Simulation of Anderson localization in two-dimensional ultracold gases for point-like disorder

Abstract

Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold gases has been elusive. We show that a cause of this difficulty is the relatively high percolation threshold of a speckle potential in two dimensions, resulting in strong classical localization. We propose a realistic point-like disorder potential that circumvents this percolation limit with localization lengths that are experimentally observable. The percolation threshold is evaluated for experimentally realistic parameters, and a regime of negligible classical trapping is identified. Localization lengths are determined via scaling theory, using both exact scattering cross sections and the Born approximation, and by direct simulation of the time-dependent Schrödinger equation. We show that the Born approximation can underestimate the localization length by four orders of magnitude at low energies, while exact cross sections and scaling theory provide an upper bound. Achievable experimental parameters for observing localization in this system are proposed.

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• Localization of ultrasound in a three-dimensional elastic network
• Continuum Percolation Thresholds in Two Dimensions
• A high-accuracy algorithm for designing arbitrary holographic atom traps
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• Quantum simulating the electron transport in quantum cascade laser structures
• Equilibrium phases of dipolar lattice bosons in the presence of random diagonal disorder
• The effect of disorder on the phase diagrams of hard-core lattice bosons with cavity-mediated long-range and nearest-neighbor interactions
• Effects of disorder upon transport and Anderson Localization in a finite, two dimensional Bose gas
• Phase diagrams of the disordered Bose-Hubbard model with cavity-mediated long-range and nearest-neighbor interactions
• The impact of speckle disorder on a superfluid Fermi system
• Selective final state spectroscopy and multifractality in two-component ultracold Bose-Einstein condensates: a numerical study
• From percolation transition to Anderson localization in one-dimensional speckle potentials