# Vortices in Bose-Einstein condensates with $\mathcal{PT}$-symmetric gain and loss

## TL;DR

This paper explores how $ ext{PT}$-symmetric gain and loss in Bose-Einstein condensates affect vortex states, revealing conditions for their existence, transitions, and dynamic behaviors in open quantum systems.

## Contribution

It introduces a method to analyze vortex states in $ ext{PT}$-symmetric potentials, highlighting their stability and transition conditions in open Bose-Einstein condensates.

## Key findings

- Stationary vortex states exist under specific $ ext{PT}$-symmetry conditions.
- Transitions between vortex and non-vortex states are characterized.
- Non-stationary vortex dynamics are influenced by $ ext{PT}$ symmetry.

## Abstract

We investigate vortex excitations in dilute Bose-Einstein condensates in the presence of complex $\mathcal{PT}$-symmetric potentials. These complex potentials are used to describe a balanced gain and loss of particles and allow for an easier calculation of stationary states in open systems than in a full dynamical calculation including the whole environment. We examine the conditions under which stationary vortex states can exist and consider transitions from vortex to non-vortex states. In addition, we study the influences of $\mathcal{PT}$ symmetry on the dynamics of non-stationary vortex states placed at off-center positions.