Anderson localization of elementary excitations in a one dimensional Bose-Einstein condensate

TL;DR

This paper investigates how elementary excitations in a one-dimensional Bose-Einstein condensate become localized due to weak random potentials, covering different density regimes and types of disorder, with implications for recent experimental systems.

Contribution

It provides a comprehensive analysis of localization lengths of excitations in 1D BECs under various disorder conditions and density regimes, extending understanding of Anderson localization in these systems.

Findings

Localization length varies with energy and density regime.

White noise potential causes localization in the hydrodynamical regime.

Point-like impurities induce localization across all energies.

Abstract

We study the elementary excitations of a transversely confined Bose-Einstein condensate in presence of a weak axial random potential. We determine the localization length (i) in the hydrodynamical low energy regime, for a domain of linear densities ranging from the Tonks-Girardeau to the transverse Thomas-Fermi regime, in the case of a white noise potential and (ii) for all the range of energies, in the ``one-dimensional mean field regime'', in the case where the randomness is induced by a series of randomly placed point-like impurities. We discuss our results in view of recent experiments in elongated BEC systems.