Coherent manipulation of atoms with standing light waves

Coherent manipulation of atomic momentum states is the primary goal of atom optics, and the standing light wave with its associated stimulated light forces is the primary method of achieving this goal. A description of the standing wave as two counter-propagating beams of photons leads to a natural explanation of Bragg scattering. In contrast, Kapitza-Dirac scattering, atom lithography, and the matter-wave Talbot effect are more naturally treated by considering the standing light wave as a stationary field which acts as a periodic potential for the passing atoms or atomic waves. Selected experimental and theoretical results in the various qualitatively different regimes of the standing wave-atom interaction are reviewed, with special attention given to the physical differences underlying the various behaviors and the theoretical approximations used to treat them.