Localization of weakly interacting Bose gas in quasiperiodic potential

TL;DR

This paper investigates how weak interactions affect localization in a quasiperiodic Bose gas, using multiple methods including superfluid fraction, participation ratio, classical maps, and Bogoliubov theory, revealing slow localization growth and coherence loss.

Contribution

It introduces a comprehensive analysis of localization in weakly interacting Bose gases within quasiperiodic potentials, combining quantum and classical approaches to reveal new localization behaviors.

Findings

Inverse participation ratio increases slowly post-localization transition

Multisite localization of the wave function observed

Localization manifests as chaotic dynamics in classical maps

Abstract

We study the localization properties of weakly interacting Bose gas in a quasiperiodic potential commonly known as Aubry-Andr\'e model. Effect of interaction on localization is investigated by computing the `superfluid fraction' and `inverse participation ratio'. For interacting Bosons the inverse participation ratio increases very slowly after the localization transition due to `multisite localization' of the wave function. We also study the localization in Aubry-Andr\'e model using an alternative approach of classical dynamical map, where the localization is manifested by chaotic classical dynamics. For weakly interacting Bose gas, Bogoliubov quasiparticle spectrum and condensate fraction are calculated in order to study the loss of coherence with increasing disorder strength. Finally we discuss the effect of trapping potential on localization of matter wave.