Theory of collective Raman scattering from a Bose-Einstein condensate
  Recent experiments have demonstrated superradiant Raman scattering from a Bose-Einstein condensate driven by a single off-resonant laser beam. We present a quantum theory describing this phenomenon, showing Raman amplification of matter wave due to collective atomic recoil from 3-level atoms in a $\Lambda$-configuration. When atoms are initially in a single lower internal state, a closed two-level system is realized between atoms with different internal states, and entangled atom-photon pairs can be generated. When atoms are initially prepared in both the lower internal states, a fraction of atoms recoiling in the backward direction can be generated. 
Mary M. Cola and Nicola Piovella