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Optics and Spectroscopy

Stochastic dynamics of atoms in a resonant light field in the quasi-classical approximation

A. V. Bezverbnyĭ, Alexander V. Shapovalov

Published Jul 1, 2004• 0 citations
Publisher

Abstract

The stochastic dynamics of atoms with degenerate energy levels in a resonant nonuniformly polarized laser field is considered within the framework of the quasi-classical approach. The regular force entering into the Langevin equation and the correlation function of a random force are represented in the form of expansions in spatial gradients of the total light field. Specific features of kinetic distributions that are caused by the multiplicative character of noise, by anisotropy of dissipative processes, and by the presence of a vortex component in the light-induced force are considered for the example of a model system and a two-dimensional field configuration.

DOI
10.1134/1.1781285

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The stochastic dynamics of atoms with degenerate energy levels in a resonant nonuniformly polarized laser field is considered within the framework of the quasi-classical approach. The regular force entering into the Langevin equation and the correlation function of a random force are represented in the form of expansions in spatial gradients of the total light field. Specific features of kinetic distributions that are caused by the multiplicative character of noise, by anisotropy of dissipative processes, and by the presence of a vortex component in the light-induced force are considered for the example of a model system and a two-dimensional field configuration.
The motion of slow atoms with degenerate energy levels in a resonant, nonuniformly polarized laser field is described by the Fokker-Planck equation for the atomic distribution function in phase space in terms of the semiclassical approach. Field gradient expansions are used for the spatially nonuniform coefficients of the equation. For closed atomic transitions J g =J→J e =J+1 (J g and J e are the total angular momenta of the ground and excited states, respectively), new analytical results are presented for the light pressure force and the friction and diffusion coefficients in momentum space. These results allow the kinetic effects (laser cooling, localization in optical potential wells, etc.) in a field of arbitrary one-, two-, or three-dimensional configuration to be investigated. In several cases, the new contributions to the friction coefficient are interpreted qualitatively.
The dynamical behavior of an atom interacting with a coherent and a chaotic field is investigated. Langevin equations describing the time dependent behavior of the dipole moment and population inversion are numerically integrated using Monte-Carlo techniques. The model can account for a finite correlation time for the chaotic component. Results on fluctuations in the fluorescence intensity from an ensemble of two-level atoms and the power spectra of these intensity fluctuations are presented. The effect of detuning the pump field from the resonant frequency of the two-level atoms on the fluctuations in fluorescence is studied. The effect of field fluctuations on the macroscopic polarization produced by the atoms is also reported. The fluctuation behavior of the atomic fluorescence is found to be very sensitive to the correlation time of the stochastic component.
The kinetics of atoms with degenerate energy levels in the field produced by elliptically polarized waves is considered in the semiclassical approximation. Analytic expressions for the force acting on an atom and for the diffusion coefficient in the momentum space are derived for the optical transition J g =1/2→J e = 1/2 in the slow atom approximation. These expressions are valid for an arbitrary one-dimensional configuration of the light field and for an arbitrary intensity. The peculiarities of the atomic kinetics are investigated in detail; these peculiarities are associated with ellipticity of light waves and are absent in particular configurations formed by circularly or linearly polarized waves, which were considered earlier.
The light force on slow atoms in a light field with arbitrary polarization distribution is explicitly evaluated in the case of an atomic transition J yields J with half-integer J values. The expression of the force is based on an exact analytical expression for the steady-state density matrix of the atoms. The force is naturally separated in contributions resulting from gradients of the field intensity, the polarization ellipticity, and the phase. In addition to a conservative part this force also contains a vortex component. In areas of spatial localization, where the total force vanishes, the atomic motion is governed by a potential, which in general is not harmonic for J greater than 1/2. Simple model of the formation of a one- or two-dimensional spatial atomic grating in a specific light field configuration illustrates the results.
We present a theoretical study of strong laser-atom interactions, when the laser field parameters are subjected to random processes. The atom is modelled by a two- and a three-level system, while the statistical fluctuations of the laser field are described by a pre-Gaussian model. The interaction of the laser-target is treated nonperturbatively by using the calculation method based on the Hermitian Floquet theory. Our aim consists in studying the kinetics of atomic relaxation induced by laser noise. In the resonant case with electric field strengths small with respect to the atomic unit electric strength, the present nonperturbative results are in agreement with those obtained within the rotating wave approximation of Eberly et al and Wodkiewicz et al for an atom modelled by a two-level system. We discuss some examples which demonstrate the destruction of atomic coherence by the noise, the regime of relaxation to the equilibrium state and the optical analogue of motional narrowing. We also give new results for two- and three-level systems, and for a strong laser field at exact resonance, in the case of phase, amplitude noises. The case of fluctuation due to collisions is also discussed. Our numerical results indicate that ionization effects, in the presence of laser noise, can lead to important modifications of the populations for strong laser-atom interactions. The changes in the ionization rates generated by the noise are also investigated.
We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal-level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low-light-intensity limit for atoms with a single electronic ground state, the full quantum field-theoretical representation of the model can be solved exactly by means of classical stochastic electrodynamics simulations for stationary atoms that represent cold atomic ensembles. Simulations for the optical response of atoms in a quantum degenerate regime require one to synthesize a stochastic ensemble of atomic positions that generates the corresponding quantum statistical position correlations between the atoms. In the case of multiple ground levels or at light intensities where saturation becomes important, the classical simulations require approximations that neglect quantum fluctuations between the levels. We show how the model is extended to incorporate corrections due to quantum fluctuations that result from virtual scattering processes. In the low-light-intensity limit, we illustrate the simulations in a system of atoms in a Mott-insulator state in a two-dimensional optical lattice, where recurrent scattering of light induces strong interatomic correlations. These correlations result in collective many-atom subradiant and superradiant states and a strong dependence of the response on the spatial confinement within the lattice sites.