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:cond-mat/0109418 · Physical Review A

Rotating vortex lattice in a Bose-Einstein condensate trapped in combined quadratic and quartic radial potentials

Alexander L. Fetter

Published Nov 14, 2001• 160 citations
arXivHTMLPDF

Abstract

A dense vortex lattice in a rotating dilute Bose-Einstein condensate is studied with the Thomas-Fermi approximation. The upper critical angular velocity ${\ensuremath{\Omega}}_{c2}$ occurs when the intervortex separation b becomes comparable with the vortex-core radius $\ensuremath{\xi}.$ For a radial harmonic trap, the loss of confinement as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}{\ensuremath{\omega}}_{\ensuremath{\perp}}$ implies a singular behavior. In contrast, an additional radial quartic potential provides a simple model for which ${\ensuremath{\Omega}}_{c2}$ is readily determined. Unlike the case of a type-II superconductor at fixed temperature, the onset of ${\ensuremath{\Omega}}_{c2}$ arises not only from decreasing b but also from increasing $\ensuremath{\xi}$ caused by the vanishing of the chemical potential as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}{\ensuremath{\Omega}}_{c2}.$

DOI
10.1103/physreva.64.063608

Related papers

Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap

Alexander L. Fetter, B. Jackson, S. Stringari

A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed $\ensuremath{\Omega}$ to exceed the radial harmonic frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$. In the regime $\ensuremath{\Omega}\ensuremath{\gtrsim}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity ${\ensuremath{\Omega}}_{h}$, a central hole appears in the condensate. Numerical studies confirm the predicted value of ${\ensuremath{\Omega}}_{h}$, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).

arXiv:cond-mat/0407119•Physical Review A•Jan 28, 2005•127 citations

Vortices in a rotating Bose-Einstein condensate under extreme elongation in a harmonic plus quartic trap

Chao Huang, C. H. Liu, W. C. Wu

The behaviors of a rapidly rotating Bose-Einstein condensate under extreme elongation in a two-dimensional anisotropic harmonic plus quartic trap are investigated. Due to the quartic trap, the system remains stable at high rotating velocity, $\ensuremath{\Omega}\ensuremath{\geqslant}{\ensuremath{\omega}}_{\ensuremath{\perp}}$ (${\ensuremath{\omega}}_{\ensuremath{\perp}}$ is the radial harmonic trap frequency), and vortex lattices form even in the absence of the repulsive $s$-wave interaction ($g$). When $g$ is present, the interplay between $g$ and the quartic trap potential can lead to rich vortex lattice transition states as a function of $\ensuremath{\Omega}$, to which vortex lattices vanish eventually at some higher $\ensuremath{\Omega}$.

arXiv:1206.2198•Physical Review A•Apr 8, 2010•10 citations

Rapidly rotating Bose-Einstein condensates in anharmonic potentials

G. M. Kavoulakis, Gordon Baym

Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can exhibit a rich variety of vortex phases, including a vortex lattice, a vortex lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi variational approach to determine the ground state of the condensate in the rotating frame -- valid for sufficiently strongly interacting condensates -- we determine the transitions between these three phases for a quadratic-plus-quartic confining potential. Combining the present results with previous numerical simulations of small rotating condensates in such anharmonic potentials, we delineate the general structure of the zero temperature phase diagram.

arXiv:cond-mat/0212596•New Journal of Physics•May 30, 2003•91 citations

Giant vortices in combined harmonic and quartic traps

Amandine Aftalion, Ionut Danaila

We consider a rotating Bose-Einstein condensate confined in combined harmonic and quartic traps, following recent experiments [V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004)]. We investigate numerically the behavior of the wave function which solves the three-dimensional Gross Pitaevskii equation and analyze in detail the structure of vortices. For a quartic-plus-harmonic potential, as the angular velocity increases, the vortex lattice evolves into a vortex array with hole. The merging of vortices into the hole is highly three dimensional, starting from the top and bottom of the condensate to reach the center. We also investigate the case of a quartic-minus-harmonic potential, not covered by experiments or previous numerical works. For intermediate repulsive potentials, we show that the transition to a vortex array with hole takes place for lower angular velocities, when the lattice is made up of a small number of vortices. For the strong repulsive case, a transition from a giant vortex to a hole with a circle of vortices around is observed.

arXiv:cond-mat/0309668•Physical Review A•Mar 18, 2004•93 citations

Vortex-lattice melting and critical temperature shift in rotating Bose-Einstein condensates

Julián Amette Estrada, Marc Brächet, Pablo D. Mininni

We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex-lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex-lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.

arXiv:2412.05477•Physical Review A•Feb 4, 2025•3 citations

Vortex States of Rapidly Rotating Dilute Bose-Einstein Condensates

Uwe R. Fischer, Gordon Baym

We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, Omega, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.

arXiv:cond-mat/0111443•Physical Review Letters•Apr 9, 2003•181 citations
A dense vortex lattice in a rotating dilute Bose-Einstein condensate is studied with the Thomas-Fermi approximation. The upper critical angular velocity \ensuremathΩc2{\ensuremath{\Omega}}_{c2}\ensuremathΩc2​ occurs when the intervortex separation b becomes comparable with the vortex-core radius \ensuremathξ.\ensuremath{\xi}.\ensuremathξ. For a radial harmonic trap, the loss of confinement as \ensuremathΩ\ensuremath→\ensuremathω\ensuremath⊥\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}{\ensuremath{\omega}}_{\ensuremath{\perp}}\ensuremathΩ\ensuremath→​\ensuremathω\ensuremath⊥​ implies a singular behavior. In contrast, an additional radial quartic potential provides a simple model for which \ensuremathΩc2{\ensuremath{\Omega}}_{c2}\ensuremathΩc2​ is readily determined. Unlike the case of a type-II superconductor at fixed temperature, the onset of \ensuremathΩc2{\ensuremath{\Omega}}_{c2}\ensuremathΩc2​ arises not only from decreasing b but also from increasing \ensuremathξ\ensuremath{\xi}\ensuremathξ caused by the vanishing of the chemical potential as \ensuremathΩ\ensuremath→\ensuremathΩc2.\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}{\ensuremath{\Omega}}_{c2}.\ensuremathΩ\ensuremath→​\ensuremathΩc2​.
A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed $\ensuremath{\Omega}$ to exceed the radial harmonic frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$. In the regime $\ensuremath{\Omega}\ensuremath{\gtrsim}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity ${\ensuremath{\Omega}}_{h}$, a central hole appears in the condensate. Numerical studies confirm the predicted value of ${\ensuremath{\Omega}}_{h}$, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).
The behaviors of a rapidly rotating Bose-Einstein condensate under extreme elongation in a two-dimensional anisotropic harmonic plus quartic trap are investigated. Due to the quartic trap, the system remains stable at high rotating velocity, $\ensuremath{\Omega}\ensuremath{\geqslant}{\ensuremath{\omega}}_{\ensuremath{\perp}}$ (${\ensuremath{\omega}}_{\ensuremath{\perp}}$ is the radial harmonic trap frequency), and vortex lattices form even in the absence of the repulsive sss-wave interaction (ggg). When ggg is present, the interplay between ggg and the quartic trap potential can lead to rich vortex lattice transition states as a function of $\ensuremath{\Omega}$, to which vortex lattices vanish eventually at some higher $\ensuremath{\Omega}$.
Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can exhibit a rich variety of vortex phases, including a vortex lattice, a vortex lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi variational approach to determine the ground state of the condensate in the rotating frame -- valid for sufficiently strongly interacting condensates -- we determine the transitions between these three phases for a quadratic-plus-quartic confining potential. Combining the present results with previous numerical simulations of small rotating condensates in such anharmonic potentials, we delineate the general structure of the zero temperature phase diagram.
We consider a rotating Bose-Einstein condensate confined in combined harmonic and quartic traps, following recent experiments [V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004)]. We investigate numerically the behavior of the wave function which solves the three-dimensional Gross Pitaevskii equation and analyze in detail the structure of vortices. For a quartic-plus-harmonic potential, as the angular velocity increases, the vortex lattice evolves into a vortex array with hole. The merging of vortices into the hole is highly three dimensional, starting from the top and bottom of the condensate to reach the center. We also investigate the case of a quartic-minus-harmonic potential, not covered by experiments or previous numerical works. For intermediate repulsive potentials, we show that the transition to a vortex array with hole takes place for lower angular velocities, when the lattice is made up of a small number of vortices. For the strong repulsive case, a transition from a giant vortex to a hole with a circle of vortices around is observed.
We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex-lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex-lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.
We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, Omega, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.