Exploring the supersolid phase of matter with dipolar quantum gases

Supersolids are a fundamental quantum phase of matter combining properties of crystals and superfluids. A supersolid phase was recently discovered in Bose-Einstein condensates of strongly dipolar atoms. I will discuss the exceptional properties of dipolar supersolids, spanning from double symmetry breaking to mixed superfluid and classical dynamics. I will in particular show how a supersolid can behave as a self-induced Josephson junction array, and how it is possible to deduce from the Josephson dynamics the superfluid fraction, which is the universal property quantifying the deviation of supersolids from both crystals and superfluids. I will discuss recent progresses towards the realization of ring-shaped supersolids.