wavelengths.

The Josephson oscillations between condensates in a double-well trap are known theoretically to be strongly effected by the mean-field interaction in dilute atomic gases. The most important effect is that the amplitude of oscillation in the relative population of the two wells is greatly suppressed due to the mean-field interaction, which can make it difficult to observe the Josephson effect. Starting from the work of Raghavan, Smerzi, Fantoni, and Shenoy, we calculate the maximum amplitude of oscillation in the relative population as a function of various physical parameters, such as the trap aspect ratio, the Gaussian barrier height and width, and the total number of atoms in the condensate. We also compare results for ${}^{23}\mathrm{Na}$ and ${}^{87}\mathrm{Rb}.$ Our main new result is that the maximum amplitude of oscillation depends strongly on the aspect ratio of the harmonic trap and can be maximized in a “pancake-shaped” trap, as used in the experiment of Anderson and Kasevich.

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose systems in power-law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega \mathrm{}\left(E\right)\mathrm{}\sim E^{d-1}$ for different values of d and to a three-dimensional harmonically confined ideal Bose gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.

Evolution of the density matrix in a quantum amplifier is described for initial conditions corresponding to superposition of the coherent states. The approach developed in the paper is also applicable for an arbitrary initial condition allowing the inverse Mellin transform. As such an example, we consider the evolution of the squeezed state.

A monodimensional amplified spontaneous emission model of traveling-wave pumped soft-x-ray lasers in transient collisional excitation (TCE) is presented. The model explicitly includes the influence of the local gain on the group velocity of the x-ray pulses propagating in the active medium and the saturation of the amplified x-ray signal. Complete analytical solutions of the model in a number of physically interesting cases are derived. The important parameters governing the behavior of these lasers are identified, their influence on the output is investigated, and the optimum configuration required in experiments for efficient traveling-wave pumping is discussed for conditions typical of soft-x-ray lasers in the TCE regime.

We analyze the problem of photon creation inside a perfectly conducting, rectangular, three-dimensional cavity with one oscillating wall. For some particular values of the frequency of the oscillations the system is resonant. We solve the field equation using multiple scale analysis and show that the total number of photons inside the cavity grows exponentially in time. This is also the case for slightly off-resonance situations. Although the spectrum of a cavity is in general nonequidistant, we show that the modes of the electromagnetic field can be coupled, and that the rate of photon creation strongly depends on this coupling. We also analyze the thermal enhancement of the photon creation.

We present the experimental realization of optical superlattices created by exposing laser cooled ${}^{85}\mathrm{Rb}$ atoms to a bichromatic standing-wave light field. The two light frequencies are tuned close to the $D_1$ and $D_2$ lines of ${}^{85}\mathrm{Rb}.$ The total optical potential seen by the atoms exhibits a modulation at the spatial beat period of the two light fields in addition to the typical periodicity on the scale of an optical wavelength. The bichromatic light field cools the atoms into the superlattice potential, resulting in a density modulation on a macroscopic scale. We have observed the density modulation directly in one- and three-dimensional superlattice configurations using an absorption imaging technique.

An experimental scheme for concentrating entanglement in partially entangled photon pairs is proposed. In this scheme, two separated parties obtain one maximally entangled photon pair from two previously shared partially entangled photon pairs by local operations and classical communication. A practical realization of the proposed scheme is discussed, which uses imperfect photon detectors and spontaneous parametric down-conversion as a photon source. This scheme also works for purifying a class of mixed states.