We investigate the ground state and excitation properties of a weakly interacting Bose-Einstein Condensate(BEC) under a parity-time(
PT) symmetric potential with balanced gain and loss. It is shown that the
PT-symmetry, as preserved by the macroscopic condensate, can be spontaneously broken by its Bogoliubov quasi-particles. The associated
PT-breaking transitions in the Bogoliubov spectrum can be conveniently tuned by the interaction anisotropy of BEC and the strength of
PT potential. In the
PT-unbroken regime, the real Bogoliubov modes are generally gapped, in contrast to the Hermitian case with gapless phonon mode. Moreover, it is found that the presence of
PT potential can enhance the mean-field collapse and thereby intrigue the droplet formation after incorporating the repulsive force from quantum fluctuations. These remarkable interplay effects of
PT-symmetry and interaction can be directly probed in cold atoms experiments, which shed light on intriguing collective phenomena in other non-Hermitian systems with
PT-symmetry.
We discuss tunneling properties of Bogoliubov excitations through a potential barrier. We find that the quasi-particle current carried by Bogoliubov excitations is remarkably enhanced near the potential barrier at low incident energies. This explains the increase of the transmission probability of Bogoliubov phonons in the low energy region. In addition, taking into account of the backreaction of Bogoliubov excitations on Bose condensates, we show that the quasi-particle current twists the phase of the condensate wavefunction, leading to a Josephson supercurrent through the barrier.
When an impurity interacts with a bath of phonons it forms a polaron. For increasing interaction strengths the mass of the polaron increases and it can become self-trapped. For impurity atoms inside an atomic Bose-Einstein condensate (BEC) the nature of this transition is not understood. While Feynman's variational approach to the Fröhlich model predicts a sharp transition for light impurities, renormalization group studies always predict an extended intermediate-coupling region characterized by large phonon correlations. To investigate this intricate regime and to test polaron physics beyond the validity of the Fröhlich model we suggest a versatile experimental setup that allows us to tune both the mass of the impurity and its interactions with the BEC. The impurity is realized as a dark-state polariton (DSP) inside a quasi-two-dimensional BEC. We show that its interactions with the Bogoliubov phonons lead to photonic polarons, described by the Bogoliubov-Fröhlich Hamiltonian, and make theoretical predictions using an extension of a recently introduced renormalization group approach to Fröhlich polarons.