Abstract
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.
Highlights
The parity-time (PT ) symmetry governs a fascinating class of non-Hermitian Hamiltonians whose energy spectra can be purely real and bounded below [1], analogous to the Hermitian ones
We explore the effects of quantum fluctuations on top of a PT -symmetric two-species (↑, ↓) Bose-Einstein condensate (BEC) with the non-Hermitian potential
This relation is equivalent to the bi-orthogonality of right and left eigenstates, which is crucially important for building the theories of non-Hermitian BECs as presented later
Summary
The parity-time (PT ) symmetry governs a fascinating class of non-Hermitian Hamiltonians whose energy spectra can be purely real and bounded below [1], analogous to the Hermitian ones. We explore the effects of quantum fluctuations on top of a PT -symmetric two-species (↑, ↓) Bose-Einstein condensate (BEC) with the non-Hermitian potential. (iii) The presence of VPT can enhance the mean-field collapse of the BEC, and thereby extend the droplet formation to a broader interaction regime than the Hermitian counterpart. We consider the following Hamiltonian for the interacting two-species bosons under the PT -symmetric potential (we take h = 1 throughout the paper). In order to ensure the PT symmetry of (2), we take the equal mass m↑ = m↓ ≡ m and equal intraspecies coupling g↑↑ = g↓↓ ≡ g In this case, the property of a homogeneous BEC is determined by three dimensionless parameters: the dissipation parameter γ , and two dimensionless combinations η ≡ g↑↓/g and ≡ /(gn) (n the total density of the BEC)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
