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:2212.07607 · Physical Review A

Supersolidity and crystallization of a dipolar Bose gas in an infinite tube

Joseph C. Smith, D. Baillie, P. B. Blakie

Published Mar 3, 2023• 39 citations
arXivHTMLPDF

Abstract

We calculate the ground states of a dipolar Bose gas confined in an infinite tube potential. We use the extended Gross-Pitaevskii equation theory and present a numerical method to efficiently obtain solutions. A key feature of this method is an analytic result for a truncated dipole-dipole interaction potential that enables the long-ranged interactions to be accurately evaluated within a unit cell. Our focus is on the transition of the ground state to a crystal driven by dipole-dipole interactions as the short-ranged interaction strength is varied. We find that the transition is continuous or discontinuous depending upon the average system density. These results give deeper insight into the supersolid phase transition observed in recent experiments and validate the utility of the reduced three-dimensional theory developed in [Phys. Rev. Res. 2, 043318 (2020)] for making qualitatively accurate predictions.

DOI
10.1103/physreva.107.033301

Related papers

Supersolidity in an elongated dipolar condensate

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

We present a theory for the emergence of a supersolid state in a cigar-shaped dipolar quantum Bose gas.Our approach is based on a reduced three-dimensional (3D) theory, where the condensate wave function is decomposed into an axial field and a transverse part described variationally.This provides an accurate fully 3D description that is specific to the regime of current experiments and efficient to compute.We apply this theory to understand the phase diagram for a gas in an infinite tube potential.We find that the supersolid transition has continuous and discontinuous regions as the averaged density varies.We develop two simplified analytic models to characterize the phase diagram and elucidate the roles of quantum droplets and of the roton excitation.

arXiv:2004.12577•Physical Review Research•Dec 4, 2020•83 citations

Ring solids and supersolids in spherical shell-shaped dipolar Bose-Einstein condensates

Juan Sánchez-Baena, Raúl Bombín, Jordi Boronat

We study the interplay between the anisotropy of the dipole-dipole interaction and confinement in a curved geometry by means of the extended Gross-Pitaevskii equation, which allows us to characterize the ground state of a dipolar Bose gas under the confinement of a bubble trapping potential. We do so in terms of the scattering length a and the number of particles. We observe the emergence of a wide variety of dipolar solids, consisting on arrangements of different number of droplets along a ring over the equator of the spherical shell confinement. We also show that the transition between the different phases of the system can be engineered by varying a , the number of particles or the radius of the trap, parameters, which can be experimentally tuned. Finally, we show the importance of working in microgravity conditions as gravity unstabilizes the observed dipolar solids. Published by the American Physical Society 2024

arXiv:2312.12164•Physical Review Research•Jul 29, 2024•9 citations

Binary quantum droplets and dipolar supersolids

 Joseph Smith

We consider a binary magnetic gas and develop an extended Gross-Pitaevskii theory to study the system. We apply this theory to the regime where the two- body interactions are attractive for some arrangements of the atoms, and mean- field theory predicts mechanical collapse. In this regime quantum droplets of the binary magnetic gas can emerge, stabilised by quantum fluctuations. These quantum droplets can exist in miscible and immiscible regimes, and we characterise their properties over a broad parameter space. Simplified theories are developed to describe the droplets, and benchmarked against the full numerical calculations. The system dynamics are simulated for scenarios involving droplet formation and crossing the miscible-immiscible transition. Three-body loss is modelled in the dynamical simulations to account for the dominant loss process expected in experiments. We also study the supersolidity of a single-component dipolar gas in an infinite tube potential. An accurate computational algorithm is developed to calculate the ground state of the system in a unit cell. This algorithm is used to determine the phase diagram by characterising the crystalline order and superfluid fraction. Our results reveal that a system confined in a radially harmonic trap has a continuous transition for a range of density values, but is discontinuous for densities above and below this range. The theory is used to calculate the crystalline and supersolid states of a binary magnetic gas in a tube potential.

•Jan 1, 2023•0 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

Supersolid behavior of a dipolar Bose-Einstein condensate confined in a tube

S. M. Roccuzzo, Francesco Ancilotto

Motivated by a recent experiment [L. Chomaz et al., Nat. Phys. 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein condensate (BEC) in a tubular, periodic confinement at $T=0$ within density functional theory, where the beyond-mean-field correction to the ground-state energy is included in the local density approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov--de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops a periodic linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e., (i) a finite nonclassical translational inertia along the tube axis and (ii) the appearance of two gapless modes, i.e., a phonon mode associated with density fluctuations and resulting from the translational discrete symmetry of the system, and a Nambu-Goldstone gapless mode corresponding to phase fluctuations, resulting from the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.

arXiv:1810.12229•Physical Review A•Apr 2, 2019•125 citations

GROUND-STATE PROPERTIES OF A HOMOGENEOUS 2D SYSTEM OF BOSONS WITH DIPOLAR INTERACTIONS

G. E. ASTRAKHARCHIK, J. BORONAT, J. CASULLERAS +2 more

The ground-state phase properties of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo techniques. Limitations of mean-field theory in a two-dimensional geometry are discussed. A quantum phase transition from gas to solid is found. Crystal is tested for existence of a supersolid in the vicinity of the phase transition. Existence of mesoscopic analogue of the off-diagonal long-range order is shown in the one-body density matrix in a finite-size crystal. Non-zero superfluid fraction is found in a finite-size crystal, the signal being dramatically increased in presence of vacancies.

arXiv:0707.4630•Recent Progress in Many-Body Theories•Jun 1, 2008•1 citation
We calculate the ground states of a dipolar Bose gas confined in an infinite tube potential. We use the extended Gross-Pitaevskii equation theory and present a numerical method to efficiently obtain solutions. A key feature of this method is an analytic result for a truncated dipole-dipole interaction potential that enables the long-ranged interactions to be accurately evaluated within a unit cell. Our focus is on the transition of the ground state to a crystal driven by dipole-dipole interactions as the short-ranged interaction strength is varied. We find that the transition is continuous or discontinuous depending upon the average system density. These results give deeper insight into the supersolid phase transition observed in recent experiments and validate the utility of the reduced three-dimensional theory developed in [Phys. Rev. Res. 2, 043318 (2020)] for making qualitatively accurate predictions.
We present a theory for the emergence of a supersolid state in a cigar-shaped dipolar quantum Bose gas.Our approach is based on a reduced three-dimensional (3D) theory, where the condensate wave function is decomposed into an axial field and a transverse part described variationally.This provides an accurate fully 3D description that is specific to the regime of current experiments and efficient to compute.We apply this theory to understand the phase diagram for a gas in an infinite tube potential.We find that the supersolid transition has continuous and discontinuous regions as the averaged density varies.We develop two simplified analytic models to characterize the phase diagram and elucidate the roles of quantum droplets and of the roton excitation.
We study the interplay between the anisotropy of the dipole-dipole interaction and confinement in a curved geometry by means of the extended Gross-Pitaevskii equation, which allows us to characterize the ground state of a dipolar Bose gas under the confinement of a bubble trapping potential. We do so in terms of the scattering length a and the number of particles. We observe the emergence of a wide variety of dipolar solids, consisting on arrangements of different number of droplets along a ring over the equator of the spherical shell confinement. We also show that the transition between the different phases of the system can be engineered by varying a , the number of particles or the radius of the trap, parameters, which can be experimentally tuned. Finally, we show the importance of working in microgravity conditions as gravity unstabilizes the observed dipolar solids. Published by the American Physical Society 2024
We consider a binary magnetic gas and develop an extended Gross-Pitaevskii theory to study the system. We apply this theory to the regime where the two- body interactions are attractive for some arrangements of the atoms, and mean- field theory predicts mechanical collapse. In this regime quantum droplets of the binary magnetic gas can emerge, stabilised by quantum fluctuations. These quantum droplets can exist in miscible and immiscible regimes, and we characterise their properties over a broad parameter space. Simplified theories are developed to describe the droplets, and benchmarked against the full numerical calculations. The system dynamics are simulated for scenarios involving droplet formation and crossing the miscible-immiscible transition. Three-body loss is modelled in the dynamical simulations to account for the dominant loss process expected in experiments. We also study the supersolidity of a single-component dipolar gas in an infinite tube potential. An accurate computational algorithm is developed to calculate the ground state of the system in a unit cell. This algorithm is used to determine the phase diagram by characterising the crystalline order and superfluid fraction. Our results reveal that a system confined in a radially harmonic trap has a continuous transition for a range of density values, but is discontinuous for densities above and below this range. The theory is used to calculate the crystalline and supersolid states of a binary magnetic gas in a tube potential.
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.
Motivated by a recent experiment [L. Chomaz et al., Nat. Phys. 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein condensate (BEC) in a tubular, periodic confinement at T=0T=0T=0 within density functional theory, where the beyond-mean-field correction to the ground-state energy is included in the local density approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov--de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops a periodic linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e., (i) a finite nonclassical translational inertia along the tube axis and (ii) the appearance of two gapless modes, i.e., a phonon mode associated with density fluctuations and resulting from the translational discrete symmetry of the system, and a Nambu-Goldstone gapless mode corresponding to phase fluctuations, resulting from the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.
The ground-state phase properties of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo techniques. Limitations of mean-field theory in a two-dimensional geometry are discussed. A quantum phase transition from gas to solid is found. Crystal is tested for existence of a supersolid in the vicinity of the phase transition. Existence of mesoscopic analogue of the off-diagonal long-range order is shown in the one-body density matrix in a finite-size crystal. Non-zero superfluid fraction is found in a finite-size crystal, the signal being dramatically increased in presence of vacancies.