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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Light-induced force on atoms in a monochromatic light field with arbitrary polarization

A. V. Bezverbnyĭ, Gerard Nienhuis, Anatolii M Tumaikin

Published Oct 21, 1998• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.328278

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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 light-induced force on an atom is calculated for an arbitrary field configuration, taking into account the spontaneous emission and optical pumping processes as well as the degeneracy of atomic energy levels. Two types of the optical transitions are analyzed: $J\ensuremath{\rightarrow}J$ with JJJ a half-integer and $J\ensuremath{\rightarrow}J+1$ with JJJ an arbitrary. Though the force is not potential in the general case, we introduce a scalar function $\ensuremath{\Psi}$, which plays a role of the potential energy, determining regions of localization of atoms. Applications of these results to atom nanolithography are discussed.
An analysis of general characteristics of light-induced forces is presented for arbitrary monochromatic masks in which optical pumping of atoms and spontaneous emission play an important role. Dependence of regions of localization on detuning and ellipticity is determined for cyclic transitions of two types: J å J with half-integer J and J å J + 1 with arbitrary J . Numerical simulations of atomic beam focusing with one-and two-dimensional light masks show that spatial atom distributions with narrow features and high contrast can be formed in dissipative masks. In particular, spherical aberration is substantially reduced when the pumping field is tuned to a J å J + 1 transition with large J in lin ∼ lin configuration as compared to nondissipative masks.
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.