Supersolid pattern formation and two-dimensional roton excitations

Dipolar interactions in quantum gases offer a rich landscape of new quantum states to explore. These long-range anisotropic interactions enable the formation of self-organized patterns in quantum gases [1]. Our numerical simulations show that patterns such as labyrinths and honeycombs are within reach and are analogous to patterns found in nature. One special pattern is the supersolid droplets that possess periodic structure and superfluidity. For supersolid droplets, a low-lying Goldstone mode is populated when crossing the phase transition from a condensate, and this mode is directly connected to the finite-momentum roton modes of the system. The existence of a Goldstone mode is proof of superfluidity, a requirement of supersolidity. We observed radial and angular rotons in a round trapping potential by analysing density fluctuations of in situ images [2]. These roton modes are the precursors for two-dimensional supersolids and can be used in future quantum phase searches.