We consider the coherent-population-trapping phenomenon in a thermal sodium atomic beam. We compare the different coherent-population-trapping schemes that can be established on the ${\mathrm{D}}_1$ line using the Zeeman sublevels of a given ground hyperfine state. The coherent-population-trapping preparation is examined by means of a Hanle-effect configuration. The efficiency of the coherent-population-trapping phenomenon has been examined in presence of optical pumping into hyperfine levels external to those of the excited transition. We show that both the contrast and the width of the coherent population trapping resonance strongly decrease when the optical pumping rate is increased. In the experiment, the loss rate due to optical pumping has been controlled by means of a laser repump of variable intensity.

We propose a scheme to generate mesoscopic superpositions of two squeezed states of motion using a highly anisotropic two-dimensional trap in which the ion's motion is tightly bound in the Y direction. In our scheme, the ion is driven multichromatically by three codirectional laser beams along the X axis, as well as a resonant laser beam along the Y axis. We show that, with the appropriate chosen initial states, the desired states of motion are realized in the X direction when the system reaches its steady state, which is indicated by the extinction of the fluorescence from the ion.

The magnitude of the time autocorrelation function M between states excited by two Gaussian laser pulses is calculated for both hydrogen and rubidium atoms in parallel electric and magnetic fields. M is determined by a full quantum-mechanical calculation but the peaks are identified with the periods of the shortest periodic orbits of the corresponding classical system. Qualitative agreement is obtained with experimental results, however, discrepancies are found in the relative heights of the peaks.

The ionization of hydrogen atoms in a circularly polarized (CP) microwave field is studied using classical mechanics and simulations. We first focus on the ionization of circular orbits in a model two-dimensional atom for which there have been previous simulations and studies. It has been suggested that in the ionization of both circular and elliptical states collisions with the nucleus play only a minor role. However, the ionization of circular states, in particular, is known to be strongly dependent on the details of the microwave pulse shape. We explain this observation and show that, in some cases, essentially the entire initial ensemble of atoms is ionized during the rise time of the microwave field. Under these conditions, atoms are switched directly into unbound parts of phase space and promptly scatter to infinity without collisions with the nucleus—succinctly, the rise time of the pulse is responsible for the vast majority of ionization events. We identify the conditions leading to this situation based on analytical and numerical studies of the behavior of the Jacobi constant K (energy in the rotating frame) during the rise time of the field. A large number of classical simulations are presented not only for initially circular states but also for states of medium eccentricity. For orbits that survive the pulse rise time these computations support a model of ionization that involves collisions with the core. We argue that the complexity of the ionization of hydrogen atoms in CP microwaves can be ascribed to the fact that orbits of different initial eccentricity in the original ensemble are not only switched to different regions of phase space, but also to different values of the Jacobi constant, during the rise time of the pulse.

The time evolution of atomic and molecular systems driven by periodic external fields is reformulated to combine Floquet's theorem with time-dependent representations of the atomic degrees of freedom. This approach increases the flexibility of Floquet calculations of multiphoton processes in strong radiation fields, particularly at low frequencies, by incorporating adiabatic states into the basis. The depopulation of Rydberg states of He and Na in strong microwave fields illustrates the utility of the method. In particular, a study of the depopulation of the 11s state of Na in an oscillatory field reveals a strong correspondence between dc-field Stark maps and quasienergy spectra and predicts a resonance feature associated with Landau-Zener transitions between dc Stark levels.

Laser-assisted electron-helium scattering is studied by perturbation theory for electron energies ⩽2.6 eV and ${\mathrm{CO}}_2$ laser intensities ⩽1×${10}^6$ W/${\mathrm{cm}}^2$. A model potential is adopted that gives a good description of the field-free elastic scattering. Results are presented for one- and two-photon processes. It is found that absorption cross sections are larger than those for emission. The dependences on electron energy at zero energy for absorption and at the nω thresholds for emission are analyzed. The elastic scattering within the laser pulse is discussed and related to a general sum rule involving the n-photon process probabilities.

A simple analytical solution for the problem of multiphoton detachment from negative ions by a linearly polarized laser field is found. It is valid in the wide range of intensities and frequencies of the field, from the perturbation theory to the tunneling regime, and is applicable to the excess-photon as well as near-threshold detachment. Practically, the formulas are valid when the number of photons is greater than one. They produce the total detachment rates, relative intensities of the excess-photon peaks, and photoelectron angular distributions for the hydrogen and halogen negative ions, in agreement with those obtained in other, more numerically involved calculations in both perturbative and nonperturbative regimes. Our approach explains the extreme sensitivity of the multiphoton detachment probability to the asymptotic behavior of the bound-state wave function. Rapid oscillations in the angular dependence of the n-photon detachment probability are shown to arise due to interference of the two classical trajectories, which lead to the same final state after the electron emerges at diametrically opposite sides of the atom when the field is close to maximal.

Ultracold atom collisions in the presence of a linearly polarized blueshifted laser field are studied theoretically. An analytical solution is presented within the framework of the Landau-Zener approximation. The effect of incomplete shielding is mostly accounted for by incorporating the three-dimensional character of the collisions, using a partial-wave analysis with space degeneracy. A model of two electronic states, including effects of indistinguishability of the colliding atoms, is used. The model associates the incomplete shielding with a process involving two crossing points. The theory is applied to the case of metastable xenon traps, obtaining a fair agreement with the experimental data.

Precision measurements on the 5s${\mathrm{}}^2$${\mathrm{S}}_{1\mathrm{/}2}$→5p${\mathrm{}}^2$${\mathrm{P}}_{\mathrm{j}}$→8s${\mathrm{}}^2$${\mathrm{S}}_{1\mathrm{/}2}$ two-photon, two-color polarization spectrum in atomic Rb are reported. As a result of interference between the transition amplitudes for the process, the spectrum is strongly frequency and linear polarization dependent in the vicinity of the 5s${\mathrm{}}^2$${\mathrm{S}}_{1\mathrm{/}2}$→5p${\mathrm{}}^2$${\mathrm{P}}_{1\mathrm{/}2}$ and 5s${\mathrm{}}^2$${\mathrm{S}}_{1\mathrm{/}2}$→5p${\mathrm{}}^2$${\mathrm{P}}_{3\mathrm{/}2}$ resonance transitions, with the linear polarization degree varying from nearly +100% to -100% over the approximate 500-${\mathrm{cm}}^{\mathrm{-}1}$ range of the data. For absorption of two collinearly polarized photons, complete destructive interference for the process occurs at a critical detuning from the 5s${\mathrm{}}^2$${\mathrm{S}}_{1\mathrm{/}2}$→5p${\mathrm{}}^2$${\mathrm{P}}_{3\mathrm{/}2}$ resonance transition given by ${\mathrm{\Delta }}_{\mathrm{c}}$=-155.83(3) ${\mathrm{cm}}^{\mathrm{-}1}$. The location of ${\mathrm{\Delta }}_{\mathrm{c}}$ is determined primarily by the relative transition matrix elements through the 5p${\mathrm{}}^2$${\mathrm{P}}_{\mathrm{j}}$ multiplet, but also depends significantly on contributions from more energetic np${\mathrm{}}^2$P levels. The null in the excitation occurring at the critical frequency allows experimental determination of a type of sum rule that depends only on the atomic matrix elements and the value of ${\mathrm{\Delta }}_{\mathrm{c}}$. Such sum rules are defined and presented for the present experiment in Rb and for a recent similar experiment in Na.

We observe microwave multiphoton transitions in Rydberg states of Na using intense subnanosecond half-cycle electric field pulses in a microwave transmission line. Transition probabilities from ns and nd states, ranging in principal quantum number from 18 to 40, to nearby nl (l⩾2) states are measured both as a function of pulse amplitude and the delay between two identical temporally spaced pulses. The transition rate depends strongly on both the pulse amplitude and the temporal delay between the two pulses. Nearly 100% of the population can be transferred for certain amplitudes of the half-cycle pulse. Transition probabilities are successfully described both with a dynamic Stark model and direct numerical integration of the time-dependent Schrödinger equation. Ramsey interference between two delayed pulses is observed that shows strong-field behavior. The two-pulse experiment is a technique for high-order multiphoton spectroscopy without concern for ac Stark shifts.

Recent experiments have used forced evaporative cooling to produce Bose-Einstein condensation in dilute gases. The evaporative cooling process can be optimized to provide the maximum phase-space density with a specified number of atoms remaining. We show that this global optimization is approximately achieved by locally optimizing the cooling efficiency at each instant. We discuss how this method can be implemented, and present the results for our ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ trap. The predicted behavior of the gas is found to agree well with experiment.

We study a nonlinear semiclassical and fully quantum-mechanical theory of a laser with an active medium of three-level atoms that may be initially prepared in a coherent superposition and interact with a classical external electromagnetic field. In particular, we determine the intracavity and output photon statistics of the laser light in a broad range of parameters. We find an inner sub-Poissonian statistics with a Mandel parameter close to the minimal value -1 when the laser is operating with initially prepared atoms, off resonant, and without inversion of the populations. In another regime, with, however, less favorable intracavity statistics, we find squeezing in the intensity output fluctuations of 80%, which is well above the present state of art noise reduction for this kind of coherently driven laser system.

In earlier papers, the linewidth of a micromaser was approximated by a phase diffusion rate that was obtained using a single decay rate assumption to model the decay of the electric field in the micromaser cavity. These methods gave analytic but approximate answers. Exact methods calculated the spectrum via the two-time correlation function, but required extensive numerical calculations. In this paper, we present an approximate analytic derivation of the micromaser spectrum via the two-time correlation function that is more accurate than other approximate analytic methods yet requires much less numerical calculation than the exact methods. We also review the other methods, both analytical and exact, and present numerical comparisons.

A precessing vector model has been developed for the geometrical interpretation of the adiabatic following and the optimal detuning methods, which play a decisive role in coherent population transfer in a three-level system. In our model, the Bloch vector defined by a population inversion and two-photon coherence components precesses about the torque vector consisting of an effective Rabi frequency and detuning components. The Bloch vector traces out different routes depending on combinations of the time delay of two laser pulses and detunings from the resonant frequencies. For the extreme cases where the optimal detuning with zero delay and the optimal delay with zero detunings are taken, our vector model with analytical solutions is compared with numerical solutions.

The free-induction decay (FID) after saturation by a laser radiation pulse of finite duration is studied for systems with spectral diffusion. The exact solution of the FID signal shape has been obtained in the framework of a model of noncorrelated spectral exchange. The analysis accounts for the finite duration of the saturating field and is valid at an arbitrary value of the spectral exchange rate and amplitude of the coherent field. An exact expression for the FID signal is derived in the weak-external-field limit. A self-consistent explanation of the experimental field dependence of the FID rate [A. Szabo and T. Muramoto, Phys. Rev. A 39, 3992 (1989)] is obtained using a model of slow noncorrelated spectral diffusion.

This article addresses the problem of whether it is possible to describe the effect of the atoms of material media on the field only in terms of a dielectric constant, in the regime where the field has to be treated quantum mechanically. Using a simple model of a linear lossless material medium, we start from first principles and determine the validity of the approximations required to obtain such a quantum analogue of classical macroscopic electrodynamics. This theory is derived here from the fundamental microscopic QED description of a medium, in terms of its constituent atoms in the vacuum, by taking macroscopic averages of the dynamical variables. The condition of the validity of the macroscopic approximation is obtained as the proviso for neglecting the contribution of the atoms of the medium to the quantum noise of the field. We show that macroscopic averaging is compatible with a quantum theory and does not imply any smoothening of the intrinsic quantum fluctuations of the field. Although this theory is based on a simple one-dimensional model of a single-mode cavity, it is able to describe the frequency dependence of the dielectric constant.

We show that it is possible to produce superpositions of distinct coherent states (even or odd coherent states) in a cavity where the field is pumped by two-photon parametric amplification and simultaneously undergoes two-photon absorption by a beam of three-level atoms that travel through the cavity interacting with the cavity field. Previous studies modeled the absorber with an effective Hamiltonian without involving real atomic excitation or entanglement, a procedure justified only for weak coupling of the two-photon absorbing atoms. We examine the validity of this assumption by modeling the atomic absorber dynamics from the onset. In order to study the system numerically we make use of a Monte Carlo wave-function method in which the two-photon absorbing atoms can interact with the cavity and evolve with large Rabi angles.

In this paper we review the development of a soft-x-ray laser at 21.2 nm, recently carried out at the Laboratoire de Spectroscopie Atomique et Ionique. Amplification is generated by electron collisional pumping on a ${2\mathrm{s}}^2$${2\mathrm{p}}^5$3p-${2\mathrm{s}}^2$${2\mathrm{p}}^5$3s, J=0–1 transition in neonlike zinc (${\mathrm{Zn}}^{20+}$). The lasing medium is a ∼150 μm×2 cm line plasma produced by irradiating slab Zn targets at a net intensity of ∼1.4×${10}^{13}$ W ${\mathrm{cm}}^{\mathrm{-}2}$, using a 1.06-μm, 600-ps-long pulsed laser delivering ∼350 J of net energy on the target. Accompanying the driving pulse by a 100-mJ-level prepulse train through deliberately imperfect isolation of the mode-locked laser oscillator, the J=0–1 gain coefficient ∼5 ${\mathrm{cm}}^{\mathrm{-}1}$ is generated. The emission appears in an ∼100-ps burst and precedes the lasing on both the much weaker J=2–1 lines and the x-ray continuum peak. The J=0–1 output source region, the beam spatial profile, and its time history have been measured and their relevance to the kinetics of this lasing system is discussed. A half cavity was implemented and a strong double-pass amplification at 21.2 nm with a 2-cm-long plasma obtained. With the gain-length product achieving ∼17.3 according to the particular configuration, saturation was demonstrated, which is confirmed through a schematic model of the level kinetics. To our knowledge, it is the first neonlike soft-x-ray laser where saturation on the J=0–1 line was achieved by using a half-cavity arrangement. Absolute energy measurements indicate ∼400 μJ in the half-cavity-generated beam and a peak output power of ∼5 MW, which makes this laser one of the most efficient soft-x-ray lasing systems demonstrated to date.

We discuss a system comprising a cavity with a nonlinear medium of k-order and an external coherent field excitation. We assume that the cavity field was initially in vacuum state. We show that for the case of weak external field our system behaves similarly to one described in finite-dimensional Hilbert space. Moreover, we perform numerical calculations simulating the dynamics of our system and compare the results with those of analytical attempts.

In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the detection process by calculating the auto-correlation and cross-correlations of the signal and idler beams. Four recent experiments are analyzed in detail: interference on a screen, Franson's experiments [Phys. Rev. Lett. 62, 2205 (1989)], Rarity and Tapster's experiments [Phys. Rev. Lett. 64, 2495 (1990)], and induced coherence without induced emission [X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991)].