Effects of disorder upon transport and Anderson Localization in a finite, two dimensional Bose gas

TL;DR

This paper provides theoretical evidence that disorder in a two-dimensional ultracold Bose gas leads to Anderson localization, with random impurities significantly suppressing transport and regular patterns having a lesser effect, supporting experimental findings.

Contribution

It demonstrates the impact of disorder on transport and localization in a 2D Bose gas through comparative analysis of regular and random impurity patterns.

Findings

Random impurities suppress transport and shorten localization length.

Regular impurity patterns only modestly disturb transport.

Quantum impedance differs significantly between regular and random impurity arrangements.

Abstract

Anderson localization in a two-dimensional ultracold Bose-gas has been demonstrated experimentally. Atoms were released within a dumbbell-shaped optical trap, where the channel of variable aspect ratio provided the only path for particles to travel between source and drain reservoirs. This channel can be populated with columnar (repulsive) optical potential spikes of square cross section with arbitrary pattern. These spikes constitute impurities, the scattering centres for the otherwise free propagation of the particles. This geometry does not allow for classical potential trapping which can be hard to exclude in other experimental setups. Here we add further theoretical evidence for Anderson localization in this system by comparing the transport processes within a regular and a random pattern of impurities. It is demonstrated that the transport within randomly distributed impurities is suppressed and the corresponding localization length becomes shorter than the channel length. However, if an equal density of impurities are distributed in a regular manner, the transport is only modestly disturbed. This observation corroborates the conclusions of the experimental observation: the localization is indeed attributed to the disorder. Beyond analysing the density distribution and the localization length, we also calculate a quantum `impedance' exhibiting qualitatively different behaviour for regular and random impurity patterns.