Dynamics of Supersolid state: normal fluid, superfluid, and supersolid velocities

Abstract

Landau's excitation-based argument for superfluids -- that at temperature $T=0$ the normal fluid density ${\rho }_n$ is zero -- should also apply to supersolids. Further, for a total mass density $\rho$, Leggett argues that the superfluid fraction ${\rho }_s/\rho <1$. These arguments imply that there is a missing mass. We attribute this to a supersolid density ${\rho }_L$, with ${\rho }_L\equiv \rho -{\rho }_s-{\rho }_n$, and a momentum-bearing supersolid velocity $v_{Li}$. Using Onsager's irreversible thermodynamics we derive the macroscopic dynamical equations for this system. We find that $v_{Li}$ is subject to the force of elasticity, to the negative gradient of the chemical potential per mass $\mu$ (as for the superfluid velocity $v_{si}$), and to drag against the normal fluid (leading to the interpretation of $L$ as lattice). Thus both the superfluid and supersolid components are associated with the ground state. The normal modes for such a system have a crossover in frequency, above which the normal fluid velocity $v_{ni}$ is an independent variable and below which it is locked to $v_{Li}$. For an isotropic lattice we study both the transverse response and longitudinal response. The ring geometry for atomic gas supersolid states may provide a geometry for testing these predictions.

9 pages

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Cited by in corpus (1)

• Anomalous Doppler effect in two-component Bose-Einstein condensates