# Interaction effects on $\mathcal{PT}$-symmetry breaking transition in atomic gases

## TL;DR

This paper investigates how interatomic interactions influence the parity-time ($ ext{PT}$) symmetry breaking transition in ultracold atomic gases, revealing that the transition point depends on interaction parameters and system size.

## Contribution

It introduces a model for interacting bosons under $ ext{PT}$-symmetric Hamiltonian and analyzes how interactions modify the symmetry breaking transition point.

## Key findings

- Transition point $ ext{Γ}_{
m tr}$ decreases with interaction strength and particle number.
- In the large interaction limit, $ ext{Γ}_{
m tr}$ scales as $| ext{δg}|^{-(N-1)}$.
- Signatures of $ ext{PT}$ phases are proposed for experimental detection.

## Abstract

Non-Hermitian systems having parity-time ($\mathcal {PT}$) symmetry can undergo a transition, spontaneously breaking the symmetry. Ultracold atomic gases provide an ideal platform to study interaction effects on the transition. We consider a model system of $N$ bosons of two components confined in a tight trap. Radio frequency and laser fields are coupled to the bosons such that the single particle Non-Hermitian Hamiltonian $h_{\mathcal PT}=-i \Gamma\sigma_z+J\sigma_x$, which has $\mathcal {PT}$-symmetry, can be simulated in a \emph{passive} way. We show that when interatomic interactions are tuned to maintain the symmetry, the $\mathcal {PT}$-symmetry breaking transition is affected only by the SU(2) variant part of the interactions parameterized by $\delta g$. We find that the transition point $\Gamma_{\rm tr}$ decreases as $|\delta g|$ or $N$ increases; in the large $|\delta g|$ limit, $\Gamma_{\rm tr}$ scales as $\sim|\delta g|^{-(N-1)}$. We also give signatures of the $\mathcal {PT}$-symmetric and the symmetry breaking phases for the interacting bosons in experiment.