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

Abstract

A quantum system exhibiting $\mathcal{P}\mathcal{T}$ 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.

arXiv comment12 pages, 5 figures, minor revisions, accepted for publication in Phys. Rev. A

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Cited by in corpus (4)

• Realization of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-symmetry broken states in static optical lattice potentials
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Using mixed many-body particle states to generate exact $\mathcal{P}\mathcal{T}$-symmetry in a time-dependent four-well system
• Balancing gain and loss in symmetrised multi-well potentials