Hydrodynamics of a superfluid smectic

Abstract

We determine the hydrodynamic modes of the superfluid analog of a smectic-A phase in liquid crystals, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose-Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin-orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.

20 pages

References in corpus (6)

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• Supersolid formation in a quantum gas breaking continuous translational symmetry
• Transient supersolid properties in an array of dipolar quantum droplets
• Long-lived and transient supersolid behaviors in dipolar quantum gases
• Effective Lagrangian and Topological Interactions in Supersolids
• Coexisting ordinary elasticity and superfluidity in a model of defect-free supersolid