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/0503122 · Physical Review A

Three-dimensional vortex structure of a fast rotating Bose-Einstein condensate with harmonic-plus-quartic confinement

Ionut Danaila

Published Jul 6, 2005• 51 citations
arXivHTMLPDF

Abstract

We address the challenging proposition of using real experimental parameters in a three-dimensional (3D) numerical simulation of fast rotating Bose-Einstein condensates. We simulate recent experiments [V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004); S. Stock, V. Bretin, S. Stock, F. Chevy, and J. Dalibard, Europhys. Lett. 65, 594 (2004)] using an anharmonic (quadratic-plus-quartic) confining potential to reach rotation frequencies $(\ensuremath{\Omega})$ above the trap frequency $({\ensuremath{\omega}}_{\ensuremath{\perp}})$. Our numerical results are obtained by propagating the 3D Gross-Pitaevskii equation in imaginary time. For $\ensuremath{\Omega}\ensuremath{\leqslant}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, we obtain an equilibrium vortex lattice similar (as the size and number of vortices) to experimental observations. For $\ensuremath{\Omega}>{\ensuremath{\omega}}_{\ensuremath{\perp}}$ we observe the evolution of the vortex lattice into an array of vortices with a central hole. Since this evolution was not visible in experiments, we investigate the 3D structure of vortex configurations and 3D effects on vortex contrast. Numerical data are also compared to recent theory [D. E. Sheehy and L. Radzihovsky, Phys. Rev. A 70, 063620 (2004)] describing vortex lattice inhomogeneities and a remarkably good agreement is found.

DOI
10.1103/physreva.72.013605

Related papers

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

Three-dimensional vortex configurations in a rotating Bose-Einstein condensate

Amandine Aftalion, Ionut Danaila

We consider a rotating Bose-Einstein condensate in a harmonic trap and investigate numerically the behavior of the wave function which solves the Gross-Pitaevskii equation. Following recent experiments [P. Rosenbuch, V. Bretin, and J. Dalibard, Phys. Rev. Lett. 89, 200403 (2002)], we study in detail the line of a single quantized vortex, which has a U or S shape. We find that a single vortex can lie only in the $x\ensuremath{-}z$ or $y\ensuremath{-}z$ plane. S-type vortices exist for all values of the angular velocity $\ensuremath{\Omega}$ while U vortices exist for $\ensuremath{\Omega}$ sufficiently large. We compute the energy of the various configurations with several vortices and study the three-dimensional structure of vortices.

arXiv:cond-mat/0303416•Physical Review A•Aug 11, 2003•75 citations

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

Lowest-Landau-level vortex structure of a Bose-Einstein condensate rotating in a harmonic plus quartic trap

Xavier Blanc, Nicolas Rougerie

We investigate the vortex patterns appearing in a two-dimensional annular Bose-Einstein condensate rotating in a quadratic plus quartic confining potential. We show that in the limit of small anharmonicity the Gross-Pitaevskii energy can be minimized among the lowest-Landau-level wave functions and use this particular form to obtain theoretical results in the spirit of Aftalion et al. [Phys. Rev. A 73, 011601(R) (2006)]. In particular, we show that the vortex pattern is infinite but not uniform. We also compute numerically the complete vortex structure: It is an Abrikosov lattice strongly distorted near the edges of the condensate with multiply quantized vortices appearing at the center of the trap.

arXiv:0801.3571•Physical Review A•May 29, 2008•23 citations

Nucleation of vortex arrays in rotating anisotropic Bose-Einstein condensates

David L. Feder, Charles W. Clark, Barry I. Schneider

The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.

arXiv:cond-mat/9910288•Physical Review A•Dec 8, 1999•95 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
We address the challenging proposition of using real experimental parameters in a three-dimensional (3D) numerical simulation of fast rotating Bose-Einstein condensates. We simulate recent experiments [V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004); S. Stock, V. Bretin, S. Stock, F. Chevy, and J. Dalibard, Europhys. Lett. 65, 594 (2004)] using an anharmonic (quadratic-plus-quartic) confining potential to reach rotation frequencies (\ensuremathΩ)(\ensuremath{\Omega})(\ensuremathΩ) above the trap frequency (\ensuremathω\ensuremath⊥)({\ensuremath{\omega}}_{\ensuremath{\perp}})(\ensuremathω\ensuremath⊥​). Our numerical results are obtained by propagating the 3D Gross-Pitaevskii equation in imaginary time. For \ensuremathΩ\ensuremath⩽\ensuremathω\ensuremath⊥\ensuremath{\Omega}\ensuremath{\leqslant}{\ensuremath{\omega}}_{\ensuremath{\perp}}\ensuremathΩ\ensuremath⩽\ensuremathω\ensuremath⊥​, we obtain an equilibrium vortex lattice similar (as the size and number of vortices) to experimental observations. For \ensuremathΩ>\ensuremathω\ensuremath⊥\ensuremath{\Omega}>{\ensuremath{\omega}}_{\ensuremath{\perp}}\ensuremathΩ>\ensuremathω\ensuremath⊥​ we observe the evolution of the vortex lattice into an array of vortices with a central hole. Since this evolution was not visible in experiments, we investigate the 3D structure of vortex configurations and 3D effects on vortex contrast. Numerical data are also compared to recent theory [D. E. Sheehy and L. Radzihovsky, Phys. Rev. A 70, 063620 (2004)] describing vortex lattice inhomogeneities and a remarkably good agreement is found.
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 consider a rotating Bose-Einstein condensate in a harmonic trap and investigate numerically the behavior of the wave function which solves the Gross-Pitaevskii equation. Following recent experiments [P. Rosenbuch, V. Bretin, and J. Dalibard, Phys. Rev. Lett. 89, 200403 (2002)], we study in detail the line of a single quantized vortex, which has a U or S shape. We find that a single vortex can lie only in the $x\ensuremath{-}z$ or $y\ensuremath{-}z$ plane. S-type vortices exist for all values of the angular velocity $\ensuremath{\Omega}$ while U vortices exist for $\ensuremath{\Omega}$ sufficiently large. We compute the energy of the various configurations with several vortices and study the three-dimensional structure of vortices.
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).
We investigate the vortex patterns appearing in a two-dimensional annular Bose-Einstein condensate rotating in a quadratic plus quartic confining potential. We show that in the limit of small anharmonicity the Gross-Pitaevskii energy can be minimized among the lowest-Landau-level wave functions and use this particular form to obtain theoretical results in the spirit of Aftalion et al. [Phys. Rev. A 73, 011601(R) (2006)]. In particular, we show that the vortex pattern is infinite but not uniform. We also compute numerically the complete vortex structure: It is an Abrikosov lattice strongly distorted near the edges of the condensate with multiply quantized vortices appearing at the center of the trap.
The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.
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.