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

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.

10 pages, 5 figures, additions in the text, to be published in Phys. Rev. A

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Cited by in corpus (6)

• Interaction effects on $\mathcal{P}\mathcal{T}$-symmetry breaking transition in atomic gases
• Stability and collisions of quantum droplets in PT -symmetric dual-core couplers
• Pseudo steady-state non-Gaussian EPR-steering of massive particles in pumped and damped Bose-Hubbard dimers
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Realization of balanced gain and loss in a time-dependent four-mode Bose-Hubbard model
• PT symmetry and the evolution speed in open quantum systems