Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate

We extend the semiclassical model of the collective atomic recoil laser (CARL) to include the quantum mechanical description of the center-of-mass motion of the atoms in a Bose-Einstein condensate (BEC). We show that when the average atomic momentum is less than the recoil momentum h (q) over right arrow, the CARL equations reduce to the Maxwell-Bloch equations for two momentum levels. In the conservative regime (no radiation losses), the quantum model depends on a single collective parameter, rho, that can be interpreted as the average number of photons scattered per atom in the classical limit. When rho much greater than i, the semiclassical CARL regime is recovered, with many momentum levels populated at saturation. On the contrary, when rho much greater than 1, the average momentum oscillates between zero and h (q) over right arrow, and a periodic train of 2 pi hyperbolic secant pulses is emitted. In the dissipative regime (large radiation losses) and in a suitable quantum limit, a sequential superfluorescence scattering occurs, in which after each process atoms emit a pi hyperbolic secant pulse and populate a lower momentum state. These results describe the regular arrangement of the momentum pattern observed in recent experiments of superradiant Rayleigh scattering from a BEG. (C) 2001 Elsevier Science B.V. All rights reserved.