Weak localization with nonlinear bosonic matter waves

TL;DR

This paper studies how weak localization phenomena in Bose-Einstein condensates are affected by atomic interactions, revealing a universal dephasing effect and potential weak antilocalization signatures through a combined analytical and numerical approach.

Contribution

It introduces a diagrammatic theory for nonlinear matter wave scattering in chaotic billiards, linking interaction effects to weak localization dephasing and weak antilocalization signatures.

Findings

Universal dephasing of weak localization due to interactions

Good agreement between theory and numerical reflection/transmission data

Potential observation of weak antilocalization effects

Abstract

We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross-Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions.