The photon correlation phenomenon in the resonance fluorescence of a harmonically trapped two-level ion is investigated including effects which result from the quantized motion. An analytical result is obtained for the second-order correlation function which involves the initial population distribution of the trap states. Collapses and revivals occur in the photon correlation function as a consequence of the discrete dependence of the Rabi frequencies on the vibrational excitation number.

We have investigated laser cooling of metastable helium atoms by laser light at 389 nm using inhomogeneous electric fields for compensating the varying Doppler shift. As a result of the high polarizability of the upper cooling level, we were able to compensate for the large Doppler shift associated with the UV transition frequency and the high beam velocity with moderate field strengths. The method represents an alternate way to the standard Zeeman slowing technique. It is expected to be superior in applications, where high magnetic fields cannot be tolerated.

Dielectronic recombination from a continuum of finite bandwidth has been examined down to very low electric fields, 60 mV/cm, with very high resolution. A tunable laser is used to excite atoms to the continuum of finite bandwidth, the broad $\mathrm{Ba}\hspace{0.5em}{6p}_{3/2}11d$ autoionizing state, which straddles the ${\mathrm{Ba}}^{+}\hspace{0.5em}{6p}_{1/2}$ limit. Atoms which make transitions into the high-lying $\mathrm{Ba}\hspace{0.5em}{6p}_{1/2}\mathrm{nd}$ states and radiatively decay to the bound $6snd$ states are detected by field ionization. The recombination, integrated over energy, has been measured for fields from 60 mV/cm to 28 V/cm, showing a peak at 0.5 V/cm, in agreement with expectation based on calculations done for other systems. The final-state distribution has been measured, showing that the outer electron remains a spectator in the radiative decay. At fields below 1.0 V/cm and binding energies less than 12 ${\mathrm{cm}}^{-1}$ below the ${\mathrm{Ba}}^{+}\hspace{0.5em}{6p}_{1/2}$ limit we find a deviation of our experimental results from the isolated resonance approximation.

Complete, close to 100%, population transfer between the bound vibrational-rotational states of the HF molecule in the ground electronic state is demonstrated on a picosecond time scale by means of computer simulation within the Schrödinger wave-function formalism. The laser-induced dissociation from selectively prepared moderately high vibrational-rotational states is shown to be very efficient, with the dissociation probability approaching 100%. These processes are controlled by ${\sin }^2$-shaped linearly polarized picosecond laser pulses in the infrared domain.

The hydrogen atom in weak external fields is a very accurate model for the multiphoton excitation of ultrastable high angular momentum Rydberg states, a process which classical mechanics describes with astonishing precision. In this paper we show that the simplest treatment of the intramanifold dynamics of a hydrogenic electron in external fields is based on the elliptic states of the hydrogen atom, i.e., the coherent states of $\mathrm{SO}\mathrm{}\left(4\right),$ which is the dynamical symmetry group of the Kepler problem. Moreover, we also show that classical perturbation theory yields the exact evolution in time of these quantum states, and so we explain the surprising match between purely classical perturbative calculations and experiments. Finally, as a first application, we propose a fast method for the excitation of circular states; these are ultrastable hydrogenic eigenstates that have maximum total angular momentum and also maximum projection of the angular momentum along a fixed direction.

Vibrational relaxation of trapped molecules due to collisions with cold atoms is investigated using the results of quantum-mechanical scattering calculations. Trap loss is analyzed using an exactly solvable kinetic model that includes direct collisional quenching and an indirect process of vibrational predissociation. At low atom density, the relaxation is due primarily to collisional quenching. At high atom density, the relaxation involves additional time scales due to the formation and decay of van der Waals complexes. It is shown that the most weakly bound state of the van der Waals complex for a given diatomic vibrational level controls the relaxation at all atom densities. Possible experiments using trapped molecules are discussed.

Numerical solutions of the time-dependent Schrödinger equation for one-electron two-dimensional ${\mathrm{H}}_2^{+},$ ${\mathrm{H}}_3^{2+}$ molecular ions have been obtained in order to illustrate the dependence of charge-resonance-enhanced ionization (CREI) on the angular orientation of the molecule. For ${\mathrm{H}}_3^{2+}$ both linear and triangular geometries have been considered. It is found, in general, that orientational effects on ionization rates, laser-induced dipole moments and torques, are most significant at the critical distances $R_c$ and critical angles ${\phi }_c$ of molecular geometry where CREI occurs. The calculated ionization rates and field-induced torques are used to estimate alignment times near the dissociative ionization regime of these ions in intense laser pulses. It is found that orientational trapping can occur in this regime at the critical CREI configurations.

We analyze and further develop our method of quantum-state holography for reconstructing quantum superposition states in molecules or atoms [Phys. Rev. Lett. 80, 1418 (1998)]. The technique is based on mixing the unknown object state with a known reference state generated in the same system by two delayed laser pulses, and detecting the total time- and frequency-integrated fluorescence as a function of the delay. The feasibility of the method is demonstrated by reconstructing various vibrational wave packets in sodium dimers. Both the cases of completely controlled and noisy relative phase between the laser pulses are considered. In the latter case, we use the technique of coherence observation by interference noise to recover the interference component of the fluorescence signal. Our results clearly demonstrate the robustness of quantum-state holography and the high quality of reconstruction even in the presence of the external noise.

Raman sideband excitations driven by counterpropagating Raman beams are analyzed for the trapped ion under the localization conditions in and beyond the Lamb-Dicke regime. Multiquantum vibrational couplings are demonstrated to produce significant effects on the Raman sideband transitions and the relevant Raman excitations of the trapped ion beyond the Lamb-Dicke regime. The quantum features of the vibrational states attained by exciting the motional ground state are closely associated with the nonlinear vibronic couplings, Raman excitation, and localization conditions. Quantum entanglement and quantum interference are discussed for the trapped ion under various Raman excitation and localization conditions. The results are compared with the recent experiments. Further experimental attempts are proposed to use the single trapped ${}^{25}{\mathrm{Mg}}^{+}$ ion in a linear ion trap.

The dynamics of spin-orbit autoionizing electron wave packets in Xe have been observed. Wave packets are created between the ${}^2{P}_{3/2}$ and ${}^2{P}_{1/2}$ ionization limits, with $33<\mathrm{}\mathrm{n̄}<53,$ and observed for approximately four orbit periods using the optical Ramsey method. Comparison of the experimental spectra with calculations reveals an increase in the autoionization lifetime.

When an atom diffracts in intense standing light, the periodic potential can be too strong for known solutions of the Schrödinger equation. We present general solutions of Schrödinger’s equation in strong sinusoidal media, thus generalizing dynamical diffraction theory. The solutions exhibit rich generalizations of the pendellösung phenomena.

A quantized vortex in Bose-Einstein condensation (BEC) of an alkali-metal atom gas is known to be unstable intrinsically at zero temperature. We examine two stabilization mechanisms of a vortex theoretically. (i) The finite temperature effect is shown to stabilize a vortex. (ii) An additional pinning potential, which may be produced by a focused laser beam at the vortex center, is also shown to stabilize it even at zero temperature. The mean-field calculation for BEC confined by a harmonic potential is employed. The detailed properties of a stable vortex are given, such as the spatial profiles of the condensate and noncondensate, the particle current density around the core, the whole excitation spectrum, and their temperature dependence.

We show that if two multiply occupied boson modes are in eigenstates of the Hermitian relative phase operator, then the visibility of fringes formed by the interference between the modes is necessarily less than unity. For large total occupation numbers the visibility becomes $V<~\pi /4.\mathrm{}$ States with definite relative phase and unit visibility do exist. They are related to coherent states and are not orthogonal (not eigenstates of a Hermitian phase operator). This visibility limitation may make it possible to investigate experimentally the physical role of the relative phase eigenstates in interference measurements such as those on Bose-Einstein condensates.

We report on experiments of multiple-beam atom interferometry in the time domain. Laser-cooled and trapped atoms interact with atomic “multiple beam splitters” realized by time sequences of resonant laser pulses. The output signals of the interferometers show Fabry-Perot-like high-finesse interference structures. The number of interfering de Broglie waves is adjustable and in principle not limited in this scheme. We present the experimental realization of up to 160 interfering partial waves.

We study the dynamics of the mean field model of a Bose-Einstein condensed atom cloud in a parametrically forced trap by using analytical and numerical techniques. The dynamics is related to a classical Mathieu oscillator in a singular potential. It is found that there are wide resonances which can strongly affect the dynamics even when dissipation is present. Different geometries of the forcing are discussed as well as the implications of our results.

The ground and excited states of a weakly interacting and dilute Bose-Einstein condensed gas, confined in a completely anisotropic harmonic oscillator potential, are determined at zero temperature within the Bogoliubov approximation. The numerical calculations employ a computationally efficient procedure based on a discrete variable representation (DVR) of the Hamiltonian. The DVR is efficient for problems where the interaction potential may be expressed as a local function of interparticle coordinates. In order to address condensates that are both very large ($\sim {10}^6$ atoms) and fully anisotropic, the ground state is found using a self-consistent field approach. Experience has demonstrated, however, that standard iterative techniques applied to the solution of the nonlinear partial differential equation for the condensate are nonconvergent. This limitation is overcome using the method of direct inversion in the iterated subspace (DIIS). In addition, the sparse structure of the DVR enables the efficient application of iterative techniques such as the Davidson and/or Lanczos methods, to extract the eigenvalues of physical interest. The results are compared with recent experimental data obtained for Bose-Einstein condensed alkali-metal vapors confined in magnetic traps.

Evaporative cooling of trapped atoms is studied based on the quantum kinetic theory. We extend the classical analysis of Luiten et al. [Phys. Rev. A 53, 381 (1996)] to treat Bose statistics of alkali-metal atoms. Dynamics in evaporative cooling process is described by a kinetic equation for the truncated Bose-Einstein distribution function under the assumption that the system is close to the thermal equilibrium. This approach is applicable to the “slow” evaporative cooling normally adopted in most experiments for the efficient production of Bose-Einstein condensates. Time-evolution calculations explain the current experiment well with sodium atoms using a slow evaporative cooling and demonstrate a rapid growth of condensate in the cooling process.

We study the dynamics of the relative phase between two atomic Bose-Einstein condensates coupled via collisions and via a Josephson-like coupling. We derive the equations of the motion for the relative phase and the relative number operators from the second-quantized Hamiltonian of the system using a quantum field theoretical approach. We distinguish the cases in which the two condensates are in the same trap or in two different traps and study the influence of this difference on the first-order correlation function of atomic fields. In identical traps this function does not undergo dephasing. We calculate the dephasing time for the case of different traps.

We have succeeded in measuring precisely the spin precession angle of neutrons tunneling through a Permalloy45 $\left({\mathrm{Fe}}_{55}{\mathrm{Ni}}_{45}\right)$ ferromagnetic film as a function of incident angles. The angles of additional spin precession are directly observed as a shift of neutron spin echo (NSE) signals by inserting the film in one of the Larmor precession fields of a transverse NSE spectrometer, and are well reproduced by the relative phase difference between $\uparrow$ and $\downarrow$ spin neutron wave functions, which are derived by solving the one-dimensional Schrödinger equation for the optical potentials in the film. The Larmor times are extracted from the additional spin-precession angles for nontunneling and tunneling cases.

A theory of matter-wave interference is developed in which resonant, standing-wave optical fields interact with an ensemble of two-level atoms. If effects related to the recoil the atoms undergo on absorbing or emitting radiation are neglected, the total atomic density is spatially uniform. However, when recoil effects are included, spatial modulation of the atomic density can occur for times that are greater than or comparable to the inverse recoil frequency. In this regime, the atoms exhibit matter-wave interference that can be used as the basis of a matter-wave atom interferometer. Two specific atom-field geometries are considered, involving either one or two field-interaction zones. For each geometry, the recoil-induced spatial modulation of the total atomic density is calculated. In contrast to the normal Talbot and Talbot-Lau effects, the spatially modulated density is nota periodic function of time, owing to spontaneous emission; however, after a sufficiently long time, the contribution from spontaneous processes no longer plays a role and the periodicity is restored. With a suitable choice of observation time and field strengths, the spatially modulated atomic density serves as an indirect probe of the distribution of spontaneously emitted radiation.