Two-dimensional quantum theory of collective light scattering from Bose-Einstein condensates

We present a two-dimensional description of the light scattering by collective atomic recoil for a configuration in which the pump and the scattered beams are orthogonal and the atoms are in a definite state of momentum. In the quantum recoil limit and for single-photon scattering, the analytical solution can be found explicitly, both in the good-cavity limit (i.e., with no radiation losses) and in the superradiant regime (without cavity) observed in the MIT experiment.