We introduce a semiclassical model for highly excited atomic ions moving in a magnetic field, which allows us to describe the mixing of the Landau orbitals of the center of mass in terms of the electronic excitation and magnetic field. The extent of quantum energy flow in the ion is investigated and a crossover from localization to delocalization with increasing center of mass energy is detected. Our model of the moving ion in a magnetic field turns out to be closely connected to models for transport in disordered finite-size wires.

We have used two sets of orthogonally polarized traveling-wave pulses separated in time to establish and, subsequently, rephase a spatially periodic coherence grating between the magnetic sublevels of the $F=3\mathrm{}$ ground state in a cloud of laser-cooled ${}^{85}\mathrm{Rb}$ atoms. The rephasing results in a magnetic grating echo (MGE). We have used the shape of the signals to determine both transverse and longitudinal velocity distributions and to study the effects of magnetic fields. The amplitude of the MGE with counterpropagating pulses is modulated at the atomic recoil frequency, a consequence of matter wave interference.

We present the general dielectric formalism for Bose-Einstein condensed systems in an external potential at finite temperatures. On the basis of a model arising within this framework as a first approximation in an intermediate-temperature region for the large condensate we calculate the damping of low-energy excitations in the collisionless regime.

The low-energy fluctuations of a trapped, interacting quasi-one-dimensional Bose gas are studied. Our considerations apply to experiments with highly anisotropic traps. We show that under suitable experimental conditions the system can be described as a Luttinger liquid. This implies that the correlation function of the bosons decays algebraically, preventing Bose-Einstein condensation. At significantly lower temperatures a finite-size gap destroys the Luttinger liquid picture and Bose-Einstein condensation is again possible.

The consequences of spatial symmetry breaking in two-component Bose-Einstein condensates are explored for the ${}^{85}{\mathrm{R}\mathrm{b}+}^{87}\mathrm{Rb}$ system. It is shown that the mean-field critical number of ${}^{85}\mathrm{Rb}$ atoms depends strongly on whether the single-particle wave function is symmetry preserving or symmetry breaking. This system thus provides a uniquely straightforward experimental means of observing spatial symmetry breaking.

We show that under suitable conditions, a weak nondegenerate probe may become spatially confined in a Doppler-broadened medium composed of two-level atoms due to the effect of a strong resonant copropagating pump beam. The induced spatial solitons result from the interplay of diffraction and induced focusing of the probe. Realistic conditions that include effects of probe absorption and pump reshaping on propagation are examined. In order to avoid absorption of the near-resonant probe, which would make the strong induced focusing unobservable, the unique properties of the dead zone are exploited.

Upper and lower kinematical bounds for the expectation values of arbitrary observables of driven quantum systems in mixed states are derived, and criteria for their attainability established. The results are applied to the problem of maximizing the energy of a laser-driven four-level Morse oscillator model for HF, as well as a four-level harmonic-oscillator model.

We derive stochastic Schrödinger equations describing the evolution of an optical linear amplifier conditioned on the state-selective detection of the source atoms. By applying a classical pulse to each atom immediately before the detection process we generate different stochastic Schrödinger equations including that of the quantum-jump method and quantum-state diffusion. We also study the transition from the distinct jumps of the quantum-jump method to the diffusive behavior of quantum-state diffusion and trace the effect of the information gained by the detection of the state of the atom on the state of the field.

A matter-field theory of the Casimir force is formulated in which the electromagnetic field and collective modes of dielectric media are treated on an equal footing. In our theory, the Casimir force is attributed to zero-point energies of the combined matter-field modes. We analyze why some of the existing theories favor the interpretation of the Casimir force as originating from zero-point energies of the electromagnetic field and others from those of the matter.

We have shown [Phys. Rev. Lett. 80, 3673 (1998)] that the wave-function representation Ψ(ξ)$={\sum }_j{a}_j\left[E\right]{\xi }^j{R}_{\beta }\left(\xi \right),$ developed in either configuration or momentum space for a suitable reference function $R_{\beta }\left(\xi \right),$ defines a highly accurate, multidimensional, energy-quantization procedure, once the convergent zeros of the power-series expansion coefficients $a_j\left[E\right]=0\mathrm{}\left(\overrightarrow{j}\infty \right)$ are determined. In this paper we amplify the underlying analysis and also examine some of the consequences for generating accurate wave functions.

We develop a generalized quantum Fokker-Planck theory in a non-Gaussian-Markovian model bath. The semiclassical bath adopted in this work is charactered by three parameters. One denotes the strength of system-bath coupling and the other two are chosen to interpolate smoothly the solvation dynamics between the long- and short-time regimes. The fluctuation-dissipation relation in this model bath is analyzed in detail. Based on this model bath, we derive two sets of coupled Fokker-Planck equations. These two equation sets are equivalent in the second order of system-bath coupling but different in the higher orders. The corresponding reduced Liouville equation in one set of the Fokker-Planck formulation is characterized by a memory relaxation kernel, while that in the other is by a local-time relaxation tensor. Each resulting set of Fokker-Planck equations involves only the reduced density operator and a series of well-characterized Hilbert-space relaxation operators. The present theory is valid for arbitrary time-dependent Hamiltonians and is applicable to the study of quantum coherence and relaxation in various dynamic systems.

The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum “bang-bang” control after its classical analog. Decoherence introduced by the system’s interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.

We suggest a method to perform a quantum logic gate between distant quantum bits (qubits) by off-resonant field-atom dispersive interactions. The scheme we present is shown to work ideally even in the presence of errors in the photon channels used for communication. The stability against errors arises from the paradoxical situation that the transmitted photons carry no information about the state of the qubits. In contrast to a previous proposal for ideal communication [Phys. Rev. Lett. 78, 4293 (1997)] our proposal only involves single atoms in the sending and receiving devices.

Two techniques are described that simplify the experimental requirements for measuring and manipulating quantum information stored in trapped ions. The first is a new technique using electron shelving to measure the populations of the Zeeman sublevels of the ground state, in an ion for which no cycling transition exists from any of these sublevels. The second technique is laser cooling to the vibrational ground state, without the need for a trap operating in the Lamb-Dicke limit. This requires sideband cooling in a sub-recoil regime. We present a thorough analysis of sideband cooling on one or a pair of sidebands simultaneously.

We calculated the energy and the size of the three-deuteron muonic molecule ${3d2e}^{-}{\mu }^{-},$ or ${\mathrm{D}}_3\mu .$ It turns out that this system possesses two equilibrium positions, one at distances typical for muonic molecules and a second one at the usual molecular size. We calculated, moreover, the fusion probability of the three deuterons and found that it could considerably be enhanced due to the existence of a ${}^6{\mathrm{Li}}^{*}$ threshold resonance. Our estimates indicate that this probability is considerably higher than the decay rate of the competing Auger transition.

We give exact analytical expressions for the classical distributions corresponding to the momentum representation of Rydberg states.

The effects of channel coupling and exchange interaction on the formation of resonances in negative ions are studied by solving the Schrödinger equation with an approximate wave function. These wave functions are constructed with very accurate target state wave functions which are frozen in the computation. The energy obtained is plotted against the radial expectation values of the approximate solutions. This leads to plots which are very similar to the conventional potential curve plots. However, by successively including the relevant target channels, the reason behind the formation or nonformation of a certain resonance becomes very clear. To illustrate, we show the results for nine ${\mathrm{He}}^{-}$ and two ${\mathrm{H}}^{2-}$ states.

The ground-state energies of the ions ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ have been calculated without making use of the Born-Oppenheimer approximation. Instead, the ions are treated as three-body systems whose ground states are spherically symmetric. The wave function of the ground state is taken to be a generalized Hylleraas form, but it is necessary to use high powers of the internuclear coordinate to simulate the localized motion of the nuclei. We obtain good values of the ground-state energies and compare them with those obtained from earlier calculations. Expectation values are calculated for various operators, the Fermi contact parameter, and the permanent quadrupole moment. The cusp condition is also calculated. The results are compared with the results of other calculations, where available.

Levinson’s theorem for the Schrödinger equation with a cylindrically symmetric potential in two dimensions is reestablished by the Sturm-Liouville theorem. The critical case, where the Schrödinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison to Levinson’s theorem in the noncritical case, the half bound state for the $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of the $P$ wave at zero energy to increase an additional $\pi$.

The $K{\alpha }_{1,2}$ x rays emitted from La, Tb, Ta, and U targets induced by proton nitrogen, and neon ion bombardment at incident energies between 15 and 28 MeV/nucleon have been measured with a high-resolution crystal spectrometer. The spectra reflect the decay of a K vacancy in the presence of multiple L, M, N,… shell “spectator” vacancies. The L-shell ionization probabilities for impact parameters in the interior of the target’s K shell are extracted from the measured spectra and compared with extensive theoretical calculations of ionization probabilities, based on the semiclassical separate-atom perturbation theory [semiclassical approximation (SCA)]. The projectile velocity varies from 60% to 125% of the target L electron velocity, so we can compare experimental data with theoretical predictions as a function of the relative velocity. We find that wave-function effects play an important role for an accurate calculation of the ionization probability. The experimental results agree well with the SCA predictions when Hartree-Fock-type wave functions are used [variationally determined optimized potential (SCA-OPM)]. Relativistic hydrogenic wave functions (SCA-HYD) provide a reliable description of experimental data only in the case of the uranium target. The influence of electron capture and intrashell coupling is also calculated and discussed. An independent comparison of theoretical constructed spectra with the experimental ones confirms the validity of the SCA-OPM. The hole-hole angular momentum coupling between “active” and “spectator” holes has been observed as predicted.