  A Bose-Einstein condensate in a high-finesse ring cavity scatters the photons
of a pump beam into counterpropagating cavity modes, populating a
bi-dimensional momentum lattice. A high-finesse ring cavity with a sub-recoil
linewidth allows to control the quantized atomic motion, selecting particular
discrete momentum states and generating atom-photon entanglement. The
semiclassical and quantum model for the 2D collective atomic recoil lasing
(CARL) are derived and the superradiant and good-cavity regimes discussed. For
pump incidence perpendicular to the cavity axis, the momentum lattice is
symmetrically populated. Conversely, for oblique pump incidence the motion
along the two recoil directions is unbalanced and different momentum states can
be populated on demand by tuning the pump frequency.
