A Novel Mean Field Model for Quantum Supersolids

Recent experiments have seen characteristics of the elusive quantum supersolid phase – periodic spatial ordering of a quantum liquid. This calls for theoretical tools to explain and design the experiments. [J.-R. Li et al. Nature, 543, 91–94. (2017);
H. Kadau et al. Nature, 530, 194–197. (2015)]

We derive a one-particle mean field energy functional motivated by the celebrated Gross-Pitaevskii equation. We study both the ground state properties and excited states of this energy functional. Our model describes the phase transition between a super liquid constant density state and a supersolid state with periodic order. Analysis of the properties of these phases reveals that they can coexist and that there are interesting different regimes within the solid phase. We find the analytical predictions to be in agreement with computational studies.