Numerical Simulations of an Atomic Beam Focused by an Optical Potential

Tal Kidan, Joan Adler and A. Ron

Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel.

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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 Schrodinger equation is sufficient for the description of the problem. We start from a two dimensional time dependent Schrodinger equation that is reduced to a one dimensional equation by a paraxial approximation, and then solved iteratively via Pade 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 which 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 which 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.

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