Inelastic light scattering from alkali Bose-Einstein condensates

We determine the spontaneous and stimulated non-resonant combination light scattering cross sections from a finite-size trapped alkali Bose-Einstein condensate (BEC) tor scattered radiation with frequencies which differ from the incident frequency by elementary vibrational-rotational-spin excitations of the BEC. We consider incident microwave frequency radiation not far from the hyperfine splitting resonance frequency, and incident visible frequency radiation cases. Bosonic stimulation (stimulation due to the population of quantum states by Bose-Einstein particles) is a telltale signature of BEC since it drastically affects the relative and absolute line intensities. The strongest feature in the scattered radiation is the elastic scattering peak; the intensities of red and blue shifted scattering peaks depend strongly on temperature even for temperatures below the critical temperature for BEC. The Stokes (red-shifted) peaks are more intense than the anti-Stokes (blue-shifted) peaks, and as T → O, all blue shifted features in the scattering disappear.