We investigate the focusing of three-level atoms with a bichromatic standing wave laser field, using both classical and quantum treatments of the problem. We find that, for the appropriate ratio of detunings to Rabi frequencies, the atoms will experience a periodic potential which is close to harmonic across half an optical wavelength. The field thus becomes equivalent to a periodic array of microlenses, which could be utilized to deposit lines of atoms upon a substrate. We consider and compare two regimes, differentiated by the interaction time of the atoms in the optical field. The first case considered, the Raman-Nath regime, is analogous to the thin lens regime in classical optics. The second case treats the transverse atomic motion within the light field, and investigates the distribution of atoms upon a substrate placed within the field. We investigate the extent to which this case can be modeled classically. © 1996 The American Physical Society.

Atom-optics experiments are presented using a time-modulated evanescent light wave as an atomic mirror in the trampoline configuration, i.e., perpendicular to the direction of the atomic free fall. This modulated mirror is used to accelerate cesium atoms, to focus their trajectories, and to apply a ‘‘multiple lens’’ to separately focus different velocity classes of atoms originating from a point source. We form images of a simple two-slit object to show the resolution of the device. The experiments are modelled by a general treatment analogous to classical ray optics. © 1996 The American Physical Society.

We examine the interaction of intense, femtosecond laser radiation with the large (50–200 Å) clusters produced in pulsed gas jets. Both experiment and simulation show that the plasmas produced during these interactions exhibit electron temperatures far in excess of that predicted by above-threshold ionization theory for a low-density gas. Efficient heating of the clusters by the laser is followed by rapid expansion of the clusters and long-lived x-ray emission from hot, decaying, underdense plasma. © 1996 The American Physical Society.

We analyze the collisionless motion of atoms in magnetic traps in relation to evaporative cooling. For the example of a long Ioffe quadrupole trap we investigate both the regular and stochastic regimes of motion. We emphasize a strong influence of the regime of collisionless motion on the process of evaporative cooling. For evaporation of atoms across an axial potential barrier the stochastic motion of atoms at energies above the barrier enables three-dimensional evaporation, i.e., particles acquiring in elastic collisions a total enery higher than the barrier height ${\mathit{E}}_0$ escape from the trap. The regular motion leads to axial evaporation: only atoms which due to collisions acquire an axial energy higher than ${\mathit{E}}_0$ leave the trap. The rate of axial evaporation is smaller by a factor ∼η=${\mathit{E}}_0$/T≫1, where T is the gas temperature. This has important consequences for evaporative cooling, which we discuss in relation to trapped atomic hydrogen. ©1996 The American Physical Society.

We study theoretically the spatial diffusion (transport) of two-level atoms in one- and two-dimensional optical molasses derived from counterpropagating laser beams. We use both quantum Monte Carlo and semiclassical methods to study the microscopic characteristics of the atomic motion and their effect on the macroscopic behavior of the spatial distribution. We find that there exists a certain critical depth of the optical potential below which the atomic trajectories show Lévy flights in space that last on a definite time scale (Lévy walks). This behavior leads to a transition from Gaussian spatial diffusion to anomalous diffusion while crossing this critical potential depth. We show that only atoms with very high momentum are responsible for these Lévy walks. This observation allows us to predict the critical parameters via a semiclassical Fokker-Planck equation approach. © 1996 The American Physical Society.

The high-frequency Floquet theory describing the interaction of a two-electron atom with a linearly polarized laser field is applied to the case when the characteristic parameter ${\mathrm{\alpha }}_0$=${\mathit{E}}_0$${\mathrm{\omega }}^{\mathrm{-}2}$ a.u. is large, corresponding to the dichotomy regime of the one-electron problem. We first revisit this case and extend the large-${\mathrm{\alpha }}_0$ energy-level formula obtained earlier to higher order in ${\mathrm{\alpha }}_0^{\mathrm{-}1}$. We then prove the existence of a dichotomy regime also for the two-electron atom, characterized by the two electrons being situated in disjoint electronic clouds separated by an average distance of 2${\mathrm{\alpha }}_0$. We obtain the first four terms in the expansion of the related energy-level formula in fractional powers of ${\mathrm{\alpha }}_0^{\mathrm{-}1}$. The coefficients entering this expansion have been expressed in terms of the eigenvalues of a nonseparable Schrödinger equation containing the end-point potential and of integrals over its eigenfunctions. The equation was solved using the finite element method. An infinite sequence of levels emerges. In the case of ${\mathrm{H}}^{\mathrm{-}}$ this implies the existence of a large number of light-induced excited states, some of them corresponding to two-electron excitations not subject to autodetachment. Finally, we prove that in the dichotomy regime a two-electron atom undergoes stabilization and that the ionization rates are essentially twice those for a one-electron atom with the same nuclear charge. © 1996 The American Physical Society.

We investigated the existence of coherent population trapping (CPT) as a transient effect dependent on the rate of change of interaction parameters between an atom and light waves. For that purpose we exploited the phase dependence of CPT in a closed double-Λ interaction scheme, varying the total phase of the atomic transition loop linearly in time by detuning the light waves from exact four-photon resonance. For a slowly changing phase (that is, for small detunings) we observed the subsequent creation and destruction of CPT depending on the varying phase, while for higher speed of phase change CPT disappears. An analytical solution for a special case for a double-Λ interaction scheme that can be used to understand the principles of this phenomenon is presented. A qualitative comparison with our experiment shows good agreement within the limits of our theoretical considerations, confirming the validity of the basic idea. © 1996 The American Physical Society.

The energy spectrum for a system of atoms in a periodic potential can exhibit a gap in the band structure. We describe a system in which a laser is used to produce a mechanical potential for the atoms, and a standing-wave light field is used to shift the atomic levels using the Autler-Townes effect, which produces a periodic potential. The band structure for atoms guided by a hollow optical fiber waveguide is calculated in three dimensions with quantized external motion. The size of the band gap is controlled by the light guided by the fiber. This variable band structure may allow the construction of devices that can cool atoms. The major limitation on this device would be the spontaneous emission losses. © 1996 The American Physical Society.

We present a theoretical study of high-order harmonic generation by a slowly driven ‘‘Duffing’’ anharmonic oscillator. The power spectra are shown to display a plateau of high harmonics, which ends up with a sharp cutoff. The classical dynamics is analyzed with the adiabatic invariance theorem, which yields a simple interpretation to this characteristic behavior. We compare with the quantum case by solving numerically the time-dependent Schrödinger equation, and outline the similarity between classical damping and quantum-mechanical ionization processes. This allows us, in particular, to interpret the existence of intrinsic phases between high harmonics and the driving field. We further discuss the implication of these relaxation processes on the coherence of high harmonics, as well as the existence of interference processes yielding quasiresonant structures in intensity dependences. © 1996 The American Physical Society.

We report measurements of the intensity correlations of scattered light from atoms in optical molasses. For small numbers of atoms, the observations are consistent with recent models of the Rayleigh and Raman contributions to the frequency spectrum. Magnetic fields on the order of 100 mG significantly broaden the spectrum. Radiation trapping results in reduction of the size of the correlations as well as broadening of the spectrum. © 1996 The American Physical Society.

Recent measurements on ${\mathrm{CO}}_2$-laser-assisted electron-atom collisions have shown large inconsistencies with the Kroll-Watson formula for small-angle scattering. We have carried out a detailed study to compare the predictions of Kroll-Watson theory (for both single and multimode fields) with those of conventional perturbation theory for stimulated free-free transitions. It is found that for ${\mathit{E}}_0$/2${\mathrm{\omega }}^2$≪1, where perturbation theory is valid, there are large differences with the Kroll-Watson theory. Comparisons of experimental variations with respect to scattering angle and electron energy show much better agreement with perturbation theory than with Kroll-Watson theory. A study of the angular variations in perturbation theory shows that use of the ‘‘outgoing’’ wave final state gives much better agreement with experiment than does the ‘‘ingoing’’ wave final state, which is different from the choice made in early bremsstrahlung theory. © 1996 The American Physical Society.

By relating the van der Waals dispersion interaction between two neutral polarizable particles to a field correlation function, we show that the interaction is modified by applied electromagnetic fields. The modified interaction, which has a simple physical interpretation, can vary as ${\mathit{r}}^{\mathrm{-}3}$ rather than ${\mathit{r}}^{\mathrm{-}6}$ if the applied field is nearly unidirectional. Approximate numerical estimates indicate that the effect is very small for static or low-frequency fields, but that it might be significant, particularly in cold traps, when the frequency of a quasimonochromatic applied field is near a strong absorption line. © 1996 The American Physical Society.

In this paper we analyze the transverse pattern-forming characteristics of a two-level and single-longitudinal-mode laser. The corrections to the classical empty cavity modes due to pumping and losses are specifically considered, leading to different excitation rates for the different transverse modes. The near-threshold excitation rates provide a selection mechanism that is studied and compared to the results from numerical simulations of the Maxwell-Bloch equations. © 1996 The American Physical Society.

A method for the the derivation and truncation of correlation function hierarchies for Markovian damped quantum-optical systems is presented. The theory enables the inclusion of multiphoton scattering processes which are ignored in conventional semiclassical theories. These produce observable dynamical signatures which depend on characteristic scales of photon number. Applications of the theory to intracavity optical parametric oscillation and second-harmonic generation are given. © 1996 The American Physical Society.

Instabilities and dynamical pulsations are common features of solutions of a model that includes the material variable dynamics for a laser with a polarization isotropic resonator and with a homogeneously broadened j=1→j=0 transition. These resemble in some respects features found in third-order Lamb theories under anisotropic conditions, such as splitting of the optical field into two relatively independent orthogonally polarized modes with different optical frequencies. At higher intensities the amplitudes and frequencies of these modes exhibit such strong coupling that a ‘‘two-mode’’ description loses its usefulness or effectiveness. Various periodic attractors with strong intensity and polarization pulsations are found for moderate excitation levels. Some of these attractors preserve the breaking of the polarization isotropy on average just as does any linearly polarized solution. But in some cases the dynamics restore the polarization isotropy on average. We also find other dynamical phenomena, including periodic and apparently chaotic states, often involving rapid switching between long interludes of nearly constant polarization, and homoclinic behavior. © 1996 The American Physical Society.

In this paper, we study the linewidth of a two-photon micromaser by using an exact Hamiltonian approach. We consider a three-level atomic system interacting with a single-mode radiation field. The intermediate level is considered to be off resonant with the field. In this model, under the large detuning limit, two-photon transitions result. We calculate the linewidth of a two-photon micromaser and present results in the small and large detuning limits. In the small detuning limit, single-photon behavior is evident, whereas in the large detuning limit, true two-photon behavior is exhibited. We compare the results for the linewidth, under a large detuning limit, with the results obtained by using a phenomenological, effective Hamiltonian approach. The absence of the dynamic Stark shift in a phenomenological, effective Hamiltonian leads to qualitatively different results in the two approaches. © 1996 The American Physical Society.

Using a Hertz vector formulation, it is possible to simplify the equations for beam propagation in nonlinear media without resorting to the scalar approximation. A numerical method to take advantage of the formulation is developed and applied to the problem of self-focusing. It is found that filament-like solutions can result for some values of the nonlinear index of refraction when the scalar approximation is not made even though the paraxial approximation is still used. © 1996 The American Physical Society.

Quantization of radiation has been performed from first principles in a realistic molecular medium, represented by an arbitrary number of energy levels (electronic, vibrational, rotational, etc.) for each constituent molecule. Adopting a polariton model, the field operators have been expanded in terms of normal Bose operators for polariton creation and annihilation. The expansion coefficients have been derived explicitly for the normal modes characterized by wavelengths exceeding considerably the characteristic distance of separation between the molecules. Accordingly, the formalism applies to the long-wavelength region of the spectrum for which description in terms of the macroscopic refractive index is relevant; furthermore, consideration is restricted to the nonabsorbing areas of the spectrum. The theory has been formulated in a manner that made possible a parallel and comparative consideration of operators for both the averaged (macroscopic) and local fields. Consequently, the mode expansions derived cover both the local displacement-field operator and also the averaged (macroscopic) operators for the electric, displacement, magnetic, and polarization fields, and the vectorial potential. The expansions, involving summation over an arbitrary number of branches of polariton dispersion, manifestly embody the refractive influences as well. To this end, the local-field effects intrinsically emerge within the present formalism that treats systematically the photon umklapp processes. Relations have been established between the expansion components of the local and averaged field operators. The relationships support some previous attempts to link the amplitudes of local and macroscopic field operators phenomenologically, and are also consistent with the familiar results of classical electrodynamics. Equal-time commutation relations have been demonstrated to be preserved, expressing the operators for the averaged fields in terms of the normal Bose operators. On the other hand, the commutation relations between the macroscopic fields are of the same form as those for their microscopic counterparts, subject to the coarse-graining procedure. Finally, the present study dealing with the macroscopic and local operators provides a tool for combined investigation of both propagation of the quantized fields in molecular dielectrics and also interaction of the fields with the embedded molecules or atoms. © 1996 The American Physical Society.

Using a photorefractive oscillator (PRO) with a stable resonator, we investigate patterns produced from the transverse mode families of order 0–3. The phenomena observed include vortices which move along circular or spiral trajectories and vortices which periodically change the sign of their topological charge. In addition, we observe behavior which is unlike that expected for lasers, despite the established analogy between the laser and the PRO. This includes pulsing of mode patterns which are otherwise expected to be stable, and also stable rotation of Gauss-Laguerre mode patterns. These effects indicate a much stronger self-focusing in the PRO than in lasers. © 1996 The American Physical Society.

An explicit relationship between the Lorenz-Mie resonances and nonlinear optics of a microsphere has been found. We have constructed an approximate analytic method which allows an adequate assessment of the threshold for stimulated Raman scattering in microspheres. Systematic investigation of the characteristic equation, using approximate analytic expressions, reveals that not all modes have the same quality. Some resonances with very high quality correspond to a physical situation in which the spherical waves can be envisioned as whispering-gallery light waves that are totally internally reflected by the sphere boundary, without suffering almost any loss. © 1996 The American Physical Society.