Excitation spectrum of a supersolid

Conclusive experimental evidence of a supersolid phase in any known condensed matter system is presently lacking. On the other hand, a supersolid phase has been recently predicted for a system of spinless bosons in continuous space, interacting via a broad class of soft-core, repulsive potentials. Such an interaction can be engineered in assemblies of ultracold atoms, providing a well-defined pathway to the unambiguous observation of this fascinating phase of matter. In this article, we study by first principle computer simulations the elementary excitation spectrum of the supersolid, and show that it features two distinct modes, namely a solid-like phonon and a softer collective excitation, related to broken translation and gauge symmetry respectively.