Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential

TL;DR

This paper numerically investigates how disordered potentials affect one-dimensional Bose-Einstein condensates, revealing localization effects, soliton behavior, and transport suppression under various interaction regimes.

Contribution

It provides a comprehensive numerical analysis of disorder effects on 1D Bose-Einstein condensates, including localization, soliton dynamics, and momentum space behavior, across different interaction types.

Findings

Disorder reduces the spatial extension of the condensate.

Strong disorder causes localization around zero momentum.

Attractive condensates form solitons with disorder-dependent widths.

Abstract

We present a detailed numerical study of the effect of a disordered potential on a confined one-dimensional Bose-Einstein condensate, in the framework of a mean-field description. For repulsive interactions, we consider the Thomas-Fermi and Gaussian limits and for attractive interactions the behavior of soliton solutions. We find that the disorder average spatial extension of the stationary density profile decreases with an increasing strength of the disordered potential both for repulsive and attractive interactions among bosons. In the Thomas Fermi limit, the suppression of transport is accompanied by a strong localization of the bosons around the state k=0 in momentum space. The time dependent density profiles differ considerably in the cases we have considered. For attractive Bose-Einstein condensates, a bright soliton exists with an overall unchanged shape, but a disorder dependent width. For weak disorder, the soliton moves on and for a stronger disorder, it bounces back and forth between high potential barriers.