Pattern Formation in Quantum Ferrofluids: from Supersolids to Superglasses

Abstract

Pattern formation is a ubiquitous phenomenon observed in nonlinear and out-of-equilibrium systems. In equilibrium, quantum ferrofluids formed from ultracold atoms were recently shown to spontaneously develop coherent density patterns, manifesting a supersolid. We theoretically investigate the phase diagram of such quantum ferrofluids in oblate trap geometries and find an even wider range of exotic states of matter. Two-dimensional supersolid crystals formed from individual ferrofluid quantum droplets dominate the phase diagram at low densities. For higher densities we find honeycomb and labyrinthine states, as well as a pumpkin phase. We discuss scaling relations which allow us to find these phases for a wide variety of trap geometries, interaction strengths, and atom numbers. Our study illuminates the origin of the various possible patterns of quantum ferrofluids and shows that their occurrence is generic of strongly dipolar interacting systems stabilized by beyond mean-field effects.

Maintaining supersolidity in one and two dimensions

“…Previous theoretical works have found exotic twodimensional supersolid states with either large atom numbers (∼ 10 6 ), or tight trapping (∼ 1kHz) [37][38][39]. Notably, honeycomb ground states have been predicted [37] with crystal arrays of holes rather than droplets.…”

“…Such states are appealing due to their predicted strong superfluid conductance across the crystal, without relying on low density connections between droplets. Also predicted are intriguing stripe and ring states [38], as well as labyrinthine instabilities [39] familiar in classical ferrofluids [44].…”

“…An early theoretical study in 2D predicted a rich phase diagram determined by competing metastable crystal configurations [31]. More recent works in 2D have predicted supersolid edge phases [32]; intriguing manifestations of quantum vortices and persistent currents [33][34][35][36]; honeycomb supersolids [37]; as well as ring and stripe phases [38,39].…”

“…We find that 2D supersolids may be just as favorable as their 1D counterparts, provided that one fixes the average 2D density. Through increasing the average 2D density we show how to observe the exotic ring and stripe phases [38,39] with realistic experimental parameters. Finally, we extend our variational model to study 2D crystal excitations, and benchmark this against full numerical calculations.…”

New opportunites for interactions and control with ultracold lanthanides

“…Following the demonstration of 1D supersolidity in dipolar gases, its two dimensional (2D) counterpart is currently attracting substantial renewed interest. Theoretically, recent studies have focused on the phase diagram and excitation spectra of 2D supersolid in isotropic and anisotropic traps [133][134][135], the possibility of such supersolids hosting vortices in the low-density regions [136][137][138], and on the formation of novel type of ground-states with exotic spatial patterns [133,139]. Very recently, supersolidity along two dimensions has been demonstrated in a trap of variable anisotropy [135].…”