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arXiv · 1710.08181

Realization of balanced gain and loss in a time-dependent four-mode Bose-Hubbard model

Daniel Dizdarevic·Jörg Main·Kirill Alpin·Johannes Reiff·Dennis Dast·Holger Cartarius·Günter Wunner
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Abstract

A quantum system exhibiting $\mathcal{PT}$ symmetry is a Bose-Einstein condensate in a double-well potential with balanced particle gain and loss, which is described in the mean-field limit by a Gross-Pitaevskii equation with a complex potential. A possible experimental realization of such a system by embedding it into a Hermitian time-dependent four-mode optical lattice was proposed by Kreibich et al. [Phys. Rev. A 87, 051601(R) (2013)], where additional potential wells act as reservoirs and particle exchange happens via tunneling. Since particle influx and outflux have to be controlled explicitly, a set of conditions on the potential parameters had to be derived. In contrast to previous work, our focus lies on a full many-body description beyond the mean-field approximation using a Bose-Hubbard model with time-dependent potentials. This gives rise to novel quantum effects, such that the differences between mean-field and many-body dynamics are of special interest. We further present stationary analytical solutions for the embedded wells in the mean-field limit, different approaches for the embedding into a many-body system, and a very efficient method for the evaluation of hopping terms to calculate exact Bose-Hubbard dynamics.

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Daniel Dizdarevic, Jörg Main, Kirill Alpin, Johannes Reiff, Dennis Dast, Holger Cartarius, Günter Wunner. 2018-01-09. Realization of balanced gain and loss in a time-dependent four-mode Bose-Hubbard model. https://doi.org/10.1103/physreva.97.013623

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