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Physical Review A

General diffusion equation for light-induced drift

Gerard Nienhuis, Stanisław Kryszewski

Published Aug 1, 1987• 18 citations
Publisher

Abstract

We derive a general diffusion equation for the density of an atomic vapor immersed in a buffer gas and irradiated by nearly resonant light. The combination of velocity-selective excitation with state-dependent rates of velocity-changing collisions then gives rise to a drift term, and at the same time the diffusion tensor becomes anisotropic and intensity dependent. Both the effect of light-induced drift and diffusive pulling of atoms by the light are described by this diffusion equation in a consistent and correlated fashion.

DOI
10.1103/physreva.36.1305

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Journal of Physics B Atomic and Molecular Physics•Apr 14, 1985•11 citations
We derive a general diffusion equation for the density of an atomic vapor immersed in a buffer gas and irradiated by nearly resonant light. The combination of velocity-selective excitation with state-dependent rates of velocity-changing collisions then gives rise to a drift term, and at the same time the diffusion tensor becomes anisotropic and intensity dependent. Both the effect of light-induced drift and diffusive pulling of atoms by the light are described by this diffusion equation in a consistent and correlated fashion.
Light-induced drift arises when optically excited atoms with a Doppler-selected velocity suffer a diffusive friction that is different from that of ground-state atoms. When the atoms form an optically dense system, this drift can cause a piston effect, which sweeps the atoms in the propagation direction of the field. We derive coupled differential equations for the density of atoms and the light intensity, with an explicit expression for the drift velocity in terms of easily accessible parameters. Solutions of these equations are obtained for the stationary state in a closed cell. The density at the dark end of the cell, considered as the response to the incident-light intensity as its driving force, exhibits a discontinuity resembling a second-order phase transition for an optically dense system. We also obtain solutions with a soliton character, describing a localized density packet moving at uniform speed.
The authors consider a system of optically active two-state atoms immersed in a buffer gas and irradiated by a light beam. The corresponding Bloch equations are augmented by Keilson-Storer (KS) collision kernels (1952) which account for velocity-changing collisions. Expansion of the density operator elements in the eigenfunctions of KS kernels allows one to obtain exact solutions for the Laplace transforms of the density operator elements which may be expressed as rational approximants with any prescribed degree of accuracy. As an example they apply this method to discussion of the light-induced drift effect. In particular they give analytic expressions for the drift velocity, which are illustrated by numerical results. Finally, they briefly discuss possible generalisations and applications of the presented method.
A new light-induced drift effect is discussed in which a white-light source separates a gas mixture containing a single optically active (absorbing) species and a buffer gas which does not interact with the light. A three-level model with one upper level and two closely spaced lower levels is used for the active atoms, and strong collisions with the more abundant surrounding buffer gas atoms are assumed. The intensity spectrum in the vapor (including the effects of hyperfine pumping), and the resulting drift velocity are calculated as a function of optical depth into the vapor.
We present a model for light-induced drift (LID) in the Na--noble-gas system which should enable direct comparison with experiment. In contrast to previous theories of LID based on a two-level description of the optical absorbers and on a simplified collision treatment, the present model is based on a realistic description of laser-driven Na atoms immersed in a buffer gas. Starting from the generalized Bloch equations, we introduce a rate-equation model for the velocity distributions in the four important Na levels. The velocity-changing and fine-structure-changing collisions are described using composite Keilson-Storer collision kernels in which all adjustable parameters have been eliminated by using available literature data. We apply the model in numerical calculations of LID as a function of all experimentally accessible parameters. It is found that the ground-state hyperfine splitting can have large effects on LID, whereas the excited-state fine-structure splitting has not. The paper establishes criteria for optimum LID effects; when using a single-frequency laser the maximum attainable drift velocity is predicted to be 13.8 m/s. Using a proper set of boundary conditions, we find a pressure dependence of LID qualitatively different from the predictions based on previous work. Finally, the influence of the collision model is investigated. We find that LID is independent of the shape of the collision kernel, indicating that a strong-collision model is always valid.
Abstract : The effect of light-induced drift (LID) in gases, predicted by Gel'mukhanov and Shalagin and observed later, is manifested in mechanical drift of the absorbing atoms (molecules) in response to optical excitation. The effect of LID takes place if the atom interaction with light is velocity-dependent (due to the Doppler effect), the spectrum of the exciting radiation is asymmetric with respect to the the absorption line, and the absorbing molecules experience collisions with a buffer gas, with the collision rate dependent upon their internal state. The idea of LID is the following. Suppose for the sake of definiteness that the collision frequency of the absorbing molecules with the buffer is greater in the excited state and that the exciting light is red-shifted with respect to the absorption contour. Then due to the Doppler shift, the radiation interacts mainly with the counter-moving molecules, which undergo transitions into an excited state, in which their friction upon the buffer component is increased. Due to this increase, the counter-flying molecules are slowed down, while the molecules moving in the direction of light are not affected. The net effect is a drift of the absorbing component in the direction of light. The drift alternates its direction with the change of signs of either the detaining or the difference in the collision frequencies.
A simple method which allows one to study the influence of all relaxation processes and the pumping rate on the velocity distribution of the two-level atom populations is reviewed. In particular, the author presents a treatment that consistently includes the effects of phase and velocity relaxation on the atomic coherences. This method is applied to describe the drift of absorbing atoms-the effect which is also named light-induced gas diffusion. The results of numerical calculations for the drift velocity are presented and the role of the atomic coherences in the description of this phenomenon is pointed out. The dependence of the drift velocity on various parameters is discussed and the best experimental conditions for observing this effect are suggested.