When an atom propagates through a dilute medium, the wave that describes its propagation is modified by the interaction with the medium. In the present paper, we propose to treat this modification by introducing an index of refraction. This is a natural extension of this idea so familiar for light propagation, and such an extension has already been made in the case of neutrons in dense matter. Various interesting consequences of this idea are explored, most particularly in the case of ultracold atoms as the refraction index diverges in the quantum threshold limit.

The far-field angular distributions of high-order harmonics of a 1054-nm laser, with orders ranging from the lower teens to the upper thirties, have been measured in thin, low-density Ar, Kr, and Xe targets. The 1.25-times-diffraction-limited, 1.4-ps-duration, Gaussian laser pulses were focused to intensities ranging from 3×${10}^{13}$ to 3×${10}^{14}$ W/${\mathrm{cm}}^2$, using f/70 optics. A gas target localized the gas distribution near the laser focus to a thickness of about 1 mm at pressures as low as 0.3 Torr. The weak focusing geometry and the low gas pressures created experimental conditions for which the harmonics could be thought of as emerging from a plane at the laser focus rather than a three-dimensional volume. The far-field distributions of nearly all of the harmonics exhibit narrow central peaks surrounded by broad wings of about the same angular divergence as the emerging laser beam. The spatial wings are due to an intensity-dependent phase variation among the dipole moments of the individual target atoms. This phase variation gives rise to broad spatial interferences in the scattered light due to the radial and temporal variation of the laser intensity.

We present a time-independent generalized Floquet approach for nonperturbative treatment of high-order harmonic generation (HG) in intense onea (i) determination of the complex quasienergy eigenvalue and eigenfunction by means of the non-Hermitian Floquet formalism, wherein the Floquet Hamiltonian is discretized by the complex-scaling generalized pseudospectral technique [Wang, Chu, and Laughlin, Phys. Rev. A 50, 3208 (1994)], and (ii) calculation of the HG rates based on the approach that implies the classical treatment of the electromagnetic field and quantal treatment of the atom. The method is applied to the nonperturbative study of HG by the hydrogen atom in strong laser fields with the fundamental frequencies 532 and 775 nm and their third harmonics. The results show a strong dependence on the relative phase δ between the fundamental frequency field and its harmonic. For the intensities used in calculations (1×${10}^{13}$ and 5×${10}^{13}$ W/${\mathrm{cm}}^2$ for the fundamental frequency 532 nm and 1×${10}^{13}$ and 3×${10}^{13}$ W/${\mathrm{cm}}^2$ for the fundamental frequency 775 nm, the harmonic intensity being 10 and 100 times weaker), the total photon emission rate has its maximum at δ=0 and minimum at δ=π. However, this tendency, while valid for the first several HG peaks, is reversed for the higher HG peaks. The HG spectrum for δ=π is broader and the peak heights decrease more slowly compared to the case of δ=0. These results have their analog in the multiphoton above-threshold detachment study performed recently for ${\mathrm{H}}^{\mathrm{-}}$ ions [Telnov, Wang, and Chu, Phys. Rev. A 51, 4797 (1995)].

We investigate the modal structure of Schrödinger’s equation in several evanescent light-wave gravitational traps. Three configurations are proposed that optically confine an atom inside an atom-mirror cavity: a cubical, a pyramidal, and a conical gravitational trap.

We describe planar and mostly planar current geometries for constructing microscopic magnetic traps for neutral atoms. These geometries are well-suited for fabrication from superconductors using standard microfabrication techniques. Magnetic-field gradients greater than 5×${10}^5$ G/cm, and field curvatures greater than ${10}^8$ G/${\mathrm{cm}}^2$ can be produced in microscopic traps. Trap loading could be accomplished by constructing a nested series of traps, and compressing atom clouds from larger traps into smaller ones. In the smallest magnetic microtraps the motional ground-state energy of atoms in the trap can exceed the recoil energy from resonant photons, which may allow direct laser cooling to the trap ground state. If a number of atoms can be simultaneously cooled to the ground state, the resulting ‘‘Bose clusters’’ should exhibit interesting optical behavior, since their spatial extent would be less than the resonant light wavelength.

Results of a theoretical investigation of two-photon, two-color excitation and linear depolarization spectra in atomic cesium are presented. The case of two-beam excitation, where one photon is absorbed through a quadrupole amplitude and the other through a dipole amplitude, is considered. When excitation is through a spin multiplet, the final-state population produced depends sensitively on the relative transition amplitudes through the nondengenerate spin-multiplet terms. In addition, the transition rate contains interference terms depending on the relative directions of the two beams. These terms are manifested strongly when the intermediate states are nonresonant and when the two beams have approximately the same frequency. Application of the results to the 6s${\mathrm{}}^2$${\mathit{S}}_{1/2}$→5d${\mathrm{}}^2$${\mathit{D}}_{\mathit{j}}$→11p${\mathrm{}}^2$${\mathit{P}}_{3/2}$, quadrupole-dipole transition in atomic Cs is made. Polarization-dependent excitation spectra are presented for this case. Effects of hyperfine interactions are also considered.

The superadiabatic basis scheme developed by Berry [Proc. R. Soc. London 429, 61 (1990)] is used to analyze adiabatic population transfer in the Λ system in what is known as the counterintuitive pulse scheme. For a specific choice of pulses, we find that the diabatic loss is given by the exponentially small (8-4√2)exp(-2/ε), where ε is a small parameter describing the adiabaticity of the process. We thus establish the connection between population transfer in the Λ system and general adiabatic transition theory. We project numerical solutions onto superadiabatic basis states for the real three-level system and show how the history of population transfer has a very compact and universal history in one particular superadiabatic basis.

We investigate the phase-space dynamics of a hydrogenic atom in a very intense, high-frequency laser field, by comparing the time-dependent quantum Wigner functions with the corresponding classical distributions calculated using the Monte Carlo method. In both cases we model the atom by a one-dimensional soft-core potential in order to simplify the calculation. We demonstrate the importance of nonclassical interferences in the Wigner function and show how negative parts of it observed at the peak of the pulse are associated with the formation of a coherent superposition of dressed ‘‘Kramers-Henneberger’’ (KH) eigenstates. These signatures of the quantum dynamics are eliminated towards the end of the pulse when the coherence between the KH eigenstates degrades so that the classical and the quantum mechanical phase-space distributions come into agreement.

A perturbative distorted-wave theory is presented here for evaluating weak-field two-photon spectra, collision-induced energy redistribution, and radiative escape rates, produced by radiatively damped optical collisions of atoms in ultracold atom traps. This theory complements and corroborates a complex-potential theory developed recently. Illustrations are given of the use of the present theory in producing various features of one-color or two-color photoassociation spectra, such as the excited-level bound-state resonance structure, or Condon diffraction in the continuum of the final level.

Rescattering effects in above-threshold ionization such that the electron is driven back to the ionic core by the laser field and rescatters are considered in a completely classical framework, for a laser field consisting of a linearly polarized monochromatic fundamental and its second harmonic, as a function of their relative phase. Several features appear, owing to the two-color field: the energies of the rescattered electrons extend up to 21${\mathit{U}}_{\mathit{p}}$, with ${\mathit{U}}_{\mathit{p}}$ the ponderomotive potential of the entire field; the angular distributions of the rescattered electrons are no longer symmetric with respect to an interchange of the backward and forward direction and more than one ring or side lobe may appear in either direction; the importance of rescattering can be deduced from the violation of a certain symmetry of the total above-threshold ionization rates for fixed energy with respect to the phase between the two fields; the spectra of the rescattered electrons change dramatically when the field intensity is raised from the multiphoton into the tunneling regime.

It is demonstrated that steerable bright spatial soliton pairs can be generated from Gaussian and hyperbolic secant initial profiles with spatially modulated amplitudes. The incident threshold amplitude, for the soliton pair generation, is obtained from a variational approach to the Zakharov-Shabat scattering problem [M. Desaix et al., Phys. Rev. E 50, 2253 (1994)]. It is shown, within the variational approximation, that a symmetric and real initial field distribution ${\mathit{U}}_0$(x), with an amplitude larger than the threshold value that satisfies the condition ${\mathrm{\int }}_{\mathrm{-}\mathrm{\infty }}^{+\mathrm{\infty }}$${\mathit{U}}_0$(x)dx=0, excites bright-soliton pairs. It is also found that an exact two-soliton solution of the nonlinear Schrödinger equation satisfies this condition.

Degenerate as well as nondegenerate three-level two-photon laser (TPL) models are derived. In the limit of equal cavity losses for both fields, it is shown that the nondegenerate model reduces to the degenerate one. We also demonstrate the isomorphism existing between our degenerate TPL model and that of a dressed-state TPL. All these models contain ac-Stark and population-induced shifts at difference from effective Hamiltonian models. The influence of the parameters that control these shifts on the nonlinear dynamics of a TPL is investigated. In particular, the stability of the periodic orbits that arise at the Hopf bifurcation of the system and the extension of the self-pulsing domains of the system are studied, revealing the role played by the detuning and ac-Stark parameters.

Cross focusing (defocusing), determined by the probe Kerr coefficient, which is defined as the derivative of the probe refractive index with respect to the pump intensity, is studied at points of probe nonabsorption and in the dead zone. Spatial control of the probe can be achieved not only by the probe Kerr coefficient itself but also by its strong variation with pump intensity at points of probe nonabsorption. This strong variation allows the pump beam to be used as a waveguide for the probe.

We have shown that (1+1′)-photon lasing without population inversion (LWOPI) can be achieved in a ${\mathrm{H}}_2$ molecule for emission from the lowest doubly excited autoionizing (AI) state of ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{}{}_{}{}^{}$ symmetry to the ground X${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{g}}$ (v=0,j=1) state in the presence of the resonant B${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}$ (v=4,j=2) level. We have considered both coherent and incoherent pumping of the AI state, which is the upper lasing level in this scheme. Coherent pumping of the AI state can be done by two-photon excitation from the ground to the AI state. Incoherent pumping of the AI state can be done by charge-transfer collision of a ${\mathrm{H}}_2^{+}$ ion with atomic and molecular species. For a weak coherent pumping field of intensity 6.4×${10}^7$ W/${\mathrm{cm}}^2$, a lower probe field [for the X${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{g}}$ (v=0,j=1)⇄B${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}$ (v=4,j=2) transition] of intensity 9.6×${10}^6$ W/${\mathrm{cm}}^2$ is required to obtain an appreciable gain. However, for stronger coherent fields of intensity 6.4×${10}^9$ W/${\mathrm{cm}}^2$, the lower probe intensity can be lowered by orders of magnitude without significant loss in gain. In this case, using a lower probe field of intensity 9.6×${10}^4$ W/${\mathrm{cm}}^2$, we have calculated the gain by the perturbative method. However, for a lower value of coherent field strength, 6.4×${10}^7$ W/${\mathrm{cm}}^2$, and a higher intensity of the lower probe field, 9.6×${10}^6$ W/${\mathrm{cm}}^2$, we have done nonperturbative calculations and have shown that LWOPI can be achieved only in a short range of probe pulse duration less than or equal to 3.45 ps. In all these cases, the optimum intensity for the upper probe field [for the B${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}$ (v=4,j=2)${\rightleftarrows }^1$${\mathrm{\Sigma }}_{\mathit{g}}$ transition] is 9.6×${10}^7$ W/${\mathrm{cm}}^2$. We have also compared the evolution of gain for the ${\mathrm{sech}}^2$(t/T)-shaped pulse with that for the square pulse, the pulse duration T=3.45 ps being the same in both cases.

We study the dynamics of photon-hopping conduction between impurity atoms in a photonic band gap via resonance dipole-dipole interaction (RDDI) in the low-excitation density limit. This is done both in the absence and in the presence of a localized dielectric defect mode. The random impurity atom positions are modeled by means of a Gaussian random distribution of RDDI’s with variance J and atomic line fluctuations with variance δ. By numerical calculation, we demonstrate the occurrence of a number of collective quantum features of photon-hopping conduction. These include collective enhancement of the energy-transfer rate and collectively induced transparency within the dielectric cavity mode. These effects are shown to depend sensitively on the variances J and δ. Our results suggest that RDDI mediated hopping conduction may protect atomic excitation energy from dissipation through nonradiative relaxation channels.

We have carried out an investigation of the globally coupled laser array with randomly spread eigenfrequencies. It is shown that as this spread increases, either the laser action vanishes or the coherent steady-state regime is replaced by a phase-unlocked regime. The regions of the stable phase locking have been analytically and numerically determined. It is found that the gain inertia leads to cooperative phase-locking effects when the maximum detuning is close to the relaxation frequency.

The spectrum radiated by an initially excited two-level atom in a very-high-Q cavity is studied. We consider the situation where the frequency of the vacuum field cavity mode is varied time-dependently during Rabi cycles. Under the resonance condition where the modulation frequency is the same as the vacuum Rabi frequency, we show that the vacuum Rabi splitting can be further split into two doublets. The relative heights of spectral peaks are shown to depend on the modulation phase. Furthermore, we show that the interference between different spectral peaks can break the symmetry of the spectrum.

A mathematical stability analysis is presented of the two-beam interactions in quadratic optical nonlinear media that are now attracting such a lot of attention. The averaged Lagrangian is used, within a variational method, and the analysis is based upon a Gaussian trial function. The stability is governed by parameters that can be classified into two groups. One describes spatial solitonlike beam positions and propagation directions and the other describes beam sizes and phases. It is shown that the evolution of these parameters is determined by ten, coupled, ordinary differential equations. The stationary states are proved, mathematically, to be stable for all linear phase mismatch parameter values provided the perturbations are symmetric, i.e., perturbations to beam positions and directions. However, for perturbations to beam sizes or phases, it is proved that a number of stability regimes exist, together with forbidden parameter ranges. The analytical conclusions are completely borne out by computer simulations, and some typical examples are reported here.

Many laboratories have demonstrated significant amplification on the 2${\mathit{p}}^5$3p→2${\mathit{p}}^5$3s J=0→1 transition of Ne-like ions. The slow Z scaling of the energy of this transition suggests an efficient means of demonstrating saturation at xuv wavelengths. We present a detailed analysis of lasing in Ne-like Fe slab targets, especially considering the 255 Å J=0→1 transition, which is calculated to totally dominate the output. The calculations indicate that it is possible to saturate this line with driving energies ∼30 J, even allowing for the known tendency of calculations to overestimate the gain on this line. Such driving requirements represent more than an order of magnitude increase in efficiency from what has so far been accomplished using similar systems of comparable wavelength. Small-scale facilities with high repetition rates are capable of providing the necessary driving conditions.

Optical third-harmonic generation (THG) is generally a weak process but is dipole allowed, therefore it occurs in all materials, including dielectric materials with inversion symmetry. We report that when using focused high-intensity ultrashort laser pulses, this normally weak THG process becomes highly operative at a simple air-dielectric interface and is much stronger than the bulk of most dielectric materials. We characterized this nonlinear optical response at interfaces as a phenomenological surface-enhanced THG in transmission and/or in reflection. This surface THG is further cascaded in transmission or reflection from layered composite dielectric materials of a high-low index of refraction, resulting in a marked increase in photon conversion efficiency than that of a single interface. Although the present THG efficiency is lower than that of a typical phase-matching harmonic crystal, it is important to note that the surface-enhanced optical THG is a fundamental physical process occurring at all interfaces and is relatively free from the constraint of a phase-matching condition and wavelength restriction. Using optical THG at an interface, it becomes possible to generate wavelengths at which harmonic crystals are unavailable. These findings may lead to a new development of surface-enhanced studies and prompt a reexamination of the processes of high-harmonic generation at interfaces using a focused beam.