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.

我们确定了近晶-A 液晶相的超流体类似物的流体动力学模式，即沿单个方向的规范不变性和平移不变性自发破坏的状态。这种超流体近晶提供了在具有强偶极相互作用的玻色-爱因斯坦凝聚体中实现的不公度超固态的理想化描述，以及具有自旋轨道耦合的玻色气体中的条纹相。我们表明，即使在零温度下，这些系统的基态中存在的有限法向流体密度也会产生明确定义的第二声型模式。它取代了正常近晶相的扩散渗透模式，并与 Andreev 和 Lifshitz 在传播缺陷模式方面对超固体的经典描述直接相关。为出现在纵向激发谱中的两个声速推导出解析表达式。它仅取决于与两个独立的破坏对称性相关的低能参数，即有效层压缩模量和超流体分数。