Dipolar interactions are fundamentally different from the usual van der Waals forces in real gases. Besides the anisotropy the dipolar interaction is nonlocal and as such allows for self organized structure formation . Similar to the Rosensweig instability in classical magnetic ferrofluids self-organized structure formation was expected. However on the meanfield level such a transition is instable due to the diluteness of the gaseous sample. In contrast to these predictions in 2015 we could observe the formation of a stable droplet crystal and found that this unexpected stability is due to beyond mean-field quantum corrections of the Lee-Huang-Yang type. When arranged in a 1D array also phase coherence between the droplets was observed, which was first evidence for a supersolid state of matter. Upon crossing the transition to the dipolar supersolid a Goldstone mode appears, which we have observed. The existence of this mode proofs the superfluid stiffness or the so-called phase rigidity of this new state of matter. Recently we have also measured the static structure factor across the transition which allows to show that the characteristic fluctuations correspond to elementary excitations such as the roton modes, and that the supersolid state supports both superfluid as well as crystal phonons. A recent review on the discovery of quantum dropets and dipolar supersolids can be found in ref. .
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