Subrecoil cooling can be achieved in three-level Λ-type atoms subject to counterpropagating laser beams via velocity-selective coherent population trapping [A. Aspect et al., J. Opt. Soc. Am. B 6, 2112 (1989)]. This process leads to narrow peaks in the ground but a flat structure in the excited atomic momentum distributions. By taking advantage of this difference, we construct several analytical functions from which the main cooling features (with the exception of the scaling law about the fraction of subrecoil cooled atoms) can be approximated under arbitrary parameters. This method allows us to generalize the peak-momentum width from symmetric to arbitrary degenerate Λ systems, and to discuss analytically the small dependence of the momentum distributions on the laser detuning near the two-photon resonance.

We report on the spectroscopy in a resonant vapor film, in a regime in which the inhomogeneous transit time induces a velocity selection. For cell thickness (10–1000 μm) smaller than the transverse dimensions and for low enough atomic density, the atomic trajectories are essentially free flights from wall to wall. Hence, a single laser beam irradiation is sufficient to observe sub-Doppler resonances because of the transient atomic response, which enhances the response of the slowest atoms flying nearly parallel to the wall. The peculiar features of this velocity selection are presented in the linear regime as well as in the case of saturation induced by the optical pumping. Also, we report, in the case of the Cs $D_2$ line (852 nm), on the passage from a two-level linear-response regime to an optical pumping regime when increasing the incident intensity. We also describe the influence of several other parameters, including cell thickness and laser beam size and shape, on the experimental line shapes. An extension to Doppler-free polarization spectroscopy in a thin cell with a single beam, and to saturated absorption, is also reported.

We numerically study two-photon processes using a set of harmonics from a Ti:sapphire laser and, in particular, interference effects in the above-threshold ionization spectra. We compare the situation where the harmonic phases are assumed locked to the case where they have a random distribution. Suggestions for possible experiments, using realistic parameters, are discussed.

It is shown that $100\%$ squeezed output can be produced in the resonance fluorescence from a coherently driven two-level atom interacting with a squeezed vacuum. This is only possible for $N=1/8\mathrm{}$ squeezed input, and is associated with a pure atomic state, i.e., a completely polarized state. The quadrature for which optimal squeezing occurs depends on the squeezing phase $\Phi$, the Rabi frequency $\Omega$, and the atomic detuning $\Delta$. Pure states are described for arbitrary $\Phi$, not just $\Phi =0\mathrm{}$ or $\pi$ as in previous work. For small values of N, there may be a greater degree of squeezing in the output field than the input, i.e., we have squeezing amplification.

We show that the physical mechanism of population transfer in a three-level system with a closed loop of coherent couplings is not equivalent to an adiabatic rotation of the dark state of the Hamiltonian, but corresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive tool to design pulse sequences for stimulated Raman adiabatic passage, which also give maximum population transfer under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under certain conditions for the pulses (generalized matched pulses), there exists a higher-order trapping state, which is an exact constant of motion, and analytic solutions for the atomic dynamics can be derived.

We have observed gradient spin echoes in the ground state of $\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{r}-\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{d}{}^{85}\mathrm{Rb}$ atoms through paramagnetic Faraday rotation. We have obtained the exact expression for the behavior of the echo signal under the assumption that the motion of the cold atoms is ballistic. The qualitative behaviors predicted by the theory have been confirmed experimentally. We demonstrate the usefulness of the spin echo method for the diagnosis for the atomic density distribution of cold atoms. We discuss various advantages of the spin echo as a novel method for temperature measurement.

We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (“wobbling”) of the ion relative to the center of the trap, and fluctuations of the spring constant, which are due to fluctuations of the ac component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctuating external electrical fields for a quantum gate operation (controlled-NOT) is determined and the fidelity for that operation derived.

We present a theoretical and experimental study of the efficiency of adiabatic transfer between the Zeeman substates of the cesium ground level, using the $D1\mathrm{}$ $F=\overrightarrow{4}{4}^{\prime }$ transition. In order to understand the application of the adiabatic condition to such multistate systems, we examine the separation of their energy eigenstates as a function of the number of participating states. We present a systematic investigation of the physical factors affecting the efficiency of transfer in a multistate system and we see that velocity selection plays an important role in these calculations. We use the theory to compare the suitability of adiabatic transfer with $F=\overrightarrow{1}{1}^{\prime }$ and $F=\overrightarrow{4}{4}^{\prime }$ transitions for atom optics.

Target states are specifically desired states of systems that allow the control of processes or the investigation of unique phenomena. A time-domain scheme for the excitation of such states by the interference of multiple wave packets is developed. The scheme leads to analytical results for the optical field required to excite an arbitrary target state. The scheme suggests a clear physical picture for the design process that is applicable to many systems. The design has strong similarities to the phase-conjugation process in optics. A strong point of the scheme is that it picks a simple set of solutions from the infinite number of possible solutions for a particular target state. This characteristic may be attributed to the choice of a classical wave-packet basis as the appropriate basis for this time-domain scheme. We show that a small number of pulses are sufficient to produce a wide range of target states (both classical and nonclassical target states are designed).

A method of making the dephasing time $T_{2u}$ measurement in an ensemble of inhomogeneously broadened two-level systems is proposed. This method has its origin in the spin-locking technique developed in NMR. It is shown that in spite of inhomogeneous broadening it is possible to lock the induced polarization in phase with the driving field. The amplitude of the locked polarization can be as large as half of the first maximum of the nutation signal, i.e., of the polarization bump just after the pulse switch on. Decay of the locked polarization is caused by the $T_{2u}$ dephasing or by the dephasing of the in-phase component of polarization.

We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasicontinuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of dark states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is also possible outside the Lamb-Dicke regime. We develop the model and use quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.

Photodetachment microscopy, which was originally proposed as a new method for direct measurements of ionization or detachment energies, has been applied for a determination of the electron affinity of oxygen. The electron affinities of ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ could be measured separately from a natural sample. The experimental values (obtained as wave numbers, to be multiplied by $\mathrm{hc}$ to give energy units) are 11 784.682 (20) and 11 784.612 (29) ${\mathrm{cm}}^{\mathrm{-}1}$, respectively. The measured ${}^2{P}_{1/2}{-}^2{P}_{3/2}$ fine structure of ${}^{16}{\mathrm{O}}^{\mathrm{-}}$ is 177.085 (27) ${\mathrm{cm}}^{\mathrm{-}1}$. The observed discrepancy of the electron affinity of oxygen with the value admitted so far, 11 784.648(6) ${\mathrm{cm}}^{\mathrm{-}1}$, is yet unexplained.

The mode frequencies of a weakly interacting Bose gas in a magnetic trap are studied as a function of the anisotropy of the trap. As in earlier works, the generalized Hartree-Fock-Bogoliubov equations within the Popov approximation are used for our calculations. A feature of our work is the combined use of a mode expansion in a finite basis and a semiclassical approximation of the highly excited states. The results are applied to check the accuracy of the recently suggested equivalent zero temperature condensate approximation, which involves a much simpler model.

We develop the quantum-mechanical description of output coupling of macroscopic coherent matter waves from a Bose-Einstein condensate (BEC) via a radio-frequency field in the pulsed and cw limits for both strong and weak field coupling. The theory is converted into a Fock state description to point out the stimulated (in Bose particle) nature of the output coupling. A useful analogy with the theory of molecular photodissociation is used to explain the various regimes of output coupling BECs using radiation sources. We present specific calculations of the rates of output coupling as a function of the number of Bose atoms in the condensate and the frequency, detuning, and intensity of the radio-frequency field.

We describe an interferometric method to uncover the quantum state $|\psi 〉$ describing a single-mode cavity field. The information needed to retrieve the corresponding Fock coefficients is imprinted on the quantized longitudinal motion of atoms that have interacted with the cavity field. In particular, we show that a set of four atomic momentum distributions can be analyzed easily to reconstruct $|\psi 〉$.

This paper proposes groovelike potential structures for the observation of quantum information processing by trapped particles. As an illustration the effect of quantum statistics at a 50-50 beam splitter is investigated. For noninteracting particles we regain the results known from photon experiments, but we have found that particle interactions destroy the perfect bosonic correlations. Fermions avoid each other due to the exclusion principle and hence they are far less sensitive to particle interactions. For bosons, the behavior can be explained with simple analytic considerations which predict a certain amount of universality. This is verified by detailed numerical calculations.

We describe a method for studying the dynamics of a condensate in a weakly interacting, dilute Bose gas which is based on a finite-temperature extension of the Gross-Pitaevskii equation. We present a general finite-temperature linear response formalism for nonuniform systems and give explicit results for homogeneous ones, where we can link our treatment to well-known results. This treatment leads to a consistent $V^2$ calculation of the excitations for a weakly interacting Bose gas, including Landau and Beliaev damping as well as collisional lifetimes. We do not make use of the Popov approximation, but include pair and triplet anomalous averages to second order in the interaction potential and thus obtain a gapless theory for the excitations of a weakly interacting homogeneous gas. We also show how the formalism can be used to obtain self-consistent theories. We explicitly derive gapless equations for a weakly coupled finite-temperature condensate with a static thermal component and give a clear criterion of their validity in trapped systems.

We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\overrightarrow{K}{K}_n^{\mathrm{eff}}{=J}_n{(E}_{\omega }/\omega )K$ for the $n\mathrm{th}$ LAT under the influence of the potential modulations, where $E_{\omega }$ and ω are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.

We present a theoretical study of the ground state of a Bose-Einstein condensate with repulsive interparticle interactions in a double-well potential, using a restricted variational principle. Within such an approach, there is a transition from a single condensate to a fragmented condensate as the strength of the central barrier of the potential is increased. We determine the nature of this transition through an approximate analytic solution as well as a numerical solution of our model, in the regime where the interparticle interactions can be treated perturbatively. The degree of fragmentation of the condensate is characterized by the degrees of first- and second-order spatial coherence across the barrier.

We present a kinetic theory for Bose-Einstein condensation of a weakly interacting atomic gas in a trap. Starting from first principles, we establish a Markovian kinetic description for the evolution towards equilibrium. In particular, we obtain a set of self-consistent master equations for mean fields, normal densities, and anomalous fluctuations. These kinetic equations generalize the Gross-Pitaevskii mean-field equations, and merge them consistently with a quantum-Boltzmann-equation approach.