Mean-field approach to dipole-dipole interaction in an optical lattice

We compare the influence of quantum statistics and atom-atom interaction in bright and dark one-dimensional optical lattices for atoms using quantum rate equations. Via a Hartree-Fock-type mean-field approach we derive an effective nonlinear single-atom equation and solve it self-consistently for a prescribed atomic density. Using a simplified dipole-dipole interaction potential, we show that the atomic energy bands are very sensitive to the mean atomic density, even in a parameter regime where temperature and band populations exhibit only a very small density dependence. Bright lattices show energy shifts towards smaller band separations, while the effect is in the opposite direction and smaller for dark lattices. In general, dipole-dipole interaction strongly dominates the influence of quantum statistics, except for very large detunings, where the spontaneous emission rate is very small. [S1050-2947(99)51610-7].