Diffraction of atoms from a standing-wave Schrödinger field

Abstract
The diffraction of cold atoms from the standing-wave Schrödinger field of a single atom in a microtrap is investigated. The diffraction patterns for both elastic and inelastic diffraction are derived, where inelastic diffraction is accompanied by transitions of the trapped atom between different trap states. The diffraction pattern corresponding to the elastic channel reveals the Fourier transform of the spatial distribution of the probability density associated with the Schrödinger wavefunction of the trapped atom. Diffraction patterns associated with inelastic channels reveal the convolution of the participating trap states in the momentum representation.