Dynamic evolution of expanding Bose–Einstein condensates in the presence of a three-dimensional random optical speckle potential

Abstract

We study the diffusion of an expanding Bose-Einstein condensate released from a harmonic trap in a three-dimensional speckle disorder potential. To this end, we use the first Born approximation and examine the density profiles at short and long times. Analytical results are presented in different regimes. The spatiotemporal evolution of the density profiles is examined. We find that at long times and for a fixed disorder strength, the profile of the atomic average density decreases in power law. The time evolution of the typical size of the condensate is explored numerically.

Anisotropy effects on the quantum transport of atomic matter waves

“…It is thus related to the finite disorder correlation length. These results are comparable with those found in the literature [24], where q á ñ = cos 1 3 for all kξ = 1. Now let us analyze the scattering mean free path ℓ s in terms of the pertinent parameter ε/ε ξ .…”

“…In this paper, we report on the systematic study of the weak localization effects in the anisotropic transport properties of matter wave in 3D optical potentials employing the first Born approximation (FBA). This latter has been recently proven effective in analyzing the elastic scattering time of matter waves [23], the dynamic evolution of expanding BECs [24], diffusion and localization in optical disordered potentials (see e.g. [12,35]), and good agreement is obtained with experimental and numerical data [23].…”

“…It has been found that the transport of atomic matter waves in three-dimensional (3D) media is significantly affected by three parameters: the disorder amplitude, the initial wave energy and the correlation energy induced by disorder. Quite recently, the dynamic evolution of expanding Bose-Einstein condensates (BECs) in 3D random potential has been deeply examined in space and time [24].…”