 
Summary: Numerical simulations of an atomic beam focused by an optical
potential
T. Kidan, a! Joan Adler, and A. Ron
Physics Department, TechnionIsrael Institute of Technology, Haifa 32000, Israel
(Received 15 August 1997; accepted 14 May 1998)
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 lightatom interaction may be treated as a conserving potential ~neglecting
spontaneous emission! so that the Schro ˜ dinger equation is sufficient for a description of the
problem. We start from a twodimensional timedependent Schro ˜ dinger equation that is reduced to
a onedimensional 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 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. @S08941866~98!016058#
INTRODUCTION
