We consider the Raman process developing in a disordered medium of alkali-metal atoms when the scattered modes are trapped on a closed transition. Our theoretical analysis, based on numerical simulations of the Bethe-Salpeter equation for the light correlation function, which includes all Zeeman states and light polarization, lets us track the stimulated amplification as well as the losses associated with the inverse anti-Stokes scattering channel. We discuss possible conditions when this process could approach the instability point and enter the regime of random lasing.

We consider a quantum theory of elastic light scattering from a macroscopic atomic sample existing in the Bose-Einstein condensate (BEC) phase. Following the second quantized formalism we introduce a set of coupled and closed diagram equations for the polariton propagator contributing to the T -matrix and scattering amplitude. Our approach allows us to follow important density corrections to the quasi-energy structure caused by static interaction and radiation losses associated with incoherent scattering in the case of near resonance excitation.