Novel quantum phases: dipolar quantum droplets and supersolidity

The first experimental realization of quantum droplets in dipolar condensates has highlighted the importance of quantum fluctuations, which were later shown to be the main source of system's stability against the dipolar collapse. The droplets were predicted and shown to be self-bound beyond the critical atom number even without the trap. Further novel quantum phases, such as the long sought-after supersolidity, can emerge in geometrically constrained multi-droplet systems. Here we use an approach based on the extended Gross-Pitaevskii equation, which includes quantum depletion and beyond-local density approximation gradient corrections, to numerically and variationally study their effects on the properties of quantum droplets and supersolids in ring-shaped systems.