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arXiv:1403.3821 · Physical Review Letters

Mobility Edge for Cold Atoms in Laser Speckle Potentials

Dominique Delande, Giuliano Orso

Published Aug 6, 2014• 87 citations
arXivHTMLPDF

Abstract

Using the transfer-matrix method, we numerically compute the precise position of the mobility edge of atoms exposed to a laser speckle potential and study its dependence versus the disorder strength and correlation function. Our results deviate significantly from previous theoretical estimates using an approximate, self-consistent approach of localization. In particular, we find that the position of the mobility edge in blue-detuned speckles is much lower than in the red-detuned counterpart, pointing out the crucial role played by the asymmetric on-site distribution of speckle patterns.

DOI
10.1103/physrevlett.113.060601

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Using the transfer-matrix method, we numerically compute the precise position of the mobility edge of atoms exposed to a laser speckle potential and study its dependence versus the disorder strength and correlation function. Our results deviate significantly from previous theoretical estimates using an approximate, self-consistent approach of localization. In particular, we find that the position of the mobility edge in blue-detuned speckles is much lower than in the red-detuned counterpart, pointing out the crucial role played by the asymmetric on-site distribution of speckle patterns.
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Recent experiments in noninteracting ultracold atoms in three-dimensional speckle potentials have yielded conflicting results regarding the so-called mobility edge, i.e., the energy threshold separating Anderson localized from diffusive states. At the same time, there are theoretical indications that most experimental data overestimate this critical energy, sometimes by a large amount. Using extensive numerical simulations, we show that the effect of anisotropy in the spatial correlations of realistic disorder configurations alone is not sufficient to explain the experimental data. In particular, we find that the mobility edge obeys a universal scaling behavior, independently of the speckle geometry.
We study Anderson localization of ultracold atoms in weak one-dimensional speckle potentials using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between energy regions where localization lengths differ by orders of magnitude. We also point out that the correction to the Born term explicitly depends on the sign of the potential. Our results are in agreement with numerical calculations in a regime relevant for experiments. Finally, we analyze our findings in the light of a diagrammatic approach.