We generalize the recently formulated theory of high-order harmonic generation by low-frequency laser fields to the case of high-order sum and difference frequency mixing in a two-color field of noncommensurate frequencies in the optical-infrared regime. Our theoretical description includes both the single-atom response and propagation. We observe a different behavior of the sum and difference frequency mixing processes, in the single-atom response as well as in the propagation results. The results of our calculations including propagation compare very well with recent experimental observations. © 1996 The American Physical Society.

A method enabling atomic velocity class selection by means of quantum interference in the two-photon ionization of an atom through two quasiresonant intermediate levels is studied. This method is compatible with the Doppler cooling in optical molasses, and it is able to attain temperatures colder than the Doppler limit. The advantages and limitations of this method are discussed. We study the effect of the competition with the Doppler cooling for temperatures lower than the Doppler limit, when the usual Doppler process heats the atoms rather than cools them. The method is shown to be limited essentially by the loss of ground-state atoms due to ionization. We also propose and study a ‘‘source’’ scheme in which new atoms are continuously injected into the system, leading to a nonvanishing stationary number of cold atoms. Finally, we propose generalizations of the method that allows us to combine it with Sisyphus-type mechanisms. © 1996 The American Physical Society.

The leading radiation forces acting on an atom or ion subject to linearly polarized Laguerre-Gaussian (LG) light are studied. Particular emphasis is laid on the orbital angular momentum effects associated with LG light. The optical Bloch equations appropriate for the adiabatic approximation are derived and used to evaluate the forces and associated torque governing the atomic motion. The steady-state dynamics of the atom are explored for atoms subject to a single beam and multiple independent counterpropagating beams. The main features responsible for the dynamics of the atom, together with the dipole potentials characteristic of Laguerre-Gaussian light, are identified and discussed. The theory is illustrated by the numerical integration of the equation of motion for ${\mathrm{Mg}}^{+}$ ions in various beam configurations. This yields information on trajectories, velocity evolution, and vibrational frequencies at potential minima. Interesting effects involving a reciprocal interplay between motions in orthogonal directions are demonstrated. Such features are purely dependent on the orbital angular momentum property of the light. Their possible use in controlling atomic motion is investigated. © 1996 The American Physical Society.

Two-color radiation has been used to investigate the physical mechanism of intense-field ionization. One color was the second harmonic of the other, and there was a well-defined phase between them which was calibrated absolutely. We measured the photoelectron yield from above-threshold ionization of krypton and xenon as this phase was varied. We show that the phase-dependent signature of tunnel ionization is present even though the electron spectra are clearly multiphoton in character. We also use the two-color phase as a probe to show evidence for core scattering during the ionization process. © 1996 The American Physical Society.

The theory of light-induced current (LIC) in plasma, and the results of experimental investigation of this effect are presented. The current was induced by laser radiation in helium and hydrogen rf discharge. The measured magnitude of this current was 1 μA in helium and 0.04 μA in hydrogen plasma. The theoretical estimations of LIC magnitude, its dependence on laser frequency detuning, and gas pressure are found to be in good agreement with experimental data. The application of LIC in measuring ionization and transport collision rates of excited atoms is also discussed. A light-induced current may have been an important mechanism in the magnetic field generation in stellar atmospheres, in particular, in the solar atmosphere. © 1996 The American Physical Society.

We investigate both theoretically and experimentally an elementary Sisyphus process occurring during the reflection of an atom onto a laser evanescent wave propagating at the surface of a dielectric prism. Cesium atoms bouncing at normal incidence may undergo a spontaneous Raman transition between their two hyperfine levels; this leads to an efficient cooling since those levels are light shifted by a different amount by the laser-atom interaction thanks to the large hyperfine splitting. We compare the measured final energy distributions after the bounce with Monte Carlo simulations. A quantitative agreement is obtained when the van der Waals interaction between the cesium atoms and the dielectric prism is taken into account. © 1996 The American Physical Society.

Using a complex basis-set expansion of the electronic wave function, we have calculated the induced shifts and widths of the first few electronic Σ levels of the ${\mathrm{H}}_2^{+}$ molecular ion in the presence of a dc field, over a range of internuclear separations. We have also calculated, through order ${\mathrm{\omega }}^2$, the shifts and widths of the 1s and 2p levels (we use the field-free united-atom-limit quantum numbers) when an ac field of low frequency ω is present. In accord with Zuo and Bandrauk [Phys. Rev. A 52, R2511 (1995)], we find that the 2p ionization width exhibits peaks as the internuclear separation is increased. We attribute these resonances to the mixing of the 2p state, which is localized in the higher well of the double-well electronic potential, with energetically nearby highly excited states that are localized in the lower well; over-the-barrier ionization from the lower well can proceed without the impediment of backscattering of the electron from the hump between the wells. Finally, we have calculated shifts and widths of various vibrational levels of the electronic ground state and the threshold intensities for dissociation of ${\mathrm{H}}_2^{+}$ from some of these vibrational levels. We compare our results with the threshold intensity measured by Ilkov et al. [Phys. Rev. A 51, R2695 (1995)] at the ${\mathrm{CO}}_2$ laser wavelength. © 1996 The American Physical Society.

We present an exact expression for the evolution of the wave function of N interacting atoms in an arbitrarily time-dependent, d-dimensional parabolic trap potential ω(t). The interaction potential between atoms is taken to be of the form ξ/${\mathit{r}}^2$ with ξ>0. For a constant trap potential ω(t)=${\mathrm{\omega }}_0$, we find an exact, infinite set of relative mode excitations. These excitations are relevant to the linear response of the system; they are universal in that their frequencies are independent of the initial state of the system (e.g., Bose-Einstein condensate), the strength ξ of the atom-atom interaction, the dimensionality d of the trap, and the number of atoms N. The time evolution of the system for general ω(t) derives entirely from the solution to the corresponding classical one-dimensional single-particle problem. An analytic expression for the frequency response of the N-atom cluster is given in terms of ω(t). We consider the important example of a sinusoidally varying trap perturbation. Our treatment, being exact, spans the ‘‘linear’’ and ‘‘nonlinear’’ regimes. Certain features of the response spectrum are found to be insensitive to interaction strength and atom number. © 1996 The American Physical Society.

We propose a scheme for generating mesoscopic superpositions of two distinguishable pair coherent states of motion in a two-dimensional ion trap. In our scheme, the trapped ion is excited bichromatically by five laser beams along different directions in the X-Y plane of the ion trap. Four of these have the same frequency and can be derived from the same source, reducing the demands on the experimentalist. We show that if the initial vibrational state is given by a two-mode Fock state, as demonstrated in recent experiments, these highly correlated two-mode ‘‘Schrödinger cat’’ states are realized when the system reaches its steady state, which is indicated by the extinction of the fluorescence emitted by the ion. © 1996 The American Physical Society.

In this paper we examine some effects of quantum interference on high harmonic generation. We demonstrate in particular that preparing the initial state in a coherent superposition of bound states leads to a harmonic spectrum with distinct plateaus with different conversion efficiencies. We show how this scheme may provide a way of controlling the coherent output that is produced in an experiment. © 1996 The American Physical Society.

An earlier study of the 6s${\mathrm{}}^2$${\mathit{S}}_{1/2}$→5d${\mathrm{}}^2$${\mathit{D}}_{\mathit{j}}$→11p${\mathrm{}}^2$${\mathit{P}}_{3/2}$ two-photon, dipole-quadrupole transition in Cs is extended by including the effect of an external static electric field. The dependence of the absorption spectrum on the relative polarizations of the two light sources is found to be greatly modified by a moderately sized electric field, the predominant effect being mixing of the resonant 6p${\mathrm{}}^2$${\mathit{P}}_{\mathit{j}}$ levels into the ground 6s${\mathrm{}}^2$${\mathit{S}}_{1/2}$ level. Compact theoretical expressions, parametrized in terms of the electric-field strength and the relative transition matrix elements through the 5d${\mathrm{}}^2$${\mathit{D}}_{\mathit{j}}$ multiplet levels, are given. Results are presented for the electric-field dependence of a linear depolarization ratio, which is very sensitive to these quantities. © 1996 The American Physical Society.

We discuss the role of light absorption by pairs of atoms (radiative collisions) in the context of a model for velocity selective coherent population trapping with emphasis on its application to metastable triplet helium. Our main interest is the application of such dark-state cooling schemes to the regime where individual quantum states get multiply occupied, a regime which is sometimes referred to with the term atom laser. We show that, because of radiative collisions, for positive detuning of the driving light fields from an atomic resonance the conditions for proliferation of the occupation numbers of the lowest lying states can only be marginally met. Multiple occupation of these states only occurs if a very efficient sub-Doppler precooling mechanism is operative. In the case of negative frequency detuning the requirements on this sub-Doppler mechanism are less restricting, provided one avoids molecular resonances. © 1996 The American Physical Society.

A system of Maxwell-Bloch type equations (MBE’s), describing stimulated Raman scattering with both Stokes and anti-Stokes waves taken into account, is investigated. We introduce variables ${\mathit{S}}_3$ and ${\mathit{S}}_{\pm }$, which are bilinear in the electromagnetic fields, and prove that the corresponding equations possess Lax representation. This fact is used to obtain additional solutions for ${\mathit{S}}_3$, ${\mathit{S}}_{\pm }$ and for the MBE’s which include solitons, periodical waves, and self-similarity solutions. The transient and bright threshold solitons are also analyzed. © 1996 The American Physical Society.

We present systematic numerical studies of the regularly pumped mesomaser. The mesomaser is a generalization of the micromaser in that more than one atom can be present at any given time in the cavity. We treat from one to five atoms present in a regular pump-scheme in which the atoms arrive individually and equidistantly in time. We find that in the limit of more photons than atoms (${\mathit{N}}_{\mathrm{ex}}$>N, ${\mathit{N}}_{\mathrm{ex}}$ setting the scale of the photon number and N being the number of atoms), for small Rabi angles Θ, and for a nonvanishing temperature (thermal photon number n¯≳0.1), the quasi-steady-state photon number changes little as a function of N (for correctly scaled other parameters), whereas the variance of the photon number for certain Rabi-angles Θ exhibits a clear linear dependence on N. This extra contribution due to the many-particle aspect of the problem scales as N/${\mathit{N}}_{\mathrm{ex}}$, thus becoming large when the number of atoms N approaches the scale ${\mathit{N}}_{\mathrm{ex}}$ of the photon number. © 1996 The American Physical Society.

We derive analytical expressions for the quantum-noise spectra of an atomic laser using a linearized input-output method. We generalize the method to the problem of injection-locked lasers. We identify three distinct spectral noise regimes in the solution, unifying previous results. The approach offers insights into the physical processes and is especially suited for comparison with experiment. The quantum spectral noise properties of the pump laser and the injected laser appear explicitly in the solution. © 1996 The American Physical Society.

We present experimental results that illustrate how laser intensity noise near the quantum-noise limit is transferred in an injection-locked cw Nd:(yttrium aluminum garnet) nonplanar ring-oscillator laser. We show that these results are in extremely good agreement with our quantum-mechanical model describing the injection locking process [T. C. Ralph, C. C. Harb, and H.-A. Bachor, Phys. Rev. A]. Three regions in the intensity-noise spectrum are identified and we show that different minimum noise levels exist in these regions. Finally, we show that the injection-locked laser can generate and preserve nonclassical states. © 1996 The American Physical Society.

Relativistic harmonic generation by the scattering of very-high-intensity laser light from fast free electrons is investigated theoretically. A general solution for the trajectory of an electron, moving initially with an arbitrary velocity in a light pulse of arbitrary intensity and polarization, is presented. This solution generalizes the classical analysis of Eberly [Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1969), Vol. 7] and that of Sarachik and Schappert [Phys. Rev. D 1, 2738 (1970)] for the trajectory of an electron initially at rest. The result is then applied to the case of effective harmonic generation in a monochromatic, circularly polarized field under three different initial conditions for the electron, namely, (a) electron initially at rest, (b) electron initially moving in the direction of light propagation (and opposite to it), and (c) electron initially crossing the radiation beam at right angles. Angular distributions of the harmonics generated by the scattering process are presented in terms of the power scattering cross section in each case. Effects of increasing the light intensity and/or the initial electron speed and/or direction on the angular distributions are discussed. It is found, among other results, that at laser intensities higher than, say ${10}^{18}$ W/${\mathrm{cm}}^2$, the low-order harmonics are suppressed while the higher-order harmonics are enhanced. © 1996 The American Physical Society.

We present a unified analysis of the quantum fluctuations and quadrature squeezing of continuous wave (cw) light propagating in a single-mode quadratic (${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$) waveguide. We retain the effects of wave-vector and group-velocity mismatch, group-velocity dispersion, and depletion by linearizing the quantum fluctuations with respect to the the exact cw nonlinear semiclassical evolution. Each of the characteristic three-wave mixing phenomena, including parametric amplification, second-harmonic generation, and special eigenmode solutions are discussed and contrasted. Regimes of strong squeezing, and the influence of classical parametric modulational instabilities and spatial bifurcations on the spectrum of squeezed quantum fluctuations, are discussed. © 1996 The American Physical Society.

The process of quadrupole radiation of an atom in the vicinity of a dielectric sphere is considered within the framework of both quantum-mechanical and classical approaches. It is shown that spontaneous transition probabilities can be calculated correctly within the framework of the classical approach. The quadrupole transition probability is shown to be capable of increasing by several orders of magnitude in the neighborhood of the microsphere, to become comparable with the intensity of dipole transitions, the frequency shifts calculated in the classical approximation being much greater than in the case of dipole transitions. © 1996 The American Physical Society.

An energy conservation law is derived for fields generated by random, statistically stationary, scalar sources of any state of coherence. It is shown that correlation-induced spectral changes are in strict agreement with this law and that, basic to the understanding of such changes, is a distinction that must be made between the spectrum of a source and the spectrum of the field that the source generates. This distinction, which is obviously relevant for spectroscopy, does not appear to have been previously recognized. © 1996 The American Physical Society.