Bose-Einstein condensates with balanced gain and loss beyond mean-field theory

TL;DR

This paper investigates the many-particle dynamics of Bose-Einstein condensates with balanced gain and loss beyond mean-field theory, revealing that purity revivals are mainly influenced by gain/loss strength rather than particle number or interactions.

Contribution

It provides analytic solutions in the non-interacting case and uses the Bogoliubov backreaction method to analyze the impact of interactions, extending understanding beyond mean-field approximations.

Findings

Purity revivals are primarily determined by gain and loss strength.

Revival timing shifts with particle number and interaction strength.

Strong revivals occur earlier with increased interaction strength.

Abstract

Most of the work done in the field of Bose-Einstein condensates with balanced gain and loss has been performed in the mean-field approximation using the PT-symmetric Gross-Pitaevskii equation. In this work we study the many-particle dynamics of a two-mode condensate with balanced gain and loss described by a master equation in Lindblad form whose purity periodically drops to small values but then is nearly completely restored. This effect cannot be covered by the mean-field approximation, in which a completely pure condensate is assumed. We present analytic solutions for the dynamics in the non-interacting limit and use the Bogoliubov backreaction method to discuss the influence of the on-site interaction. Our main result is that the strength of the purity revivals is almost exclusively determined by the strength of the gain and loss and is independent of the amount of particles in the system and the interaction strength. For larger particle numbers, however, strong revivals are shifted towards longer times, but by increasing the interaction strength these strong revivals again occur earlier.