## Abstract

We determine the hydrodynamic modes of the superfluid analog of a smectic-A liquid crystal phase, 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.

Original language | English |
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Article number | 033104 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2021 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2021 |

## Keywords

- Bose-Einstein condensation
- Cold atoms