The reflection of metastable argon atoms from evanescent waves produced by total internal reflection and surface-plasmon excitation is investigated. We study the departure from ideal specular reflection by comparing our experimental results with a Monte Carlo simulation of the reflection process. The observed broadening of the reflection beam was found to be caused predominantly by fluctuations of the diple force. We show that the surface plasmon produces significant enhancement of the evanescent-wave intensity without degrading the quality of reflection. In addition, the number of spontaneous emissions occurring during the reflection process was investigated by comparing the reflectivity of evanescent-wave mirrors based on open and closed transitions in argon. An open-transition mirror selectively reflects atoms which do not undergo spontaneous emission. For a large detuning, the average number of spontaneous emissions for reflected atoms was <0.11.

We derive the equation of state of a dilute atomic Bose gas with an interatomic interaction that has a negative scattering length and argue that two continuous phase transitions, occurring in the gas due to quantum degeneracy effects, are preempted by a first-order gas-liquid or gas-solid transition, depending on the details of the interaction potential. We also discuss the consequences of this result for future experiments with magnetically trapped spin-polarized atomic gases such as lithium and cesium.

We report on an experimental study of the frequency dependence of the microwave ‘‘ionization’’ probability for laser-excited Rb(np${)}^2$${\mathit{P}}_{3/2}$(‖${\mathit{M}}_{\mathit{J}}$‖=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4–14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-μs interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-μs time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ‘‘ionization’’ that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ‘‘ionization’’ in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ‘‘ionization’’ probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.

A subset of the electrostatic modes of a cold cloud of electrons, a non-neutral electron plasma, trapped in a Penning trap has been observed and identified using a recent theoretical model. The detection of these modes is accomplished using electronic techniques which could apply to any ion species. The modes are observed in the low-density, low-rotation limit of the cloud where the cloud approaches a two-dimensional charged disk. We observe both axially symmetric and asymmetric drumhead modes. The shape, rotation frequency, and density of the cloud are found in a real-time nondestructive manner by measuring the frequency of these modes. In addition, it is found that radio-frequency sideband cooling compresses the cloud, increasing its density. The ability to measure and control the density of a trapped ion cloud might be useful for experiments on low-temperature ion–neutral-atom collisions, recombination rates, and studies of the confinement properties of non-neutral plasmas.

We have investigated high-density Rb optical pumping in polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ targets and present measurements of collisional relaxation rates and studies of diffusion-driven wall relaxation of the Rb polarization. We show that a boundary layer resides in the vicinity of the cell walls within which a polarization gradient is established by diffusion. Absorption of the incident laser radiation within this layer leads to a striking decrease in optical-pumping efficiency for resonant light but has little effect for off-resonant light. Our theory introduces polarization-dependent slowing of optical pumping rates due to the Rb nuclear spin. We have observed a strong frequency dependence of the optical-pumping efficiency, consistent with our theoretical predictions. We report the following rate constants for collisional relaxation of Rb polarization: due to Rb (${\mathit{k}}_{\mathrm{Rb}\mathrm{-}\mathrm{Rb}}$=8×${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^3$/s), due to ${\mathrm{N}}_2$ (${\mathit{k}}_{\mathrm{N}2\mathrm{}\mathrm{-}}$Rb=8×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^3$/s), and due to ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, an upper limit of (${\mathit{k}}^3$He-Rb≤2×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^3$/s). The data and model presented are used to predict laser power and intensity requirements for high-density polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ targets.

We present results from a time-dependent two-level-plus-continuum model of multiphoton ionization in order to better understand the short-pulse photoelectron spectrum resulting from multiphoton ionization and the role of intermediate states. Both resonant and nonresonant population transfer to the upper state are found to play an important role in the multiphonon ionization process. The dynamic modeling reveals the potential for broadening and shifting peaks in the photoelectron spectrum. However, we conclude that despite the complex dynamics of the excitation, short-pulse photoelectron spectra can be used to measure ac Stark shifts of both ponderomotively and nonponderomotively shifted states in strong laser fields.

Experimental data are presented showing the channel closing of four-photon ionization of Mg. It is shown that, for circularly polarized light, the ionization versus intensity spectra exhibit sharp breaks from the normal ${\mathit{I}}^4$ intensity dependence at the critical intensity where the channel closing occurs. Above the critical intensity, the population of Rydberg states which survives the laser pulse is observed. The residual Rydberg population is found to be greatly reduced for linearly polarized light due to the relatively large probability of ionization of the low-angular-momentum Rydberg states. The data are in good agreement with a model which includes averaging over the spatial profile of the laser.

High-order harmonic generation with KrF and Ti:sapphire lasers is analyzed with an emphasis on the contribution of multiply charged ions. It is confirmed that the intensity dependence of strong optical field ionization is explained by the Ammosov-Delone-Krainov (ADK) theory or by the barrier suppression ionization model regardless of the wavelength. The harmonic distributions are compared with the single-atom responses calculated using the short-range potential model with the effective interaction intensity determined by the ADK theory. From this analysis, we propose that for the KrF laser the harmonics above the 21st in Ne and above the 13th in Ar may be due to doubly charged ions.

We apply a fully-quantum-mechanical complex-potential model to calculate the S matrix to test the validity of semiclassical methods for describing collisions of ground and excited laser-cooled Cs, Na, or Li atoms in a magneto-optical trap (MOT). The model includes the role of bound-state resonances in closed channels when the collision energy is smaller than the detuning from the atomic cooling transition. The model also illustrates the factorization of the S matrix into inner and outer parts, as used in simpler semiclassical theories. Our fully quantum results agree with other calculations that demonstrate much smaller rate coefficients for Cs collisions at low temperature than predicted by a semiclassical optical-Bloch-equation treatment. We show that an even simpler semiclassical Landau-Zener model accurately describes the S matrix at MOT temperatures and below for a weak laser intensity. There is no evidence for any significant contribution from the off-resonant excitation that is prominent in local-equilibrium models. The effect of excited-state spontaneous decay during the collision is much less for the light species Li than for the heavy species Cs. Semiclassical models still work well for Li.

We show that in the cold collisions between laser-cooled and trapped atoms the probability to survive in the excited state during the collision can be obtained, in the weak-field limit, from a simple Landau-Zener approach. This is shown by comparing the method with a fully quantum and time-dependent wave-packet treatment. We also show that the optical Bloch equation method is not the proper semiclassical tool to use at low energies, at least in its present form. The unexpectedly low quantum survival probability reported by Boesten et al. [Phys. Rev. A 48, 1428 (1993)] is in fact predicted by the semiclassical Landau-Zener approach. This in turn shows that off-resonant excitation is not important in the low-energy regime.

When the wave function of a system which breaks up is represented on a complex basis, the norm of the wave function, if evaluated as a direct sum over the basis, remains unity only for as long as the continuum is not significantly populated. However, we show that if the norm is evaluated by Padé summation, it remains unity until one of the fragments leaves the region spanned by the basis; subsequently the norm drops to a value that is simply the probability for the system not to break up, i.e., to remain intact. The probability for breakup into a particular channel must be calculated before the ‘‘critical’’ time at which the norm drops. These remarks, and others, are illustrated numerically for the case of a hydrogen atom that is photoionized by a short pulse of light.

An analytical description of long-range collisions between atoms in a laser cooling field is developed. We begin by considering an N-atom master equation. In the regime of low atomic densities (i.e., where the mean distance between two atoms is much larger than the laser wavelength) it is possible to treat the atom-atom interactions in perturbation theory. Furthermore we assume temperatures which allow a semiclassical treatment of the cooling process. The effect of the presence of other atoms can be separated analytically into two parts; an attenuation force due to the absorption of the laser beams in the atomic cloud similar to the results of Dalibard [Opt. Commun. 68, 203 (1988)], which tends to compress the atomic cloud, and a two-atom force due to photon emission and absorption cycles between different atoms. This force proves to be repulsive for the configurations studied and prevents the cloud from collapsing. The result for the first-order perturbation expansion in collision strength generalizes the model proposed by Walker, Sesko, and Wieman [J. Opt. Soc. B 8, 946 (1991)] by including additional terms, such as those associated with Raman couplings.

We present a calculation of the probe absorption spectrum of atoms in a one-dimensional optical molasses formed by a pair of counterpropagating, cross-polarized fields. When the finite angle θ between the propagation direction of a probe field and that of one of the cooling fields is taken into account, we find that, apart from the contributions to the probe absorption signal that are related to the Raman and Rayleigh resonances between the discretized atomic motional states in the molasses direction, there is also a signal arising from the recoil-induced resonances between atomic states with different center-of-mass momenta in the directions transverse to the molasses beams. The magnitudes of these different contributions are compared.

Photon-emission spectra of the ${\mathrm{H}}_2^{+}$ molecular ion in an intense, linearly polarized laser field (wavelength λ=1064 nm and intensities ${10}^{13}$≤I≤${10}^{14}$ W/${\mathrm{cm}}^2$) have been calculated using an exact method and compared to two-level models. The exact calculation requires solving a three-dimensional time-dependent Schrödinger equation which allows a full treatment of all the electronic states of ${\mathrm{H}}_2^{+}$ as a function of the internuclear separation R. Three separate excitation regions can be defined which are associated with the 1${\mathrm{\sigma }}_{\mathit{g}\mathrm{-}}$1${\mathrm{\sigma }}_{\mathit{u}}$ charge-resonant (CR) transition of the ${\mathrm{H}}_2^{+}$ molecular ion: (1) for small R, the multiphoton excitation region; (2) for intermediate R, the near-resonant excitation region; and (3) for large R, the strong-coupling region. Two- and three-level models are used for the description of these excitations of the CR states. We will show in this work that (a) in the multiphoton excitation region, an approximate solution of the laser-driven CR states is given by WKB solutions of a Mathieu equation; (b) in the near-resonant region, Rabi or Mollow triplets are obtained for all the harmonics; and (c) in the strong-coupling region, an analytic two-level solution for the CR state excitation reproduces well the exact results. The effects of ground-continuum coupling and ionization is shown to be important for laser intensities I≥${10}^{14}$ W/${\mathrm{cm}}^2$.

The spectral filtering of a field with strong quantum correlations is studied. The changes in the correlation characteristics of a field, produced by a down converter, passing through a strongly dispersive element like a Fabry-Pérot cavity, are calculated. In the special case when the central frequency of the idler and signal photons coincides with the resonance frequency of the cavity, there is a cancellation of the dispersive effects of the cavity. Detailed numerical results for the two-photon joint counting rate are presented. The effects of the absorption in the medium on the two-photon correlations are also discussed.

To examine prospects for gain in a Lyman-α recombination laser driven by a high-intensity, short-pulse laser, we calculate the residual energy in both hydrogen and helium during recombination after the ionizing pulse. The expected gain as a function of residual energy and density is then separately evaluated. The residual energy calculation includes above-threshold ionization (ATI) in the presence of a background plasma, as well as inverse-bremsstrahlung heating. At electron densities over ${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$ but below critical density, the plasma reduces the ATI energy by approximately a factor of 2, but without a previously reported dependence on the pulse width. Inverse-bremsstrahlung heating can be significant, but is not dominant for the parameters considered. Detailed recombination-laser gain calculations were performed for the Ly-α transitions of both H and He, using Stark profiles to represent the laser line cross section. To obtain gain of near 2 ${\mathrm{cm}}^{\mathrm{-}1}$ lasting at least a few ps, the H plasma temperature must be less than 3.5 eV and electron density between 4×${10}^{17}$ and 4×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$; for He, the temperature must be less than 15 eV and the electron density between 2×${10}^{18}$ and 2×${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$. Our calculations indicate that these conditions can be satisfied for H, if the driving laser intensity is above 4×${10}^{14}$ W ${\mathrm{cm}}^{\mathrm{-}2}$, and for He, if the laser intensity is above 1.7×${10}^{16}$ W ${\mathrm{cm}}^{\mathrm{-}2}$ and the wavelength is below 0.6 μm.

A codimension-two Hopf bifurcation and the coexistence of multiple attractors of a two-photon laser with an injected signal are investigated. The quasiperiodic motion with two incommensurate frequencies (2-torus) may arise directly from a stationary solution through the type-III codimension-two bifurcation mechanism. We analyze conditions and identify the quasiperiodic motion in terms of time-dependent solutions and Poincaré maps. Moreover, the coexistence of multiple attractors in the vicinity of the type-III bifurcation point and the symmetry-breaking bifurcation can be observed as well.

We theoretically analyze doubly resonant infrared-visible sum-frequency (DR IVSFG) and difference-frequency generation (DR IVDFG) from a monolayer of adsorbates at an interface. Our calculated results with a model molecule indicate that the resonant amplitude of nonlinear optical susceptibility of DR IVDFG and DR IVSFG processes conveys information about the electron-vibration coupling in adsorbates. Moreover, owing to a dephasing-rephasing procedure involved, DR IVDFG can also be developed into a sensitive probe for investigating the coherent phase relaxation process in adsorbed molecules without the complication of inhomogeneous broadening.

The scalar analog of electromagnetism in one dimension is discussed with reference to a cavity formed by a distribution of dielectric material with dielectric constant ε̃(x,ω). Provided that for large ω, ε̃(x,ω) or its spatial derivative of any order has a discontinuity in x at the edge of the cavity (e.g., the interface between two materials), the discrete quasinormal modes (QNM’s) of the system are shown to form a complete set inside the cavity. In terms of these, time-independent perturbation of the dielectric constant can be formulated. Both the completeness relation and the perturbative series are verified explicitly, for example, in the context of which the QNM’s are also analyzed and shown to belong to two classes: those that are intrinsically absorptive (which decouple when the absorption is switched off) and those that are intrinsically leaky in character.

A computer simulation of the ${\mathrm{Er}}^{3+}$ 3-μm crystal laser considering the full rate-equation scheme up to the ${}_{}{}^4{}_{}{}^{}$${\mathit{F}}_{7/2}$ level has been performed. The influence of the important system parameters on lasing and the interaction of these parameters has been clarified with multiple-parameter variations. Stimulated emission is fed mainly by up-conversion from the lower laser level and in many cases is reduced by the quenching of the lifetime of this level. However, also without up-conversion a set of parameters can be found that allows lasing. Up-conversion from the upper laser level is detrimental to stimulated emission but may be compensated by cross relaxation from the ${}_{}{}^4{}_{}{}^{}$${\mathit{S}}_{3/2}$ level. For a typical experimental situation we started with the parameters of ${\mathrm{Er}}^{3+}$:${\mathrm{LiYF}}_4$. In addition, the host materials ${\mathrm{Y}}_3$${\mathrm{Al}}_5$${\mathrm{O}}_{12}$ (YAG), ${\mathrm{YAlO}}_3$, ${\mathrm{Y}}_3$${\mathrm{Sc}}_2$${\mathrm{Al}}_3$${\mathrm{O}}_{12}$ (YSGG), and ${\mathrm{BaY}}_2$${\mathrm{F}}_8$, as well as the possibilities of codoping, are discussed. In view of the consideration of all excited levels up to ${}_{}{}^4{}_{}{}^{}$${\mathit{F}}_{7/2}$, all lifetimes and branching ratios, ground-state depletion, excited-state absorption, three up-conversion processes as well as their inverse processes, stimulated emission, and a realistic resonator design, this is, to our knowledge, the most detailed investigation of the ${\mathrm{Er}}^{3+}$ 3-μm crystal laser performed so far.