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arXiv:2604.01751

Sound propagation in striped supersolid cold gases at zero temperature

Elena Poli, Giovanni Italo Martone, S. Stringari, Alessio Recati

Published Apr 2, 2026• 0 citations
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Abstract

We present a unified hydrodynamic approach for the sound propagation in the stripe phases realized in ultracold dipolar gas and spin-orbit-coupled BEC platforms at zero temperature. Despite the deep difference of the two platforms at a microscopic level, a similar hydrodynamic description can be formulated at a macroscopic level. The main difference between the two platforms is the lack of Galilean invariance in the spin-orbit case, resulting in a different identification of the normal (nonsuperfluid) component of the density, which leads to new terms in the equation for the current. In both cases the spectrum comprises two sounds, reflecting the spontaneous breaking of the U(1) and translational symmetries. Both sounds exhibit an anisotropic behavior. A comparison with the first and second sounds of the smectic-A liquid crystal is also presented.

DOI
10.48550/arxiv.2604.01751

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We present a unified hydrodynamic approach for the sound propagation in the stripe phases realized in ultracold dipolar gas and spin-orbit-coupled BEC platforms at zero temperature. Despite the deep difference of the two platforms at a microscopic level, a similar hydrodynamic description can be formulated at a macroscopic level. The main difference between the two platforms is the lack of Galilean invariance in the spin-orbit case, resulting in a different identification of the normal (nonsuperfluid) component of the density, which leads to new terms in the equation for the current. In both cases the spectrum comprises two sounds, reflecting the spontaneous breaking of the U(1) and translational symmetries. Both sounds exhibit an anisotropic behavior. A comparison with the first and second sounds of the smectic-A liquid crystal is also presented.
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.
We investigate the collective excitations of anisotropic dipolar supersolids in planar confinement, focusing on triangular and stripe phases in situations where the dipoles are titled to have a component in the plane. We look at systems in parameter regimes where phase transitions are both continuous and discontinuous. Using Bogoliubov–de Gennes calculations and hydrodynamic theory, we identify the elastic parameters that govern the long-wavelength dynamics, including two orientational coefficients that capture the broken rotational symmetry induced by dipole tilt. Analytical expressions for the speeds of sound are obtained along the principal axes for triangular supersolids and along any propagation direction for the stripe supersolid. Our results provide a unified framework for understanding sound propagation in anisotropic dipolar supersolids and establish connections to recent experiments on sound propagation in striped Bose-Einstein condensates.
We investigate the collective excitations of anisotropic dipolar supersolids in planar confinement, focusing on triangular and stripe phases in situations where the dipoles are titled to have a component in the plane. Using Bogoliubov-de Gennes calculations and hydrodynamic theory, we identify the elastic parameters that govern the long-wavelength dynamics, including two orientational coefficients that capture the broken rotational symmetry induced by dipole tilt. Analytical expressions for the speeds of sound are obtained along the principal axes for triangular supersolids and along any propagation direction for the stripe supersolid. Our results provide a unified framework for understanding sound propagation in anisotropic dipolar supersolids and establish connections to recent experiments on sound propagation in striped Bose-Einstein condensates.
Using Bogoliubov theory we calculate the excitation spectrum of a spinor Bose-Einstein condensed gas with an equal Rashba and Dresselhaus spin-orbit coupling in the stripe phase. The emergence of a double gapless band structure is pointed out as a key signature of Bose-Einstein condensation and of the spontaneous breaking of translational invariance symmetry. In the long wavelength limit the lower and upper branches exhibit, respectively, a clear spin and density nature. For wave vectors close to the first Brillouin zone, the lower branch acquires an important density character responsible for the divergent behavior of the structure factor and of the static response function, reflecting the occurrence of crystalline order. The sound velocities are calculated as functions of the Raman coupling for excitations propagating orthogonal and parallel to the stripes. Our predictions provide new perspectives for the identification of supersolid phenomena in ultracold atomic gases.
By employing the formalism of hydrodynamics, we derive novel analytic predictions for the Doppler effect in superfluids with broken Galilean invariance and hosting persistent currents at zero temperature. We consider two scenarios: when Galilean invariance is broken explicitly (by external potentials) and spontaneously, as it happens in a supersolid. In the former case, the presence of a stationary current affects the propagation of sound via an anomalous Doppler term proportional to the density derivative of the superfluid fraction. In supersolids, where, according to Goldstone theorem, distinct sounds of hybrid superfluid and crystal nature can propagate, the Doppler effect can be very different for each sound. Quantitative estimates of the Doppler shifts are obtained for Bose-Einstein condensed atomic gases, described by Gross-Pitaevskii theory. The estimates are obtained both calculating the thermodynamic parameters entering the hydrodynamic results and from full time-dependent simulations.
By calculating the density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. We find that the velocity of sound along the direction of spin-orbit coupling is deeply quenched and vanishes when one approaches the second-order phase transition between the plane-wave and the zero momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, providing the onset of the transition to the stripe phase. Our findings point out the occurrence of a strong anisotropy in the dynamic behavior of the gas. A hydrodynamic description accounting for the collective oscillations in both uniform and harmonically trapped gases is also derived.