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

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