  Measurements of spatial diffusion of cold atoms in optical lattices have
revealed anomalous super-diffusion, which is controlled by the depth of the
optical lattice. We use first passage time statistics to derive the diffusion
front of the atoms. In particular, the distributions of areas swept under the
first passage curve till its first arrival, and of areas under the Bessel
excursion are shown to be powerful tools in the analysis of the atomic cloud. A
rather general relation between first passage time statistics and diffusivity
is discussed, showing that first passage time analysis is a useful tool in the
calculation of transport coefficients. A brief introduction to the
semi-classical description of Sisyphus cooling is provided which yields a rich
phase diagram for the dynamics.
