Transport and the first passage time problem with application to cold atoms in optical traps

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.