We present a mean field analysis of the effects of molecular rotation on the excitation spectrum and stability of ultracold dipolar gases. For an unpolarized homogeneous gas interacting with a pure dipole-dipole interaction, we find that for the rotational state L = 1 the dipole-dipole interaction causes a splitting of the translation-rotation energy levels into a single M = 0 and a doubly degenerate M = ±1 excitation. For all other rotational states, the dipole-dipole interaction does not lead to coupling of translations and rotations and therefore has no effect on the rotational degeneracy of the excitations. The addition of arbitrarily small electric fields is found to introduce instabilities similar to those known to arise in the fully polarized dipolar gas. As in the case of a fully polarized gas, addition of a large enough short range repulsive potential is seen to stabilize the system, with the critical value of the repulsive interaction required for stabilization being larger when rotations are included.
Homogeneous quantum gases open up new possibilities for studying many-body phenomena and have now been realized for a variety of systems. For gases with short-range interactions the way to make the cloud homogeneous is, predictably, to trap it in an ideal (homogeneous) box potential. We show that creating a close to homogeneous dipolar gas in the roton regime, when long-range interactions are important, actually requires trapping particles in soft-walled (inhomogeneous) box-like potentials. In particular, we numerically explore a dipolar gas confined in a pancake trap which is harmonic along the polarization axis and a cylindrically symmetric power-law potential
rp radially. We find that intermediate
p's maximize the proportion of the sample that can be brought close to the critical density required to reach the roton regime, whereas higher
p's trigger density oscillations near the wall even when the bulk of the system is not in the roton regime. We characterize how the optimum density distribution depends on the shape of the trapping potential and find it is controlled by the trap wall steepness.