Pattern Formation in Oblate Quantum Ferrofluids: from Supersolids to Superglasses *

Pattern formation is a ubiquitous phenomenon observed in nonlinear and out-of-equilibrium systems. In equilibrium, pattern formation can occur in classical ferrofluids, which exhibit strong dipolar interactions. Here we study quantum ferrofluids, for which density patterns that form in elongated geometries were recently shown to be manifestations of supersolids. We theoretically investigate the phase diagram of quantum ferrofluids in oblate trap geometries and find a wide range of exotic states of matter. In analogy to the patterns in classical ferrofluids, we find honeycomb and labyrinthine states featuring strong density connections. They can be considered two-dimensional manifestations of quantum liquids that spontaneously develop crystalline or amorphous density patterns. Supersolid droplets with two-dimensional crystal structures represent the beginning of the phase diagram at low densities. We show that the quantum fluctuations, responsible for the stabilization of these exotic phases, lead to modified scaling properties generally applicable to quantum ferrofluids in which beyond-mean field effects are important. This allows to find  the supersolid droplet, honeycomb and superglass labyrinthine states for a wide variety of trap geometries, interaction strengths, and atom numbers. Our study illuminates the origin of the various possible morphologies of quantum ferrofluids, highlights their emergent supersolid and superglass properties and shows that their occurrence is generic of strongly dipolar interacting systems stabilized by beyond mean-field effects.