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

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 Schrodinger 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.