Coherence and correlation functions of quasi-2D dipolar superfluids at zero temperature

We use the Bogoliubov theory of Bose-Einstein condensation to study the properties of dipolar particles (atoms or molecules) confined in a uniform two-dimensional geometry at zero temperature. We find equilibrium solutions to the dipolar Gross-Pitaevskii equation and the Bogoliubov-de Gennes equations. Using these solutions we study the effects of quantum fluctuations in the system, particularly focussing on the instability point, where the roton feature in the excitation spectrum touches zero. Specifically, we look at the behaviour of the noncondensate density, the phase fluctuations, and the density fluctuations in the system. Near the instability, the density-density correlation function shows a particularly intriguing oscillatory behaviour. Higher order correlation functions display a distinct hexagonal lattice pattern formation, demonstrating how an observation of broken symmetry can emerge from a translationally symmetric quantum state.