Dissipative Transport of Trapped Bose-Einstein Condensates through Disorder

TL;DR

This paper develops an analytic hydrodynamic model for the dissipative transport of trapped Bose-Einstein condensates through disorder, successfully matching experimental data and revealing how interactions reduce disorder effects and influence damping.

Contribution

It introduces a simple yet comprehensive theoretical framework for understanding dissipative transport of finite-size Bose-Einstein condensates in disordered potentials, with analytic expressions and experimental validation.

Findings

Quantifies dissipative regimes with slow and fast damping.

Shows interactions reduce effective disorder strength.

Predicts power-law dependence of damping on interactions.

Abstract

After almost half a century since the work of Anderson [Phys. Rev. {\bf 109}, 1492 (1958)], at present there is no well established theoretical framework for understanding the dynamics of interacting particles in the presence of disorder. Here, we address this problem for interacting bosons near $T=0$, a situation that has been realized in trapped atomic experiments with an optical speckle disorder. We develop a theoretical model for understanding the hydrodynamic transport of \emph{finite-size} Bose-Einstein condensates through disorder potentials. The goal has been to set up a simple model that will retain all the richness of the system, yet provide analytic expressions, allowing deeper insight into the physical mechanism. Comparison of our theoretical predictions with the experimental data on large-amplitude dipole oscillations of a condensate in an optical-speckle disorder shows striking agreement. We are able to quantify various dissipative regimes of slow and fast damping. Our calculations provide a clear evidence of reduction in disorder strength due to interactions. The analytic treatment presented here allows us to predict the power law governing the interaction dependance of damping. The corresponding exponents are found to depend sensitively on the dimensionality and are in excellent agreement with experimental observations. Thus, the adeptness of our model, to correctly capture the essential physics of dissipation in such transport experiments, is established.