Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

TL;DR

This paper investigates how a weak, time-dependent disorder potential influences the shape and deformation of a Bose-Einstein condensate, revealing non-equilibrium effects and the importance of the disorder switching protocol.

Contribution

It introduces a time-dependent perturbative mean-field approach to study non-equilibrium condensate deformation under controlled disorder switching.

Findings

Deformation includes equilibrium and dynamically-induced parts.

Switching off disorder leaves a long-time dynamically-induced deformation.

Deformation signals non-equilibrium steady states in disordered Bose gases.

Abstract

We consider a time-dependent extension of a perturbative mean-field approach to the dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially equilibrated Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part, that actually corresponds to adiabatic switching on the disorder, and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. We also present an appropriate generalization to inhomogeneous trapped condensates. Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.