Symmetry and Self-Bound Droplets in Dipolar Molecular Gases

Recent experiments with degenerate molecular gases dressed by elliptically polarized microwave fields have enabled new control of dipolar interactions via engineered anisotropy. We reveal a symmetry structure of the dipolar interaction that generates degeneracies among the interaction parameters, enabling a classification of spatial symmetries and equilibrium shapes of the gases. Exploiting these symmetries, we analyze solutions including beyond-meanfield quantum fluctuations, and develop a complementary variational theory. We map out the phase diagram of self-bound droplets and characterize their widths, energies, and densities.