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Computers in Physics

Numerical simulations of an atomic beam focused by an optical potential

T. Kidan, Joan Adler, A. Ron

Published Sep 1, 1998• 4 citations

Abstract

We present a model to describe the behavior of an atomic beam in a focusing experiment and discuss its implementation. Such modeling is relevant to the development of atom lithography. For simplicity, the light-atom interaction may be treated as a conserving potential (neglecting spontaneous emission) so that the Schrödinger equation is sufficient for a description of the problem. We start from a two-dimensional time-dependent Schrödinger equation that is reduced to a one-dimensional equation by a paraxial approximation, and then solved iteratively via Padé approximation. The solution is implemented in an interactive routine with Matlab(5.x) to compute and visualize the atomic wave packet development as it propagates through the laser light optical potential. We present examples of our implementation, starting with cases that have known analytic solutions such as propagation of the atomic wave packet through free space and through a parabolic potential. We also present a case that does not have a simple analytic solution, namely the propagation of the atomic wave packet through a focusing optical potential, which has a Gaussian profile in the propagation direction and a parabolic profile in the perpendicular direction. © 1998 American Institute of Physics.

DOI: 10.1063/1.168718

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The motion of paraxial atomic beams in a laser radiation field is studied within the framework of a parabolic equation. Exact analytical solutions of the parabolic equation are found for a variety of potentials featuring a nonuniformity in the propagation direction. Special attention is paid to the propagation of cold atomic beams in the gradient field of the TEM01* laser radiation mode. Explicit analytical expressions are found for the position of the focal points, focal spot radius, and spatial intensity distribution.

We present a theoretical model for the propagation of non-self-interacting atom laser beams. We start from a general propagation integral equation and we use the same approximations as in photon optics to derive tools to calculate the atom-laser-beam propagation. We discuss the approximations that allow one to reduce the general equation whether to a Fresnel-Kirchhoff integral calculated by using the stationary phase method, or to the eikonal. Within the paraxial approximation, we also introduce the

ABCD

matrices formalism and the beam quality factor. As an example, we apply these tools to analyze the recent experiment by Riou et al. [Phys. Rev. Lett. 96, 070404 (2006)].