Diffraction of atoms by a standing wave at Gaussian initial momentum distribution of amplitudes

The role of the initial-state preparation in the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum-mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from a maximum possible value (determined by the limiting speed of stimulated photon re-emission) to zero. Consequently, the standing wave presents an effective mirror for Gaussian atoms, the reflection angle being controllable.