Binary Bose-Einstein condensates in a disordered time-dependent potential

TL;DR

This paper investigates how weak disorder and interspecies interactions influence the non-equilibrium dynamics of binary Bose-Einstein condensates, revealing localization effects and out-of-equilibrium steady states relevant for Floquet condensates.

Contribution

It introduces a time-dependent perturbation theory framework to analyze the interplay of disorder and interactions in binary condensates, highlighting the emergence of localized and out-of-equilibrium states.

Findings

Disorder induces localization in both species over time.

The system supports a periodically changing steady state.

Disorder can lead to stationary out-of-equilibrium states.

Abstract

We study the non-equilibrium evolution of binary Bose-Einstein condensates in the presence of weak random potential with a Gaussian correlation function using the time-dependent perturbation theory. We apply this theory to construct a closed set of equations that highlight the role of the spectacular interplay between the disorder and the interspecies interactions in the time evolution of the density induced by disorder in each component. It is found that this latter increases with time favoring localization of both species. The time scale at which the theory remains valid depends on the respective system parameters. We show analytically and numerically that such a system supports a steady state that periodically changing during its time propagation. The obtained dynamical corrections indicate that disorder may transform the system into a stationary out-of-equilibrium states. Understanding this time evolution is pivotal for the realization of Floquet condensates.