Localization of excited states of Bose-Einstein Condensates in presence of disorder

TL;DR

This paper investigates how excited states of Bose-Einstein Condensates localize in disordered media, revealing energy-dependent localization in 1D and complex vortex effects in 2D, with implications for topological excitations.

Contribution

It provides new insights into the localization behavior of excited states in BECs under disorder, including the effects of vorticity and phase dislocations.

Findings

Excited states localize exponentially with decreasing localization length at higher energies in 1D.

Vortices cause phase dislocations and jumps in localized states in 2D.

Localization behavior in BECs shares similarities with topological excitations in superfluids.

Abstract

We study the onset of localization from excited states of trapped Bose- Einstein Condensates expanding in presence of Gaussian uncorrelated random disorder. In 1D systems, we observe that for a fixed ratio between the disorder strength and the initial energy, excited states localize exponentially with a localization length that decreases as the energy of the initial state increases. Moreover, the localized state keeps the shape of the initial state wave function with an exponential tail. In 2D, we analyze the interplay between vorticiy and localization by examining the dispersion of a state containing a vortex on it in a disordered media. Despite localization can be associated to islands of constant phase, the presence of a vortex in the initial state leads to dislocations and phase jumps in the localized state. The study of dispersion of a bosonic condensate with vorticity bears similarities to the stability of topological excitations in 2D p-wave fermionic superfluids.