The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disk-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in three dimensions as well as with the scaling law predicted for an interacting gas in two dimensions.

In atom optics, optical wave theory has been very successful in describing the diffraction of atoms by microfabricated structures. For a molecule, however, with a binding energy smaller than the kinetic energy and with a non-negligible diameter, wave optics may no longer be adequate due to the effects of finite size and breakups. To study the role of the two effects we consider the diffraction of weakly bound diatomic systems such as the helium dimer. We find striking deviations from classical optics, in particular from Babinet’s principle, and use the results to clarify the role of finite size and breakups, respectively, in the diffraction from strips, slits, and transmission gratings. As an application the determination of the ${\mathrm{He}}_2$ size by transmission through holes and by diffraction experiments is investigated.

Steady-state dynamics of a Λ atom in a ring cavity driven by two coherent fields are studied for arbitrary detunings, arbitrary incoherent pumping, and coherent driving intensities. Effects of both cavity and effective atom number on electromagnetically induced transparency (EIT) are pointed out. New physical pictures for cavity EIT are given in terms of collective cooperative coefficients and dispersion experienced by the probe. In the regime of smaller collective cooperative coefficients, an absorption-gain profile is reduced to that of a general EIT estimated by the imaginary part of a corresponding dipole moment, and its transparency window is directly proportional to power broadening, if the total Rabi frequency is large enough. But in the region of larger collective cooperative coefficients which means a dense atomic medium, longer optical path, or high-Q cavity, EIT is determined not only by the imaginary part but also by the real part of the corresponding dipole moment, which results in the possibility of observing an EIT central peak with a subnatural width, while there may be nearly no power broadening.

A Hamiltonian describing the interaction of a two-level system with an oscillator and an external field that induces transitions between the two levels is analyzed using the quantum mechanical (QM) solution and a semiclassical (SC) approximation. The Hamiltonian can describe coherent optical transitions and coherences in electron transfer processes. We focus on strongly driven systems where coherent oscillations of the populations of the two-level system are important and show that in this regime the SC approximation is a good representation of the QM behavior. The results are interpreted by constructing appropriate Landau-Zener-Massey parameters.

We describe a versatile method for slowing molecules (or atoms) which relies on high-field-seeking states created by the polarizability interaction with a nonresonant laser field. A pulsed supersonic beam expansion is employed to precool the molecules internally and to narrow their velocity spread. The molecules are scooped at right angles by a nonresonant laser beam steered by a scanner and decelerated on a circular path by gradually reducing the beam’s angular speed.

Toroidal dipole (anapole) moments and magnetic fields due to inversion symmetry breaking by an external electric field are studied for the alkali-metal atoms from Li to Rb. It is demonstrated that a hydrogenic atomic model is inadequate for this purpose, while a nonhydrogenic model based on the quantum-defect method yields numbers for the anapole moments in excellent agreement with those predicted by a semiempirical product rule.

In the theory of quantum transmission of information the concept of fidelity plays a fundamental role. An important class of channels, which can be experimentally realized in quantum optics, is that of Gaussian quantum channels. In this work we present a general formula for fidelity in the case of two arbitrary Gaussian states. From this formula one can get a previous result [H. Scutaru, J. Phys. A 31, 3659 (1998)], for the case of a single mode. The concept of fidelity used in this paper is the standard one [D. Bures, Trans. Am. Math. Soc. 135, 199 (1969); A. Uhlmann, Rep. Math. Phys. 9, 273 (1976); R. Josza, J. Mod. Opt. 41, 2314 (1994)]. It can be defined by $F({\rho }_1,{\rho }_2{)}^{\underset{=}{\mathrm{def}}}{\max }_{|{\psi }_1〉,|{\psi }_2〉}|〈{\psi }_1|{\psi }_2〉{|}^2,$ where $|{\psi }_i〉,$ $i=1,2\mathrm{}$ are purifications of the density matrices ${\rho }_i.$

Quantum dense coding has been demonstrated experimentally in terms of quantum logic gates and circuits in quantum computation and NMR technique. Two bits of information have been transmitted through manipulating one of the maximally entangled two-state quantum pairs, which is completely consistent with the original ideal of the Bennett-Wiesner proposal. Although information transmission happens between spins over interatomic distance, the scheme of entanglement transformation and measurement can be used in other processes of quantum information and quantum computing.

An analysis of the eigenstates of a symmetry-broken spin-boson Hamiltonian is performed by computing Bloch and Husimi projections. The eigenstate analysis is combined with the calculation of absorption bands of asymmetric dimer configurations constituted by monomers with nonidentical excitation energies and optical transition matrix elements. Absorption bands with regular and irregular fine structures are obtained and related to the transition from the coexistence to a mixing of adiabatic branches in the spectrum. It is shown that correlations between spin states allow for an interpolation between absorption bands for different optical asymmetries.

Basic geometrical and dynamical properties of the ${}^3{\mathrm{He}}^{2+}{\mu }^{-}{e}^{-}$ and ${}^4{\mathrm{He}}^{2+}{\mu }^{-}{e}^{-}$ helium-muonic atoms are determined from high-precision, variational calculations. Only the bound ground states with $L=0\mathrm{}$ are discussed. The estimated hyperfine splitting between ${}^{1/2}S$ and ${}^{3/2}S$ states in the ${}^3{\mathrm{He}}^{2+}{\mu }^{-}{e}^{-}$ atom is $\Delta \nu =4166.389\mathrm{}\hspace{0.5em}\mathrm{MHz}.$ The analogous result for the hyperfine splitting between ${}^{0}S$ and ${}^{1}S$ states in the ${}^4{\mathrm{He}}^{2+}{\mu }^{-}{e}^{-}$ atom is $\Delta \nu =4464.555\mathrm{}\hspace{0.5em}\mathrm{MHz}.$ Both obtained figures agree very well with the known experimental values. The evaluated hyperfine splitting for the ${}^6{\mathrm{Li}}^{3+}{\mu }^{-}{e}^{-}$ ion is $\approx 29311.4\hspace{0.5em}\mathrm{MHz}$ and for the ${}^7{\mathrm{Li}}^{3+}{\mu }^{-}{e}^{-}$ ion is $\approx 36790.8\hspace{0.5em}\mathrm{MHz}.$

We present a study of the influence of the constant uniform electric field on the doubly excited resonances of the positronium negative ion associated with the $N=3\mathrm{}$ positronium threshold. The calculation is performed in the framework of the complex coordinate rotation method which obtains results both for the real part of the energy (position of the resonance) and for the imaginary part of the energy (related to the width of the resonance). Results are given for the $M=0\mathrm{}$ Stark components of the Feshbach ${}^1{S}^e\mathrm{}\left(1\right),$ ${}^1{P}^o\mathrm{}\left(1\right),$ and ${}^1{D}^e\mathrm{}\left(1\right)\mathrm{}$ resonances.

Charge transfer and fragmentation in collisions of sodium cluster ions with caesium atoms have been investigated theoretically within a microscopic framework called nonadiabatic quantum molecular dynamics. To illustrate the complexity of nonadiabatic cluster collisions, in particular the interplay between charge transfer and fragmentation, ${\mathrm{Na}}_4^{+}(2.7\mathrm{}$ $\mathrm{keV})+\mathrm{Cs}$ collisions are studied in detail with special emphasis on methodical aspects. It is shown that integral and exclusive charge transfer cross sections can be understood only if all types of fragmentation processes including statistical decay are taken into account. The influence of the cluster structure (isomers, temperature, size) on measured and measurable cross sections is studied for different charge transfer channels as well as for fragmentation. In particular, cross sections for the exotic formation of caesium anions in such collisions are predicted.

We have studied the propagation of an autoionizing radial Rydberg wave packet in barium. The wave packet is formed when a short laser pulse directly excites two quasibound $\mathrm{low}-n$ ${5d}_{5/2}\mathrm{nd}$ Rydberg states that are embedded in the continuum above the first ionization threshold. This two-state autoionizing radial wave packet interacts strongly with $\mathrm{high}{-n}^{\prime }$ Rydberg states associated with the adjacent ${5d}_{3/2}{n}^{\prime }d$ series. Time-dependent electron-electron scattering leads to the formation of three distinct bound radial wave packets that oscillate with very different Kepler periods and periodically decay through autoionization. Experimentally, we have probed the temporal oscillations between the different wave packets with a second, time-delayed, laser pulse using bound-state interferometry. Theoretically, we use three-channel quantum-defect theory to construct and propagate the multiconfigurational wave packet to view its spatial distribution as a function of time.

The total and partial photoionization cross sections, branching ratios, and photoelectron angular-distribution asymmetry parameters have been calculated for atomic radium $\mathrm{}(Z=88\mathrm{})\mathrm{}$ for all subshells from the $7s$ valence shell down to the deep $n=3\mathrm{}$ subshells. The relativistic random-phase approximation, the relativistic random-phase approximation modified to include relaxation effects, and the relativistic random-phase approximation modified to include relaxation effects and Auger decay were all used to determine the relative importance of various many-body effects such as interchannel coupling, core relaxation, and Auger decay. Comparisons are made between the various theoretical models and experimental data for the total cross sections. Interchannel coupling was found to be important for most subshells. Relaxation effects were found to be significant for calculations of the total cross section above the $5d$ threshold and to have a very large effect on the $5p$ partial photoionization cross section.

The rotational dynamics of a molecule interacting with a linearly polarized intense laser field is investigated. A high-frequency Floquet approach proceeding to an adiabatic separation between “fast” field-oscillation modes and “slow” molecular rotational motion is adopted, which leads to an approximate effective Hamiltonian. A thorough analysis of the validity of the approximation is provided by examining the neglected terms. The HCN molecule, within a linear rigid-rotor description, is taken as an illustration of the model. The anisotropic interaction of the electric-field vector of the intense laser radiation with the permanent dipole moment and the polarizability of the molecule creates aligned pendular states. These states are eigenfunctions of an effective Hamiltonian governed by a ${\cos }^2\theta$ potential (with $\theta$ the angle between the molecular axis and the field vector) and serve as a basis for the interpretation and prediction of alignment dynamics. The results show, in particular, the difference in the alignment properties of linear HCN when excited by sudden versus adiabatic laser pulses, where adiabatic transport from field-free to pendular states can be evoked.

We use a method based on optical coherent transients to study the vibrational coherence lifetimes of atoms trapped in the potential wells of a near-resonant optical lattice in the oscillating regime. The dependence of the positions and widths of the vibrational Raman resonances of the coherent transient spectra on the intensity, detuning, and geometry of the lattice beams is investigated and the results are compared with theoretical predictions. It is shown that the principal source of broadening of the vibrational Raman resonances is the anharmonicity of the light-shift potential wells. We also perform time-resolved measurements of the vibrational excitation of atoms equilibrating in an optical lattice.

Ionization rates and photoelectron spectra of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ in intense laser fields are investigated theoretically on the basis of the Floquet theory linked up with the theory of resonance scattering. The profile of photoelectron spectrum changes drastically due to overlapping resonance, which occurs when the mean spacing of the Floquet vibrational levels of a neutral molecule is narrower than their ionization widths. In the overlapping regime the ionization rate exhibits a “stabilization” phenomenon, i.e., decreases with increasing field strength.

We solve the equations of the two-dimensional time-dependent Thomas-Fermi model for ${\mathrm{Cl}}_2$ molecule exposed to an intense subpicosecond laser field. We investigate the influence of the spreading of an electronic wave packet in the direction perpendicular to the molecular axis on the dynamics of the multielectron dissociative ionization process. We compare the response of the diatomic system to both linearly and circularly polarized laser pulses.

We discuss a photoionization version of the photoexcitation model of Corless and Stroud [Phys. Rev. Lett. 79, 637 (1997)]. In the photoexcitation model, a np hydrogenic state of $n\gg 1$ was excited from the ground $1s$ state and the excited population was allowed to migrate to other angular momentum states within the one n only due to strongly nonresonant electric-dipole $|\Delta n|=0,$ $|\Delta l|=1\mathrm{}$ Rydberg-to-Rydberg couplings. When, as is the essence of the photoexcitation model, the same one n-manifold approximation is made in the model of high-n Rydberg-state photoionization, a number of interesting photoionization effects are obtained. Among them, the most spectacular seems to be the emission of photoelectrons in the “forbidden” directions and the suppression of ionization when compared to the Fermi golden rule predictions. However, we show on the basis of an approximate analysis that these photoionization effects can be strongly diminished when additional n manifolds around the selected one are included in the model. Thus, we conclude that the one n-manifold approximation overestimates results when applied to the problem of high-n Rydberg-state photoionization.

The effect of fourth-order coherence on ultrafast modulation spectroscopy with phase-conjugation geometry (PCUMS) in a cascade three-level system is investigated using chaotic and phase-diffusion models. It has been found that the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transitions, and the modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behavior of the beat signal. The different roles of the phase fluctuation and amplitude fluctuation can be investigated in the time domain. The cases where the pump beams have either a narrow or broad band linewidth are considered and it has been found that for both cases a Doppler-free precision in the measurement of the energy-level difference between two states can be achieved. The difference between the PCUMS and the DeBeer, UMS [D. DeBeer et al., Phys. Rev. Lett. 56, 1128 (1986)] is discussed as well from a physical viewpoint.