Weak localization with interacting Bose-Einstein condensates

We study the quasi-stationary propagation of Bose-Einstein condensates through two-dimensional mesoscopic scattering geometries that correspond to disorder potentials [1] or to ballistic billiard con nements with chaotic classical dynamics [2]. Our theoretical approach is based on the two-dimensional Gross-Pitaevskii equation, which is numerically integrated in order to determine reflection and transmission probabilities associated with self-consistent stationary scattering states, and which represents the starting point for an analytical description of the scattering process in terms of a nonlinear diagrammatic theory. Both numerically and analytically, we nd that the presence of the atom-atom interaction within the condensate gives rise to signatures of weak antilocalization, i.e. to an inversion of the coherent backscattering peak in disordered systems [1] and to a reduction, instead of an enhancement, of the retro-reflection probability in chaotic billiard geometries [2]. Short-path contributions associated, in particular, with self-retraced trajectories are conjectured to be at the origin of this antilocalization phenomenon.
References:
[1] M. Hartung, T. Wellens, C. A. M uller, K. Richter, and P. Schlagheck, PRL 101, 020603 (2008).
[2] T. Hartmann, J. Michl, C. Petitjean, T. Wellens, J.-D. Urbina, K. Richter, and P. Schlagheck,
Ann. Phys., in press, (arXiv:1112.5603).