Interaction effects on $\mathcal{PT}$-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 $h_{\mathcal PT}=-i Γσ_z+Jσ_x$, 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 $δg$. We find that the transition point $Γ_{\rm tr}$ decreases as $|δg|$ or $N$ increases; in the large $|δg|$ limit, $Γ_{\rm tr}$ scales as $\sim|δg|^{-(N-1)}$. We also give signatures of the $\mathcal {PT}$-symmetric and the symmetry breaking phases for the interacting bosons in experiment.

4 pages, 4 figures