Dipole-dipole selection rules for an atom laser cavity

The effects of a recently proposed quasi-one-dimensional atom cavity on dipole-dipole collisions in a trapped atomic sample are investigated. It is shown that the cavity geometry leads to a high degree of selectivity in the allowed exchange of momentum during transitions between cavity modes. Furthermore, by a temporal modulation of the trap potential at the frequency corresponding to the energy defect of the momentum-selected transition, energy selectivity can also be achieved. Hence, in a properly designed atom laser cavity, the combined effects of energy and momentum selection rules give rise to a mode selectivity which is analogous to the mode selectivity in an optical laser.