Self-Bound Superfluid Membranes and Monolayer Crystals of Ultracold Polar Molecules

We investigate the physics of ultracold dipolar molecules using path-integral quantum Monte Carlo simulations, and construct the complete phase diagram extending from weak to strong interactions and from small to mesoscopic particle numbers. Our calculations predict the formation of self-bound quantum droplets at interaction strengths lower than previous estimates for molecular condensates. Strikingly, we observe that, for stronger interactions, the oblate quantum droplet transitions to a two-dimensional sheet or superfluid membrane with a thickness of a single molecule. As interactions are increased further the system continually loses superfluidity while correlations develop, and is eventually found to undergo a transition to a crystalline monolayer that remains self-bound without external confinement. The spontaneous formation of such two-dimensional phases from a three-dimensional quantum gas is traced back to the peculiar anisotropic form of the dipole-dipole interaction generated by microwave dressing of rotational molecular states. For sufficiently large particle numbers, crystallization takes place for comparably low interaction strengths that do not promote two-body bound states and should thus be observable in ongoing experiments without limitations from three-body recombination.