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Excitations and anisotropic sound in planar supersolids with tilted dipoles

Reuben Cook

Published Jul 6, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.82348/our-archive.00263

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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.
We present a theoretical study of the excitations of the two-dimensional supersolid state of a Bose-Einstein condensate with either dipole-dipole interactions or soft-core interactions. This supersolid state has three gapless excitation branches arising from the spontaneously broken continuous symmetries. Two of these branches are related to longitudinal sound waves, similar to those in one-dimensional supersolids. The third branch is a transverse wave arising from the nonzero shear modulus of the two-dimensional crystal. We present the results of numerical calculations for the excitations and dynamic structure factor characterizing the density fluctuations and study their behavior across the discontinuous superfluid to supersolid transition. We show that the speeds of sound are described by a hydrodynamic theory that incorporates generalized elastic parameters, including the shear modulus. Furthermore, we establish that dipolar and soft-core supersolids manifest distinct characteristics, falling into the bulk-incompressible and rigid-lattice limits, respectively.
Two-component supersolids can exhibit in-phase or out-of-phase component density modulations, corresponding to density and spin supersolids, respectively. We formulate a general hydrodynamic theory for the collective dynamics of multicomponent supersolids, guided by their broken symmetries and conservation laws. We benchmark it against microscopic calculations for a binary dipolar condensate confined to an infinite tube, finding quantitative agreement for the sound speeds of all three Goldstone branches throughout the density- and spin-supersolid regions. The resulting relations link collective-mode measurements to elastic coefficients and superfluid fractions.
We examine the low-energy excitations of a dilute supersolid state of matter with a one-dimensional crystal structure. A hydrodynamic description is developed based on a Lagrangian, incorporating generalized elastic parameters derived from ground state calculations. The predictions of the hydrodynamic theory are validated against solutions of the Bogoliubov--de Gennes equations, by comparing the speeds of sound, density fluctuations, and phase fluctuations of the two gapless bands. Our results are presented for two distinct supersolid models: a dipolar Bose-Einstein condensate in an infinite tube and a dilute Bose-Einstein condensate of atoms with soft-core interactions. Characteristic energy scales are identified, highlighting that these two models approximately realize the bulk incompressible and rigid lattice supersolid limits.
The behavior of dipolar Bose-Einstein condensates in planar geometries is investigated, focusing on the effects of the polarization orientation. While perpendicular polarization produces a phase diagram with hexagonal, stripes, and honeycomb phases ending at a single critical point, the presence of an in-plane polarization component transforms the critical point into three critical lines, separating two phases at a time and changing radically the appearance of the phase diagram. All transition lines contain first- and second-order regions, while the phase diagram itself shows a resemblance with those displayed by quasi-one-dimensional dipolar systems. Finally, we investigate the effect of introducing an in-plane polarization on the structural properties of the phases and determine the superfluid fraction. Our results show that this process induces an axial deformation on the hexagonal and honeycomb phases, resulting in an anisotropic behavior in the long distance properties of the system like superfluidity. We expect that the rich phenomenology observed provides motivation for new experiments and theoretical works.
We investigate the microscopic structure of the long-wavelength acoustic excitations of two-dimensional dipolar supersolids with triangular and honeycomb crystal order. Using Bogoliubov--de Gennes calculations, we determine the density, phase, current, and lattice-displacement fluctuations associated with the three acoustic modes. We develop a procedure to extract the lattice displacement directly from the microscopic density perturbation, allowing the modes to be identified as one transverse and two longitudinal branches. The displacement field further separates the density fluctuations into contributions from crystal strain and particle transport relative to the lattice. This reveals that the lower longitudinal mode can have large strain and defect-density fluctuations that substantially cancel in the total density response. We show that the long-wavelength fluctuation amplitudes agree with hydrodynamic theory, which is specified entirely by the elastic coefficients of the supersolid. Our analysis provides a microscopic connection between Bogoliubov excitations and the crystalline and superfluid degrees of freedom of two-dimensional supersolids, and identifies their signatures in density- and current-sensitive probes.