Quantum fluctuations on top of a $\mathcal{P}\mathcal{T}$-symmetric Bose-Einstein Condensate

Abstract

We investigate the effects of quantum fluctuations in a parity-time($\mathcal{P}\mathcal{T}$) symmetric two-species Bose-Einstein Condensate(BEC). It is found that the $\mathcal{P}\mathcal{T}$-symmetry, though preserved by the macroscopic condensate, can be spontaneously broken by its Bogoliubov quasi-particles under quantum fluctuations. The associated $\mathcal{P}\mathcal{T}$-breaking transitions in the Bogoliubov spectrum can be conveniently tuned by the interaction anisotropy in spin channels and the strength of $\mathcal{P}\mathcal{T}$ potential. In the $\mathcal{P}\mathcal{T}$-unbroken regime, the real Bogoliubov modes are generally gapped, in contrast to the gapless phonon mode in Hermitian case. Moreover, the presence of $\mathcal{P}\mathcal{T}$ potential is found to enhance the mean-field collapse and thereby intrigue the droplet formation after incorporating the repulsive force from quantum fluctuations. These remarkable interplay effects of $\mathcal{P}\mathcal{T}$-symmetry and interaction can be directly probed in cold atoms experiments, which shed light on related quantum phenomena in general $\mathcal{P}\mathcal{T}$-symmetric systems.

arXiv comment11 pages, 4 figures

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