# Realization of $\mathcal{PT}$-symmetric and $\mathcal{PT}$-symmetry broken states in static optical lattice potentials

## TL;DR

This paper demonstrates how to create and control $ ext{PT}$-symmetric and broken states in a Bose-Einstein condensate within an optical lattice, using localized loss and initial current settings, revealing new ways to realize non-Hermitian physics.

## Contribution

It introduces a method to generate $ ext{PT}$-symmetric and broken states in a BEC with localized loss, expanding the understanding of non-Hermitian systems in optical lattices.

## Key findings

- Creation of $ ext{PT}$-symmetric and broken states via initial current control.
- The embedded two-mode subsystem mimics non-Hermitian two-mode dynamics.
- Localized loss reduces the condensate size needed for realization.

## Abstract

R. Labouvie et al. [Phys. Rev. Lett. 116, 235302 (2016)] have described an experiment with a weakly interacting Bose-Einstein condensate trapped in a one-dimensional optical lattice with localized loss created by a focused electron beam. We show that by setting suitable initial currents between neighboring sites it is possible to create $\mathcal{PT}$-symmetric quasi-stationary and $\mathcal{PT}$-symmetry broken decaying states in an embedded two-mode subsystem. This subsystem exhibits gain provided by the coupling to the reservoir sites and localized loss due to the electron beam, and shows the same dynamics as a non-Hermitian two-mode system with symmetric real and antisymmetric imaginary time-independent potentials, except for a proportionality factor in the chemical potential. We also show that there are three other equivalent scenarios, and that the presence of a localized loss term significantly reduces the size of the condensate required for the realization.