Anderson localization in optical lattices with correlated disorder

Abstract

We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are determined as a function of the disorder strength, ranging from vanishing disorder up to the critical disorder intensity where the two mobility edges merge and the whole band becomes localized. Our theoretical analysis is based both on continuous-space models which take into account the details of the spatial correlation of the speckle pattern, and also on a simplified tight-binding model with an uncorrelated distribution of the on-site energies. The mobility edges are computed via the analysis of the energy-level statistics, and we determine the universal value of the ratio between consecutive level spacings at the mobility edge. We analyze the role of the spatial correlation of the disorder, and we also discuss a qualitative comparison with available experimental data for interacting atomic Fermi gases measured in the moderate interaction regime.Comment: 9 pages, 7 figure

Wave‐Packet Dynamics in Chains with Disorder‐Type Ornstein–Uhlenbeck and Static Electric Field

“…From the experimental point of view, we think that these results could be observed in appropriately designed random microwave waveguides [30,31] or optical lattices. [17,32]…”

At the edge of mobility

“…They add to the recent exact numerical calculations performed for similar systems 9,10 . But the theory is largely incomplete.…”

Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

“…Sinha et al [76] study the Kibble-Zurek mechanism for generalized AA model with an energy-dependent mobility edge. Experimentally, the observation of the mobility edge has been reported in non-interacting ultra-cold atomic systems with a three-dimensional speckle disorder [11][12][13][14] and different numerical methods are proposed to estimate the position of E c [14,[84][85][86][87][88]. By monitoring the time evolution of the density imbalance and the global size of the atom cloud, the direct experimental research of the mobility edge in a one-dimensional quasi-random optical lattice of an initial charge-density wave state [47] is in good agreement with the theoretical results [89].…”