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

TL;DR

This paper proposes a realistic point-like disorder model for two-dimensional ultracold gases to observe Anderson localization, overcoming classical percolation limits, and provides theoretical and simulation evidence for observable localization lengths.

Contribution

It introduces a novel point-like disorder potential that bypasses the high percolation threshold in 2D ultracold gases, enabling experimental observation of Anderson localization.

Findings

Percolation threshold limits classical localization in 2D speckle potentials.

Exact scattering cross sections and scaling theory accurately estimate localization lengths.

Born approximation significantly underestimates localization lengths at low energies.

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 Schr\"{o}dinger 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.