Out-of-equilibrium dynamical properties of Bose-Einstein condensates in a ramped up weak disorder

TL;DR

This paper investigates the out-of-equilibrium dynamics of Bose-Einstein condensates under weak disorder ramp-up, revealing reversible and irreversible deformations, analytical solutions for exponential ramps, and properties of the resulting steady state.

Contribution

It provides a theoretical framework for understanding the dynamical evolution and steady state properties of condensates during disorder ramp-up, including analytical expressions for specific protocols.

Findings

Decomposition of condensate deformation into equilibrium and dynamical parts.

Analytical time-dependent expressions for exponential ramp-up.

Identification of a long-time out-of-equilibrium steady state.

Abstract

We theoretically study how the superfluid and condensate deformation of a weakly interacting ultracold Bose gas evolve during the ramp-up of an external weak disorder potential. Both resulting deformations turn out to consist of two distinct contributions, namely a reversible equilibrium one, already predicted by Huang and Meng in 1992, and a nonequilibrium dynamical one, whose magnitude depends on the details of the ramping protocol. For the specific case of the exponential ramp-up protocol, we are able to derive analytical time-dependent expressions for the above quantities. After a sufficiently long time, a steady state emerges that is generically out of equilibrium. We take the first step in investigating its properties by studying its relaxation dynamics. In addition, we analyze the two-time correlation function and elucidate its relation to the equilibrium and the dynamical part of the condensate deformation.