Calculating trajectories for atoms in near-resonant lightfields

We review several methods for calculating the time development of the inter nal state and the external motion of atoms in near-resonant light fields, w ith emphasis on studying the focussing of atomic beams into microscopic and potentially nanoscopic patterns. Three different approaches are considered : two-level semiclassical, multi-level semiclassical, and the Monte Carlo w avefunction method. The two-level semiclassical technique of McClelland and Scheinfein (1991) and McClelland (1995) is extended to three dimensions, a nd used to calculate the trajectories of atoms and the imaging properties o f a simple lens formed from a near-resonant travelling TEM01 mode laser. Th e model is then extended to multi-level atoms, where we calculate the densi ty matrix for the internal state of a sample of thermal atoms in a standing wave, and show how cooling processes can be simulated. Finally, we use the Monte Carlo wavefunction method to calculate the internal state of the ato m, and compare the results and required computation time to those of the mu lti-level semiclassical technique.