Dynamics of atoms in optical lattices

Optical lattices are formed when cold atoms get trapped in the periodic arr ay of optical potential wells created by a number of traveling light waves. Exact periodicity is guaranteed when the number of traveling waves exceeds the number of dimensions by no more than one. We present a few simple exac tly solvable models for the transport of atoms over a lattice in the tight binding limit. One model concerns the spreading of an atom by tunneling thr ough the barriers and by momentum recoil induced by optical pumping. Anothe r model gives results for the amplitude of Bloch oscillations, which occur when a uniform is added to the periodic potential. Finally the dissipative spreading of the quasimomentum due to optical pumping is modeled.