Coupled Goldstone Modes in Supersolids

Supersolids are quantum phases of matter that exhibit both superfluid and crystal-like properties and have experienced renewed interest due to recent experiments on graphene substrates^[1] and dipolar BEC gases^[2]. In this talk we present a homogenisation technique on a Gross-Pitaevskii model with a non-local interaction term and calculate elastic constants, inertial fraction and speeds of sound for a general supersolid of arbitrary interaction potential and dimension. We verify our results numerically and extend the discussion by developing a technique to apply this formalism to other systems of interest. We discuss also the application of a Bogoliubov fluctuation technique and compare results between the two formalisms.

[1] J. Nyeki, A. Phillis, A. Ho, D. Lee, P. Coleman, J. Parpia, B. Cowan, and J. Saunders, “Intertwined superfluid and density wave order in two-dimensional 4 he,” Nature Physics, vol. 13, no. 5, pp. 455–459, 2017.

[2] L. Chomaz, D. Petter, P. Ilzhofer, G. Natale, A. Trautmann, C. Politi, G. Durastante, R. Van Bijnen, A. Patscheider, M. Sohmen, et al., “Long-lived and transient supersolid behaviors in dipolar quantum gases,” Physical Review X, vol. 9, no. 2, p. 021012, 2019.