Interaction effects on $\mathcal{P}\mathcal{T}$-symmetry breaking transition in atomic gases

Abstract

Non-Hermitian systems having parity-time ($\mathcal{P}\mathcal{T}$) 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 $h_{\mathcal{P}T}=-i\Gamma {\sigma }_z+J{\sigma }_x$, which has $\mathcal{P}\mathcal{T}$-symmetry, can be simulated in a \emph{passive} way. We show that when interatomic interactions are tuned to maintain the symmetry, the $\mathcal{P}\mathcal{T}$-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 ${\Gamma }_{\mathrm{tr}}$ decreases as $|\delta g|$ or $N$ increases; in the large $|\delta g|$ limit, ${\Gamma }_{\mathrm{tr}}$ scales as $\sim |\delta g{|}^{-(N-1)}$. We also give signatures of the $\mathcal{P}\mathcal{T}$-symmetric and the symmetry breaking phases for the interacting bosons in experiment.

4 pages, 4 figures

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• Stability and collisions of quantum droplets in PT -symmetric dual-core couplers
• Quantum fluctuations on top of a $\mathcal{P}\mathcal{T}$-symmetric Bose-Einstein Condensate
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