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We investigate the ground state and low-lying excitations of a Bose-Einstein condensate (BEC) of dipolar molecules interacting via short-range contact and long-range dipole­ dipole interactions (ddi). We find the mean field ground state via the variational principle using a separable bosonic wave function as the variational state. This state can be refined to include small excitations in the form of plane waves, and the results of the variational calculation are a set of dispersion relations for the low-lying excitations. We analyze the polarization and stability of the ground state as a function of the strength of the external polarizing electric field, the strength of the ddi, and the strength of the contact interactions. In a certain parameter regime of strong contact interactions that oppose the dipole -dipole interactions, we identify a possible signature of a first -order phase transition: the polarization of the gas discontinuously flips as the electric field is continuously ramped through zero field. By examining the dispersion relations, we find that the ground state in this parameter regime is unstable.





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