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

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