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 $J_g=2\mathrm{}\to J_e=3\mathrm{}$ 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 $J_g=1/2\mathrm{}\to J_e=3/2\mathrm{}$ 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.