Local dynamics of laser cooling in an optical lattice

Using the basis of Wannier states, we study the local dynamics of polarization gradient cooling for an atom driven on a J(g)=2-->J(e)=3 transition by a one-dimensional optical lattice. This analysis allows us to formulate a physical picture of the cooling mechanism, analogous to Sisyphus cooling for a J(g)=1/2-->J(e)=3/2 atom, which depends strongly on coherences in the Zeeman sublevels of the ground state. In addition, we are able to explain the steady-state properties of the laser-cooled atoms in a regime where the standard semiclassical analysis breaks down.