Pattern formation in quantum ferrofluids: From supersolids to superglasses

Self-bound dipolar droplets and supersolids in molecular Bose-Einstein condensates

“…3. We find a wide variety of different phases, which include the well known droplet supersolids, but also honeycomb and pumpkin phases, as well as nearly degenerate ring and labyrinth states, which have recently gained significant interest [31,32,84]. Notably, we find that these more exotic phases become more dominant in the phase diagram as a dd is increased.…”

“…We consider an oblate potential with trap frequencies ω x,y,z = 2π×(100, 100, 200) Hz, and map out the phase diagrams for various dipolar lengths a dd . Scaling relations allow to easily generalize the results for this trap to other sets of parameters [32].…”

“…In addition to the experimentally observed droplet supersolids, it has been shown theoretically that approaching the saturation density limit is connected to the emergence of other exotic supersolid states [31,32,84]. Rather than being formed by droplet arrays, these states are characterized by more complex density patterns.…”

“…This value corresponds to a dipolar interaction strength that is up to three orders of magnitude larger than the one in magnetic atoms like dysprosium or erbium. We emphasize that, given the universal nature of the collisional processes on the one hand [68,69] and the the scaling properties of the extended Gross-Pitaevskii equation on the other hand [32], the results presented in the following can easily be generalized to other molecules, including typical laser-coolable species.…”

“…This counterintuitive behavior leads to a rich phase diagram that contains, for example, self-bound quantum droplets [5,6] and supersolid states [7][8][9][10]. While many aspects like rotonic excitation spectra [11][12][13][14][15][16][17][18][19], anisotropic superfluidity [20,21], droplet formation [1,6,22], crystallization in 1D [23][24][25][26][27][28], 2D [3,18,19,29,30] and into more exotic patterns [31,32], have been extensively discussed for weakly-dipolar magnetic atoms, systematic studies for molecules, with their much larger and tunable electric dipole moments, have so far remained scarce. Here, we show that Bose-Einstein condensates of ground-state molecules are ideal candidates to further explore the rich phase diagrams of dipolar Bose gases in experiments [33].…”