Mean-field dynamics of a two-mode Bose-Einstein condensate subject to noise and dissipation

TL;DR

This paper derives a mean-field model for a two-mode Bose-Einstein condensate with noise and dissipation, revealing altered phase space structures and metastable behavior, with results validated against full many-body simulations.

Contribution

It introduces a non-Hermitian mean-field equation for open two-mode Bose-Einstein condensates, connecting phenomenological models with full quantum dynamics.

Findings

Dissipation causes fixed points to change from elliptic/hyperbolic to attractive/repulsive.

Metastable behavior increases condensate purity.

Mean-field results agree well with full quantum simulations.

Abstract

We discuss the dynamics of an open two-mode Bose-Hubbard system subject to phase noise and particle dissipation. Starting from the full many-body dynamics described by a master equation the mean-field limit is derived resulting in an effective non-hermitian (discrete) Gross-Pitaevskii equation which has been introduced only phenomenologically up to now. The familiar mean-field phase space structure is substantially altered by the dissipation. Especially the character of the fixed points shows an abrupt transition from elliptic or hyperbolic to attractiv or repulsive, respectively. This reflects the metastable behaviour of the corresponding many-body system which surprisingly also leads to a significant increase of the purity of the condensate. A comparison of the mean-field approximation to simulations of the full master equation using the Monte Carlo wave function method shows an excellent agreement for wide parameter ranges.