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 welldefined 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.

Exciting the Goldstone Modes of a Supersolid Spin-Orbit-Coupled Bose Gas

“…More recently, a renewed interest has emerged in the context of ultracold atomic gases, and experimental evidence of typical supersolid features has been reported in Bose-Einstein condensates inside optical resonators [6], spin-orbit-coupled configurations [7,8], and in cold gases interacting with longrange dipole forces [9][10][11]. An important property of supersolidity with respect to ordinary superfluids is the appearance of additional gapless (Goldstone) modes in the excitation spectrum, resulting from the broken translational symmetry [2,[12][13][14][15][16][17][18][19][20][21]. While these modes have already been the object of first experimental investigation in harmonically trapped dipolar gases [22][23][24][25], so far no experimental observation has been reported in spinorbit-coupled configurations.…”