Hermitian four-well potential as a realization of a PT-symmetric system

TL;DR

This paper proposes a realistic experimental setup using a four-well Hermitian system to emulate PT-symmetric behavior in Bose-Einstein condensates, bridging theoretical models with practical implementation.

Contribution

It introduces a four-well Hermitian model that replicates PT-symmetric dynamics, providing conditions and parameters for experimental realization.

Findings

Derived conditions for PT-symmetric behavior in a four-well system

Calculated stationary and oscillatory solutions under these conditions

Linked the four-mode model to the Gross-Pitaevskii equation for experimental parameters

Abstract

A PT-symmetric Bose-Einstein condensate can be theoretically described using a complex optical potential, however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum mechanical realization of a PT-symmetric system, where the PT-symmetric currents of a two-well system are implemented by coupling two additional wells to the system, which act as particle reservoirs. In terms of a simple four-mode model we derive conditions under which the two middle wells of the Hermitian four-well system behave exactly as the two wells of the PT-symmetric system. We apply these conditions to calculate stationary solutions and oscillatory dynamics. By means of frozen Gaussian wave packets we relate the Gross-Pitaevskii equation to the four-mode model and give parameters required for the external potential, which provides approximate conditions for a realistic experimental setup.