Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2308.05981 · Physical Review Letters

Sound, Superfluidity, and Layer Compressibility in a Ring Dipolar Supersolid

Marija Šindik, Tomasz Zawiślak, Alessio Recati, S. Stringari

Published Apr 3, 2024• 29 citations
arXivHTMLPDF

Abstract

We propose a protocol to excite the Goldstone modes of a supersolid dipolar Bose-Einstein condensed gas confined in a ring geometry. By abruptly removing an applied periodic modulation proportional to cos(φ), where φ is the azimuthal angle, we explore the resulting oscillations of the gas by solving the extended Gross-Pitaevskii equation. The value of the two longitudinal sound velocities exhibited in the supersolid phase are analyzed using the hydrodynamic theory of supersolids at zero temperature, which explicitly takes into account both the superfluid and the crystal nature of the system. This approach allows for the determination of the layer compressibility modulus as well as of the superfluid fraction, f_{S}, in agreement with the Leggett estimate of the nonclassical moment of inertia.

DOI
10.1103/physrevlett.132.146001

Related papers

Hydrodynamics of a superfluid smectic

Johannes Hofmann, W. Zwerger

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.

arXiv:2012.06569•Journal of Statistical Mechanics Theory and Experiment•Mar 1, 2021•26 citations

Supersolid phase of a spin-orbit-coupled Bose-Einstein condensate: A perturbation approach

Giovanni Italo Martone, S. Stringari

The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.

•Jan 1, 2021•21 citations

Supersolid phase of a spin-orbit-coupled Bose-Einstein condensate: A perturbation approach

Giovanni Italo Martone, S. Stringari

The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.

arXiv:2107.06425•SciPost Physics•Nov 17, 2021•0 citations

Rotating a Supersolid Dipolar Gas

S. M. Roccuzzo, Albert Gallemí, Alessio Recati +1 more

Distinctive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment of inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation, we show that the moment of inertia determines the value of the frequency of the scissors mode, which is significantly affected by the reduction of superfluidity in the supersolid phase. The case of an in-plane isotropic trapping is instead well suited to study the formation of quantized vortices, which are shown to be characterized, in the supersolid phase, by a sizeable deformed core, caused by the presence of the surrounding density peaks.

arXiv:1910.08513•Physical Review Letters•Jan 31, 2020•92 citations

Compressibility and speeds of sound across the superfluid-to-supersolid phase transition of an elongated dipolar gas

P. B. Blakie, Lauriane Chomaz, D. Baillie +1 more

We investigate the excitation spectrum and compressibility of a dipolar Bose-Einstein condensate in an infinite tube potential in the parameter regime where the transition between superfluid and supersolid phases occurs. Our study focuses on the density range in which crystalline order develops continuously across the transition. Above the transition the superfluid shows a single gapless excitation band, phononic at small momenta and with a roton at a finite momentum. Below the transition, two gapless excitations branches (three at the transition point) emerge in the supersolid. We examine the two gapless excitation bands and their associated speeds of sound in the supersolid phase. Our results show that the speeds of sound and the compressibility are discontinuous at the transition, indicating a second-order phase transition. These results provide valuable insights into the identification of supersolid phenomena in dipolar quantum gases and the relationship to supersolidity in spin-orbit coupled gases.

arXiv:2306.04794•Physical Review Research•Sep 6, 2023•20 citations

Excitations of a two-dimensional supersolid

Elena Poli, D. Baillie, Francesca Ferlaino +1 more

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.

arXiv:2407.01072•Physical Review A•Nov 4, 2024•21 citations
We propose a protocol to excite the Goldstone modes of a supersolid dipolar Bose-Einstein condensed gas confined in a ring geometry. By abruptly removing an applied periodic modulation proportional to cos(φ), where φ is the azimuthal angle, we explore the resulting oscillations of the gas by solving the extended Gross-Pitaevskii equation. The value of the two longitudinal sound velocities exhibited in the supersolid phase are analyzed using the hydrodynamic theory of supersolids at zero temperature, which explicitly takes into account both the superfluid and the crystal nature of the system. This approach allows for the determination of the layer compressibility modulus as well as of the superfluid fraction, f_{S}, in agreement with the Leggett estimate of the nonclassical moment of inertia.
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.
The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.
The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.
Distinctive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment of inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation, we show that the moment of inertia determines the value of the frequency of the scissors mode, which is significantly affected by the reduction of superfluidity in the supersolid phase. The case of an in-plane isotropic trapping is instead well suited to study the formation of quantized vortices, which are shown to be characterized, in the supersolid phase, by a sizeable deformed core, caused by the presence of the surrounding density peaks.
We investigate the excitation spectrum and compressibility of a dipolar Bose-Einstein condensate in an infinite tube potential in the parameter regime where the transition between superfluid and supersolid phases occurs. Our study focuses on the density range in which crystalline order develops continuously across the transition. Above the transition the superfluid shows a single gapless excitation band, phononic at small momenta and with a roton at a finite momentum. Below the transition, two gapless excitations branches (three at the transition point) emerge in the supersolid. We examine the two gapless excitation bands and their associated speeds of sound in the supersolid phase. Our results show that the speeds of sound and the compressibility are discontinuous at the transition, indicating a second-order phase transition. These results provide valuable insights into the identification of supersolid phenomena in dipolar quantum gases and the relationship to supersolidity in spin-orbit coupled gases.
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.