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A Bose-Einstein condensate in a high-finesse ring cavity scatters the photonsof a pump beam into counterpropagating cavity modes, populating abi-dimensional momentum lattice. A high-finesse ring cavity with a sub-recoillinewidth allows to control the quantized atomic motion, selecting particulardiscrete momentum states and generating atom-photon entanglement. Thesemiclassical and quantum model for the 2D collective atomic recoil lasing(CARL) are derived and the superradiant and good-cavity regimes discussed. Forpump incidence perpendicular to the cavity axis, the momentum lattice issymmetrically populated. Conversely, for oblique pump incidence the motionalong the two recoil directions is unbalanced and different momentum states canbe populated on demand by tuning the pump frequency.

Controlled generation of momentum states in a high-finesse ring cavity