Bogoliubov theory of a Bose-Einstein condensate of rigid rotor molecules

We consider a BEC of rigid rotor molecules confined to quasi-2d through harmonic trapping. The molecules are subjected to an external electric field which polarizes the gas, and the molecules interact via dipole-dipole interactions. We present a description of the ground state and low-energy excitations of the system including an analysis of the mean-field energy, polarization, and stability. Under large electric fields the gas becomes fully polarized and we reproduce a well known density-wave instability which arises in polar BECs. Under smaller applied electric fields the gas develops an in-plane polarization leading to the emergence of a new global instability as the molecules "tilt". The character of these instabilities is clarified by means of momentum-space density-density structure factors. A peak at zero momentum in the spin-spin structure factor for the in-plane component of the polarization indicates that the tilt instability is a global phonon-like instability.