Weak localization with nonlinear bosonic matter waves

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.

Intensity distribution of non-linear scattering states

“…Indeed, previous theoretical studies have focused on the question how coherent backscattering in disordered potentials is modified by the presence of the atom-atom interaction [10]. These studies were recently complemented by our investigations on weak localization in the nonlinear transport through ballistic scattering geometries that exhibit chaotic dynamics [11]. While a semiclassical analysis of this nonlinear scattering problem predicted a dephasing of the interference phenomenon that gives rise to coherent backscattering, signatures for weak antilocalization were obtained in the numerically computed reflection and transmission probabilities [11].…”

“…In contrast to Ref. [11], however, we focus here not on transport observables such as the reflection and transmission probabilities through the billiard, but rather on the intensity distributions of stationary scattering states within the billiard. These intensity distributions are to be compared with the theoretical predictions that are obtained from the Random Wave Model (RWM) [12][13][14][15], which, in the linear case, represents probably the most powerful approach to describe the universal spatial cor-relations of eigenstates arising from the classical chaotic behavior due to the presence of a spatial confinement.…”

“…These studies were recently complemented by our investigations on weak localization in the nonlinear transport through ballistic scattering geometries that exhibit chaotic dynamics [11]. While a semiclassical analysis of this nonlinear scattering problem predicted a dephasing of the interference phenomenon that gives rise to coherent backscattering, signatures for weak antilocalization were obtained in the numerically computed reflection and transmission probabilities [11]. This effect was attributed to the specific role of non-universal short-path contributions, in particular to self-retraced paths the presence of which gives rise to a reduction of coherent backscattering as compared to the universal prediction.…”

“…[11], i.e., the quasi-stationary transport of bosonic matter waves through two-dimensional ballistic scattering geometries that exhibit chaotic classical dynamics. In contrast to Ref.…”

The dissipative Bose-Hubbard model

“…As a final note, we report that a semiclassical approach based on interfering paths in Fock space has been recently introduced directly for discrete systems, such as for a closed BoseHubbard model [174][175][176]. Also a semiclassical Gutzwiller trace formula is brought forward [177] for the Bose-Hubbard model in the chaotic regime [178][179][180][181].…”