Realizing PT-symmetric non-Hermiticity with ultra-cold atoms and Hermitian multi-well potentials

TL;DR

This paper explores how to implement PT-symmetric non-Hermitian systems using ultra-cold atoms in multi-well potentials, demonstrating stable solutions even with interactions, through variational methods.

Contribution

It introduces a method to realize PT-symmetric non-Hermiticity with ultra-cold atoms in multi-well setups, validated by variational approaches.

Findings

PT-symmetric currents can be induced with additional wells

Stable solutions persist despite interactions

Simplified and accurate variational methods confirm results

Abstract

We discuss the possibility of realizing a non-Hermitian, i.e. an open two-well system of ultra-cold atoms by enclosing it with additional time-dependent wells that serve as particle reservoirs. With the appropriate design of the additional wells PT-symmetric currents can be induced to and from the inner wells, which support stable solutions. We show that interaction in the mean-field limit does not destroy this property. As a first method we use a simplified variational ansatz leading to a discrete nonlinear Schr\"odinger equation. A more accurate and more general variational ansatz is then used to confirm the results.