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Journal of Experimental and Theoretical Physics

Kinetics of atoms in the field produced by elliptically polarized waves

Прудников Олег Николаевич, А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Mar 1, 2004• 20 citations
Publisher

Abstract

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.

DOI
10.1134/1.1705695

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Journal of Experimental and Theoretical Physics•May 1, 2008•1 citation
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 kinetics of atoms in a bichromatic field formed by waves with an arbitrary elliptical polarisation is considered. Analytical expressions are derived for the force and the friction and diffusion coefficients within the model of an atom with the j g = 1/2 → j e = 3/2 optical transition. These expressions are presented in the general form as an expansion in gradients of light field parameters. Some specific features of the kinetics of atoms are found, which are due to the interference contributions to the friction and diffusion coefficients. The kinetics of atoms in the field of an optical lattice formed as a result of the interference of a wave with a uniform elliptical polarisation and a nonuniformly polarised dissipative field is analysed.
We examine the kinetics of atoms with their ground and excited states being degenerate in the projection of angular momentum. The atoms are located in a standing wave with uniform elliptical polarization. Using the j g =1/2→j e =1/2 transition as an example, we show that the friction and diffusion of atoms strongly depend on the ellipticity of the field. For instance, in the low saturation limit the frictional force contains, in addition to the ordinary Doppler friction term, a term that can be interpreted as Sisyphean friction. Under certain conditions, the contributions reflecting the degeneracy of the ground state are dominant, with the result that the values of the friction and diffusion coefficients (and hence the rate of kinetic processes) may differ from the values predicted by the two-level atomic model by several orders of magnitude.
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.
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 dependence of the magnetooptical force on the ellipticity of the polarization of light beams is studied in terms of a one-dimensional model for closed J g → J e optical transitions. A linear velocity and magnetic-field approximation is used to find analytical expressions for the magnetooptical force for a number of transitions. In the light fields formed by waves with an elliptical polarization, qualitatively new contributions are shown to appear; they have an even dependence on the detuning of the light field and do not disappear even in the case of an exact resonance. An analysis of these results demonstrates that a magnetooptical trap can stably operate at the zero detuning of the field. Numerical methods are used to investigate the nonlinear dependence of the force on the atom velocity and the magnetic field and to estimate the characteristic atom trapping rate and the number of trapped atoms.