Quantum fluctuations on top of a mathcal{PT}-symmetric Bose-Einstein Condensate

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