Physical Review A | 2019
Interaction effects on the PT -symmetry-breaking transition in atomic gases
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.