We apply linear-response analysis to the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate in a vortex state, and apply it to a system of rubidium atoms confined in a time-averaged orbiting potential trap. The excitation frequencies of a vortex differ significantly from those of the ground state, and may therefore be used to obtain a spectroscopic signature of the presence of a vortex state.

We investigate the quantum interference between two Bose-Einstein condensates formed in small atomic samples composed of a few thousand atoms both by imposing Bose broken gauge symmetry from the outset and also using an explicit model of atomic detection. In the former case we show that the macroscopic wave function collapses and revives in time, and we calculate the characteristic times for current experiments. Collapses and revivals are also predicted in the interference between two Bose-Einstein condensates which are initially in Fock states, a relative phase between the condensates being established via atomic detections corresponding to uncertainty in the number difference between them.

We study an output coupler for matter waves that could be used to develop a cw atom-laser, based on current Bose-Einstein-condensation experiments with alkali-metal atoms. Assuming a cw pump mechanism for the condensate and taking into account losses due to outgoing atoms allows a description of the output by a coherently driven and damped Schrödinger equation. By contrast to a pulsed atom-laser output the stationary outgoing matter wave is extremely monoenergetic. Phase fluctuations of the condensate and technical noise limit the coherence length of the output beam. Using a Monte Carlo simulation we obtain the spatial correlation function of the output wave function, also including the influence of gravity.

The modified random-phase-approximation (RPA) method with the self-consistent separable residual forces (SRPA) is proposed for the description of multipole electric oscillations of valence electrons in sodium clusters. The method allows one to study the coupling of different kinds of collective motion. As a particular case, the coupling of surface and volume modes is considered. The SRPA is applied to neutral and singly charged spherical sodium clusters in a wide size region ${(N}_e=8,20,40,58,92,138,196,440,952)$ and good agreement with experimental data is achieved. This testifies to the applicability of the separable ansatz, which has the essential advantage of avoiding diagonalization of the RPA matrices and thus drastically simplifies the RPA calculations. The latter could be quite urgent for very large and deformed clusters where an extended configuration space and, consequently, high-rank RPA matrices are used. The predictions for $E2\mathrm{}$ and $E3\mathrm{}$ collective excitations are presented. The results obtained with the self-consistent Kohn-Sham and phenomenological Woods-Saxon single-particle schemes are exhibited and different parameters for the Woods-Saxon potential are proposed.

We present a systematic study of the optimized geometries of several small closed-shell lithium clusters, as well as energy differences between isomers, using a variety of density functional and post-Hartree-Fock quantum chemical methods. Using different Gaussian basis sets we compare and contrast the results of the calculations for Li${}_2$, Li${}_3^{+}$, Li${}_4$, Li${}_5^{+}$, and Li${}_6$ including two and three isomers of the latter two clusters, respectively. On the basis of these results a few guidelines for economically but nevertheless reliably studying lithium clusters are proposed.

A possibility is analyzed to find the one-electron effective potential that leads to ${3n}_r+l$ grouping of energy levels observed in medium-size sodium clusters. The related quantum Sturmian problem has particular solutions in the form of focusing potentials. The family of these potentials has interesting properties related to inversion in the sphere and stereographic projection; one of them was successfully applied to interpret grouping of energy levels specific to atoms (building-up rule for the periodic system of elements). The general solution of an analogous classical problem is found and some of its special realizations are discussed.

We study C${}_{60}$ with the use of the March model [N. H. March, Proc. Camb. Philos. Soc. 48, 665 (1952)]. A spherical shell model is invoked to treat the nuclear potential, where the nuclear and core charges are smeared out into a shell of constant surface charge density. The valence electron distribution and the electrostatic potential are efficiently computed by integration of the Thomas-Fermi equation, subject to the shell boundary conditions. Total energy is numerically calculated over a range of shell radii, and the mechanical stability of the model is explored with attention to the constraints of Teller’s theorem [E. Teller, Rev. Mod. Phys. 34, 627 (1962)]. The calculated equilibrium radius of the shell is in fair agreement with experiment.

We investigate the wave-packet dynamics of electrons bound in the nonseparable potential of cesium in a static electric field using time-domain Ramsey interferometry. Specially shaped wave packets with low radial dispersion enable us to view the interaction between the wave packet and the atomic core. Experiments in cesium, together with quantum defect calculations of cesium and hydrogen, demonstrate changes in the motion and shape of these wave packets due to core scattering.

We propose two quantum error-correction schemes which increase the maximum storage time for qubits in a system of cold-trapped ions, using a minimal number of ancillary qubits. Both schemes consider only the errors introduced by the decoherence due to spontaneous emission from the upper levels of the ions. Continuous monitoring of the ion fluorescence is used in conjunction with selective coherent feedback to eliminate these errors immediately following spontaneous emission events.

A general framework is given of how to derive expressions for high-harmonic generation in close analogy to the derivation of the Keldysh amplitude for ionization. As in the former, the approximation made consists of neglecting the effect of the binding potential in intermediate states. The approach can be used for arbitrary binding potentials, but is best suited to short-range potentials at high intensities. It is almost exact for a zero-range potential for arbitrary intensity. Various models that have been used before by some of the authors, such as the effective dipole model and the zero-range potential model, emerge as special cases. The relation between the $S$-matrix element for high-harmonic generation and the dipole-moment expectation value is discussed, as well as the relation of both to the dipole-dipole correlation function. An exact functional relationship between high-harmonic generation and the total ionization rate is presented. For the case of an elliptically polarized monochromatic driving field, the polarization properties of the emitted harmonics, viz. their ellipticity and the offset angle of their polarization ellipse, are evaluated for both the zero-range potential model and the effective-dipole model, and compared. The predictions of both models generally agree, there are, however, some qualitative differences for the harmonics around the end of the plateau.

The motion of a Rydberg electron in crossed electric and magnetic fields is a widely encountered and poorly understood problem of great complexity. We explain photoabsorption experiments that probe the electron’s intricate periodic motions. In particular, we show how the Coulomb center acts as a selector of planar versus three-dimensional motion and investigate the stability and ionization behavior of trajectories that start at the nucleus.

Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time $T_2^{\prime }$ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102–124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.

Numerical solutions of the time-dependent Schrödinger equation are presented to study the behavior of one and two electrons in symmetric and nonsymmetric linear molecules H${}_3^{2+}$ and H${}_3^{+}$. Enhanced ionization, as discovered earlier in diatomic molecules H${}_2^{+}$ and H${}_2$ are shown to occur also in triatomic systems at critical internuclear separations that are determined by both field-induced barrier localization of the electron and charge resonance (CR) transitions. Two-electron effects manifest themselves through their influence on CR transition moments and electron collisions at large intensities.

We investigate the time evolution of the population inversion as well as the $Q$ function for center-of-mass motion for a two-level ion, interacting with single-mode laser light field, in an anharmonic-oscillator trap. The anharmonicities of the trap are quantified in terms of the deformation parameter of the $q$-analog trap. For $\tau =0.003\mathrm{}$ ${(q=e}^{\tau })$ the collapses and revivals of population inversion become well-defined facilitating experimental observation, but for large $\tau \sim 0.1$ the time dependence of population inversion is completely wiped out. The quasiprobability function shows an atypical behavior with a single peak at $t=0\mathrm{}$ splitting up into as many as seven fragments (at $t=130\mathrm{}$) during collapse and at a later time these segments come together to signal the revival of population inversion. A small degree of anharmonicity is seen to enhance the coherence of the ion-trap system, whereas for large $\tau$ ($\sim 0.1$ in the present context) the coherence is completely lost.

Using a representation of the (first-order) Dirac Coulomb Green function in terms of an expansion over a Sturmian basis, we have computed two-photon probability amplitudes for transitions in hydrogenic atoms from the ground state towards states in the $L$ and $M$ shells. The treatment takes care of the relativistic structure of the atoms according to the Dirac theory and of the fully retarded interaction with the electromagnetic field. We present in detail the Sturmian-like expansion for the Dirac Coulomb Green function and we discuss the relative importance of relativistic and retardation effects occurring for higher nuclear charge $Z$. Comparison is made also with the nonrelativistic Schrödinger treatment, retardation included or not.

We propose an atomic funnel composed of an evanescent-light mirror produced in a conical hollow prism. The funneling of cold Rb atoms released from a magneto-optical trap is simulated in the scheme of the evanescent-light-induced Sisyphus cooling for compensating the heating by gravity. A geometric method of the conversion of a Gaussian light beam into a doughnut-shaped light beam suitable for the atomic funnel is also experimentally demonstrated by means of a double-cone prism. Under the assumption of a proper optical intensity distribution over the inner surface of a specific conical hollow prism, the Monte Carlo simulation including the van der Waals interaction shows that a half of the released Rb atoms can be collected and the mean temperature of the collected atoms is low enough for the application to be guided with a bent hollow optical fiber.

The threshold for H-atom ionization by elliptically polarized microwave fields is discussed within the classical-mechanics framework using the Chirikov overlap criterion. It is shown that the trends observed in the recent experiment [M. R. W. Bellermann et al. Phys. Rev. Lett. 76, 892 (1996)] are qualitatively reproduced by the theory; the origin of the remaining discrepancy is discussed. Increased stability of some orbits with respect to the perturbation due to the elliptically polarized microwaves has been related to vanishing widths of the corresponding resonance islands. Analytic Chirikov overlap prediction is compared with results of numerical simulations.

We investigate theoretically the Sisyphus cooling of three-level atoms due to interaction with the evanescent field developed on the surface of a conical-hollow atom trap. We treat the total processes in a fully random way so that quantitative and realistic results are obtained by Monte Carlo simulation. We show that the trapped atoms, when released inside the hollow region, are cooled down to the final temperature of 30 $\mu$K, independent of the intial conditions, with negligible loss (about 1%) of the atoms. We also find that the mean height of the collected atoms is about 1 mm from the apex of the conical hollow with the trap radius of 0.5 mm. This system may be useful to realize an atomic funnel or a cold atomic beam for atom optical experiments such as atom interferometer and atom lithography.

In a famous 1965 paper [Phys. Rev. 138, B979], J. H. Shirley calculates the time-averaged transition probability for an atom in a periodic field in terms of the eigenvectors and eigenvalues of the time-independent Floquet Hamiltonian. It is shown in the present paper that, for the specific case considered by Shirley, a two-state atom in a sinusoidal field, Shirley’s solution can be simplified considerably. Also, Shirley’s results are generalized to include, for an arbitrary atom-field system, the time-varying components of the transition probability as well.

This paper analyzes the process of population transfer between two discrete states via a common continuum by using two partially overlapping delayed laser pulses. The incoherent ionization channels, the Stark shifts, and the nonzero Fano parameter are taken into account. An analytic approximation to the final-state population is derived for Gaussian pulse shapes.