Coupling approach for the realization of a $\mathcal{PT}$-symmetric potential for a Bose-Einstein condensate in a double well

TL;DR

This paper demonstrates how to realize a $ ext{PT}$-symmetric potential in a Bose-Einstein condensate by coupling it to an environment, enabling effective non-Hermitian dynamics through a physical setup.

Contribution

It introduces a method to achieve $ ext{PT}$ symmetry in BECs via environmental coupling, providing a practical framework for experimental realization.

Findings

The approach is viable with numerical simulations confirming stability.

Specific environmental conditions are identified for stationary $ ext{PT}$-symmetric states.

Potential vulnerabilities due to the delta-shaped potential are discussed.

Abstract

We show how non-Hermitian potentials used to describe probability gain and loss in effective theories of open quantum systems can be achieved by a coupling of the system to an environment. We do this by coupling a Bose-Einstein condensate (BEC) trapped in an attractive double-delta potential to a condensate fraction outside the double well. We investigate which requirements have to be imposed on possible environments with a linear coupling to the system. This information is used to determine an environment required for stationary states of the BEC. To investigate the stability of the system we use fully numerical simulations of the dynamics. It turns out that the approach is viable and possible setups for the realization of a $\mathcal{PT}$-symmetric potential for a BEC are accessible. Vulnerabilities of the whole system to small perturbations can be adhered to the singular character of the simplified delta-shaped potential used in our model.