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arXiv:1607.08164 · Physical Review Letters

Anderson Transition of Cold Atoms with Synthetic Spin-Orbit Coupling in Two-Dimensional Speckle Potentials

Giuliano Orso

Published Mar 6, 2017• 30 citations
arXivHTMLPDF

Abstract

We investigate the metal-insulator transition occurring in two-dimensional (2D) systems of noninteracting atoms in the presence of artificial spin-orbit interactions and a spatially correlated disorder generated by laser speckles. Based on a high order discretization scheme, we calculate the precise position of the mobility edge and verify that the transition belongs to the symplectic universality class. We show that the mobility edge depends strongly on the mixing angle between Rashba and Dresselhaus spin-orbit couplings. For equal couplings a non-power-law divergence is found, signaling the crossing to the orthogonal class, where such a 2D transition is forbidden.

DOI
10.1103/physrevlett.118.105301

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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.
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling theory predicts a quantum phase transition at a critical energy, the mobility edge, separating localized from diffusive states and underpinning metal-insulator transitions in electronic systems. Despite decades of experimental efforts, a direct observation of this emblematic transition for matter waves has remained elusive. Previous attempts with ultracold atoms were hindered by strong and uncontrolled energy broadening, resulting in indirect, sometimes inaccurate, and model-dependent estimates of the mobility edge. Here we implement a novel energy-resolved scheme to prepare atomic matter waves with a narrow energy distribution and track their expansion dynamics over long timescales. This allows for a direct observation of the three-dimensional Anderson transition in a laser-speckle disordered potential, and for a precise measurement of the mobility edge that is independent of any underlying theoretical modeling. Our measurements show excellent agreement with state-of-the-art numerical predictions over a wide range of disorder strengths, resolving long-standing discrepancies between prior experiments and theory. Beyond the three-dimensional Anderson transition, our approach opens new avenues for quantitative investigations of quantum critical phenomena in spatially disordered systems, including the roles of dimensionality, symmetry class, and interactions.