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arXiv:cond-mat/0702591 · Physical Review Letters

Superfluidity versus Anderson Localization in a Dilute Bose Gas

Tobias Paul, Peter Schlagheck, P. Lebœuf, Nicolas Pavloff

Published May 23, 2007• 85 citations
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Abstract

We consider the motion of a quasi-one-dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of stationary flow. One is subsonic and corresponds to superfluid motion. The other one is supersonic and dissipative and shows Anderson localization. We compute analytically the interaction-dependent localization length. We also explain the disappearance of the supersonic stationary flow for large disordered samples.

DOI
10.1103/physrevlett.98.210602

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We numerically study the Anderson localization in an oscillating one-dimensional Rydberg-dressed Bose-Einstein condensate with weak random disorder in which the range of the interaction, the blockade radius Rc{R}_{\mathrm{c}}Rc​, is variable. Without disorder, the uniform system can undergo a superfluid-supersolid transition at ${R}_{\text{c}}={l}_{\mathrm{c}}\ensuremath{\simeq}1.7{\ensuremath{\xi}}_{0}$ with ${\ensuremath{\xi}}_{\text{0}}$ the zero-range healing length. When ${\ensuremath{\xi}}_{0}$ exceeds the disorder correlation length ${\ensuremath{\sigma}}_{\mathrm{D}}$, we show that exponential localization occurs in the equilibrium condensate when ${R}_{\mathrm{c}}\ensuremath{\le}{l}_{\mathrm{c}}$, while Gaussian localization occurs when Rc>lc{R}_{\mathrm{c}}>{l}_{\mathrm{c}}Rc​>lc​. The latter suggests that the kkk wave for a long-ranged interacting system could decay Gaussianly with weak random disorder.