Light-wave mixing and scattering with quantum gases.

We present a semiclassical theoretical framework on light-wave mixing and scattering with single-component quantum gases. We show that these optical processes originating from elementary excitations with dominant collective atomic recoil motion are stimulated Raman or hyper-Raman in nature. In the forward direction the wave-mixing process, which is the most efficient process in normal gases, is strongly reduced by the condensate structure factor even though the Bogoliubov dispersion relation automatically compensates the optical-wave phase mismatch. In the backward direction, however, the free-particle-like condensate structure factor and Bogoliubov dispersion result in highly efficient light-wave mixing and collective atomic recoil motion that are enhanced by a stimulated hyper-Raman gain and a very narrow two-photon motional state resonance.