Superfluid Liquid Crystals and Supersolids

The second lecture discusses the requirements for realizing a supersolid phase where BEC coexists with a mass density wave. Based on the Leggett bound on the superfluid fraction in phases with a periodic density modulation and the well understood example of superfluidity in optical lattices, it is shown that supersolids require a finite density of defects in their ground state. Such a situation is generically present in the density wave along the axial direction of dipolar gases in cigar-shaped traps which appears for dipolar lengths exceeding the short range scattering length. The emerging supersolid is a superfluid version of a smectic liquid crystal. It exhibits a novel low energy mode due to wave like propagation of defects, as predicted by Andreev and Lifshitz.