Dynamics of atoms in optical lattices

Optical lattices are formed when cold atoms get trapped in the periodic array 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 exactly 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 through the barriers and by momentum recoil induced by optical pumping. Another 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.