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Journal of Experimental and Theoretical Physics Letters

Exact solution of the problem of laser focusing of an atomic beam

В. В. Климов, Vladilen S Letokhov

Published Nov 1, 1999• 3 citations
Publisher

Abstract

The exact solution (Green’s function) of a parabolic equation describing the motion of neutral atoms in the field of a hollow TEM 01 * mode of laser radiation is found. The positions of the focus and the width of the focal spot are found on the basis of this solution for various configurations of the laser atomic beam.
DOI
10.1134/1.568243

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We propose a new method to generate a focused hollow laser beam by using an azimuthally distributed 2π-phase plate and a convergent thin lens,and calculate the intensity distribution of the focused hollow beam in free propagation space.The relationship between the waist w0 of the incident collimated Gaussian beam and the dark spot size of the focused hollow beam at the focal point,and the relationship between the focal lenght f of the thin lens and the dark spot size are studied respectively.The optical potential of the blue-detuned focused hollow beam for^85 Rb atoms is calculated.Our study shows that when the larger waist w of the incident Gaussian beam and the shorter focal length f of the lens are chosen,we can obtain an extremely small dark spot size of the focused hollow beam,which can be used to form an atomic lens with a resolution of sereval angstroms.
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The focusing of a neutral atomic beam using near-resonant laser light is considered. The results of a path integral solution to the Schrodinger in the stationary phase approximation are presented. The details of the derivation of the propagation kernel are presented elsewhere [1]. This approach is general and allows us to deal with "thick" laser lenses. Numerical results for the focusing of a Gaussian atomic beam are presented. These results show that spot diameters on the order of 20 Angstroms are obtainable for many reasonable choices of laser and atomic beam parameters, and that for most of these cases the thin lens approximation is not valid.
Recently, the focusing of an atomic beam using a laser has been considered by Balykin and Letokhov.1 Their calculations explicitly assume the thin lens approximation. Here, using path integral techniques, we derive the focal length and lowest-order aberrations of the laser atomic beam lens as a function of both laser and atomic beam parameters without making the thin lens approximation. Starting from the basic form of the potential energy for an atom in a laser beam, the propagation kernel is derived for the TEM(01)* or donut mode beam. From this result the focal length and lowest-order aberrations can be found for any atomic beam profile. We consider in particular a Gaussian atomic beam. Both the full 3-D propagation kernel and its paraxial approximation are discussed. We show how the paraxial case can be obtained from the 3-D case via a stationary phase approximation of the propagation equation.