Three-dimensional spatial diffusion in optical molasses

Non-Gaussian velocity distributions in optical lattices

“…Tsallis function Beyond the linear regime for atomic velocity, the friction force and the velocity diffusion coefficients have to be refined into [13,20]:…”

Anomalous diffusion and Tsallis statistics in an optical lattice

“…The fact that the steady-state solution of Eq. (1) is non-Gaussian is of course well-known [16,17,19]. Surprisingly, however, it has not been realized that this precisely corresponds to a Tsallis distribution.…”

“…Let us first remind that the distribution (5) is not normalizable for a Tsallis index 3 ≤ q or, equivalently, for αp 2 c ≤ D 0 . Physically, this means that the cooling force is too weak, compared to the random momentum fluctuations, to maintain the particle in a steady state around p = 0 (this is often referred to as décrochage [16,17]). On the other hand, in the limit where q → 1 (D 0 ≪ αp 2 c ), the stationary solution (5) reduces to the standard Maxwell-Boltzmann distribution,…”

“…Depending on the depth of the optical potential, three different regimes can be identified [14,[16][17][18][19][20]: (i) diffusive motion in deep potentials, (ii) ballistic motion in shallow potentials and (iii) an intermediate regime in between (of main interest here) where anomalous (non-Gaussian) diffusion takes place. The existence of Lévy-like diffusion with long jumps below a given potential threshold has been predicted by Marksteiner et al [19] and later experimentally verified by a group at the MPQ in Garching by studying the dynamics of a single ion in a one-dimensional optical lattice [20].…”

“…After spatial averaging, the Rayleigh equation for the corresponding semiclassical Wigner function W (p, t) can be written as [16,17,19],…”