Self-bound droplets in quasi-two-dimensional dipolar condensates

We study the ground-state properties of self-bound dipolar droplets in quasi-two-dimensional geometry by using the Gaussian state theory. We show that there exist two quantum phases corresponding to the macroscopic squeezed vacuum and squeezed coherent states. We further show that the radial size versus atom number curve exhibits a double-dip structure, as a result of the multiple quantum phases. In particular, we find that the critical atom number for the self-bound droplets is determined by the quantum phases, which allows us to distinguish the quantum state and validates the Gaussian state theory.