Ground-state properties and elementary excitations of quantum droplets in dipolar Bose-Einstein condensates

Recent experiments have revealed the formation of stable droplets in dipolar Bose-Einstein condensates. This surprising result has been explained by the stabilization given by quantum fluctuations. We study in detail the properties of a Bose-Einstein condensate in the presence of quantum stabilization. The ground-state phase diagram presents three main regimes: mean-field regime, in which the quantum correction is perturbative; droplet regime, in which quantum stabilization is crucial; and a multistable regime. In the absence of a multistable region, the condensate undergoes a crossover from the mean-field to the droplet solution marked by a characteristic growth of the peak density that may be employed to clearly distinguish quantum stabilization from other stabilization mechanisms. Interestingly, quantum stabilization allows for three-dimensionally self-bound condensates. We characterized these self-bound solutions, and discuss their realization in experiments. We conclude with a discussion of the lowest-lying excitations both for trapped condensates, and for self-bound solutions.