Spatial diffusion in a periodic optical lattice: revisiting the Sisyphus effect

We numerically study the spatial diffusion of an atomic cloud experiencing Sisyphus cooling in a three-dimensional lin$\bot$lin optical lattice in a broad range of lattice parameters. In particular, we investigate the dependence on the size of the lattice sites which changes with the angle between the laser beams. We show that the steady-state temperature is largely independent of the lattice angle, but that the spatial diffusion changes significantly. It is shown that the numerical results fulfil the Einstein relations of Brownian motion in the jumping regime as well as in the oscillating regime. We finally derive an effective Brownian motion model from first principles which gives good agreement with the simulations.