Bose-Einstein condensates with gain and loss: quantum master equation and purity oscillations.
A Bose-Einstein condensate (BEC) trapped in a double-well potential, where in one well particles are removed and in the other particles are added, can in the mean-field limit be described by a PT-symmetric Gross-Pitaevskii equation. Indeed, most of the work done in the field of BECs with balanced gain and loss has been performed in the mean-field approximation. We present a quantum master equation describing a BEC with particle loss on one lattice site and particle gain on the other. Its mean-field limit is a non-Hermitian PT-symmetric Gross-Pitaevskii equation. Many aspects of the dynamics of both equations are in excellent agreement. However, the many-particle description exhibits a much richer structure. With this approach we uncover a new generic feature of PT-symmetric BECs. We show that the purity of the condensate’s single-particle density matrix periodically drops to small values but then is nearly completely restored. This indicates that during the oscillations the particles leave the single-particle orbital of the condensed phase and return afterwards to an almost perfect mean-field state. The oscillations have a direct impact on the average contrast in interference experiments, which periodically vanishes and recurs.
The seminar is part of a one-day workshop entitled “New mathematical methods for open quantum systems.” Details of timings and the location can be foind on the Maths Events feed here. The programme can also be found here.