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Chinese Physics Letters

Quantum-Mechanical Simulation of an Atomic Beam Focused by an Optical Standing Wave

He Ming, Wang Jin, X.H. Tu, Kaijun Jiang, Yi Wang, Mingsheng Zhan

Published Feb 22, 2002• 1 citation
Publisher

Abstract

Recent experiments have demonstrated that the light pressure force from an optical standing wave (SW) focuses an atomic beam to sub-micrometre dimensions. We start from a two-dimensional time-dependent Schrödinger equation and reduce it to a one-dimensional equation by a paraxial approximation. We calculate some theoretical limits on the focusing of an atomic beam by an SW optical field. It is found that two parameters, the atomic velocity and the intensity of the laser beam, play an important role in determining the deposition quality.

DOI
10.1088/0256-307x/19/3/302

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Recent experiments have demonstrated that the light pressure force from an optical standing wave (SW) focuses an atomic beam to sub-micrometre dimensions. We start from a two-dimensional time-dependent Schrödinger equation and reduce it to a one-dimensional equation by a paraxial approximation. We calculate some theoretical limits on the focusing of an atomic beam by an SW optical field. It is found that two parameters, the atomic velocity and the intensity of the laser beam, play an important role in determining the deposition quality.
Recent experiments have demonstrated that the light pressure force from an optical standing wave (SW) focuses an atomic beajm to sub-micrometre dimensions.We start from a two-dimensional time-dependent Schrodinger equation and reduce in to a one-dimensional equation by a paraxial approximation.We calculate some theoretical limits on the focusing of an atomic beam by an SW optical field.It is found that two parameters,the atomic velocity and the intensity of the laser beam,play an important role in determining the deposition quality.
The light pressure force from an optical standing wave (SW) can focus an atomic beam to submicrometer dimensions. To make the best of this technique it is necessary to find a set of optimal experimental parameters. In this paper we consider theoretically the chromium atoms focusing and demonstrate that the focusing performance depends not only on the strength of but also on the time atoms take to traverse the force field. The general conclusions drawn can easily be applied to other atoms. To analyze the problem we numerically integrate a coupled time-dependent Schro¨dingerSchr{\"{o}}dingerSchro¨dinger equation over a wide range of experimental parameters. It is found that an optimal atomic beam speed-laser intensity pair does exist, which could give substantially improved focusing over the one with the experimental parameters given in the literature. It is also shown that the widely used classical particle optics approach can lead to erroneous predictions.
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.
Summary form only given. Recently it has been demonstrated that neutral atomic beams can be focused by use of a laser as an atom-optical lens. Standing wave atom-optical (SW) lenses have been of particular interest because of the potential for both high-resolution and high-throughput lithography. In this paper, using sub-Doppler optical cooling schemes in conjunction with mechanical collimation, and a SW with /spl sigma/=56 /spl mu/m, we have been able to achieve <20 nm resolution with contrast of at least 10:1, focusing a thermal atomic sodium beam using 589-nm light corresponding to the D/sub 2/ transition.
The focusing of atoms to nanometer-scale dimensions by a near-resonant standing-wave light field is examined from a particle optics perspective. The classical equation of motion for atoms traveling through the lens formed by a node of the standing wave is derived and converted to a spatial trajectory equation. A paraxial solution is obtained, which results in simple expressions for the focal properties of the lens, useful for estimating its behavior. Aberrations are also discussed, and an exact numerical solution of the trajectory equation is presented. The effects on focal linewidth of angular collimation and velocity spread in the atomic beam are investigated, and it is shown that angular collimation has a much more significant effect than velocity spread, even when the velocity spread is thermal.