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/0511547 · Physical Review A

Low-lying twisting and acoustic modes of a rotating Bose-Einstein condensate

Frédéric Chevy

Published Apr 13, 2006• 10 citations
arXivHTMLPDF

Abstract

We present a calculation of the low lying spectrum of a rotating Bose-Einstein condensate. We show that in a cylindrical geometry, there exist two linear branches, one associated with usual acoustic excitations, the other corresponding to a twisting mode of the vortex lattice. Using a hydrodynamical approach, we derive the elasticity coefficient of the vortex lattice and calculate the spectrum of condensate in a three-dimensional harmonic trap with cylindrical symmetry.

DOI
10.1103/physreva.73.041604

Related papers

Excitation spectrum of vortex lattices in rotating Bose-Einstein condensates

Seok Jin Choi, Leslie O. Baksmaty, Sungjong Woo +1 more

Using the coarse-grain averaged hydrodynamic approach, we calculate the excitation spectrum of vortex lattices sustained in rotating Bose-Einstein condensates. The spectrum gives the frequencies of the common-mode longitudinal waves in the hydrodynamic regime, including those of the higher-order compressional modes. Reasonable agreement with the measurements taken in a recent experiment is found, suggesting that one of the longitudinal modes reported in the experiment is likely to be the $n=2,m=0$ mode.

arXiv:cond-mat/0306549•Physical Review A•Sep 29, 2003•19 citations

Zero-energy states in rotating trapped Bose-Einstein condensates

Tapio Simula

Abstract. We have calculated low-lying quasiparticle excitation spectra of rotating three-dimensional Bose-Einstein condensates. As opposed to the prediction of hydrodynamic continuum theories, we find a minimum in the Tkachenko mode spectrum at intermediate rotation frequencies of the harmonic trap. Such a minimum can harbour a Tkachenko quasiparticle with zero excitation energy. We discuss the experimental signatures of such a zero mode. ar X iv

•Aug 16, 2016•2 citations

Zero-energy states in rotating trapped Bose–Einstein condensates

Tapio Simula

We have calculated low-lying quasiparticle excitation spectra of rotating three-dimensional Bose-Einstein condensates. We find, as opposed to the prediction of hydrodynamic continuum theories, a minimum in the Tkachenko mode spectrum at intermediate rotation frequencies of the harmonic trap. Such a minimum can harbour a Tkachenko quasiparticle with zero excitation energy. We discuss the experimental signatures of such a zero mode.

arXiv:1207.5892•Journal of Physics Condensed Matter•Jun 21, 2013•4 citations

Nonclassical scissors mode of a vortex lattice in a Bose-Einstein condensate

Carlos Lobo, Yvan Castin

We show that a Bose-Einstein condensate with a vortex lattice in a rotating anisotropic harmonic potential exhibits a very low frequency scissors mode. The appearance of this mode is due to the SO(2) symmetry breaking introduced by the vortex lattice. The corresponding Goldstone mode in an isotropic trap becomes, in an anisotropic trap, a scissors mode, whose frequency is finite and tends to zero with the trap anisotropy $ϵ$, with a generic $\sqrt{ϵ}$ dependence. We present analytical formulas giving the mode frequency in the low $ϵ$ limit and we show that the mode frequency for some class of vortex lattices can tend to zero as $ϵ$ or faster. We demonstrate that the standard classical hydrodynamics approach fails to reproduce this low frequency mode, because it does not contain the discrete structure of the vortex lattice.

arXiv:cond-mat/0506452•Physical Review A•Oct 17, 2005•17 citations

Kelvin modes of a fast rotating Bose-Einstein condensate

Frédéric Chevy, S. Stringari

Using the concept of diffused vorticity and the formalism of rotational hydrodynamics we calculate the eigenmodes of a harmonically trapped Bose-Einstein condensate containing an array of quantized vortices. We predict the occurrence of a new branch of anomalous excitations, analogous to the Kelvin modes of the single vortex dynamics. Special attention is devoted to the excitation of the anomalous scissors mode.

arXiv:cond-mat/0305559•Physical Review A•Nov 3, 2003•20 citations

Oscillations of a Bose-Einstein Condensate Rotating in a Harmonic Plus Quartic Trap

Marco Cozzini, Alexander L. Fetter, B. Jackson +1 more

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities Omega where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency sqrt[6]Omega in the rotating frame, irrespective of the mode multipolarity m, as well as a class of low energy modes with frequency proportional to |m|/Omega. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.

arXiv:cond-mat/0411106•Physical Review Letters•Mar 16, 2005•25 citations
We present a calculation of the low lying spectrum of a rotating Bose-Einstein condensate. We show that in a cylindrical geometry, there exist two linear branches, one associated with usual acoustic excitations, the other corresponding to a twisting mode of the vortex lattice. Using a hydrodynamical approach, we derive the elasticity coefficient of the vortex lattice and calculate the spectrum of condensate in a three-dimensional harmonic trap with cylindrical symmetry.
Using the coarse-grain averaged hydrodynamic approach, we calculate the excitation spectrum of vortex lattices sustained in rotating Bose-Einstein condensates. The spectrum gives the frequencies of the common-mode longitudinal waves in the hydrodynamic regime, including those of the higher-order compressional modes. Reasonable agreement with the measurements taken in a recent experiment is found, suggesting that one of the longitudinal modes reported in the experiment is likely to be the n=2,m=0n=2,m=0n=2,m=0 mode.
We show that a Bose-Einstein condensate with a vortex lattice in a rotating anisotropic harmonic potential exhibits a very low frequency scissors mode. The appearance of this mode is due to the SO(2) symmetry breaking introduced by the vortex lattice. The corresponding Goldstone mode in an isotropic trap becomes, in an anisotropic trap, a scissors mode, whose frequency is finite and tends to zero with the trap anisotropy ϵϵϵ, with a generic ϵ\sqrt{ϵ}ϵ​ dependence. We present analytical formulas giving the mode frequency in the low ϵϵϵ limit and we show that the mode frequency for some class of vortex lattices can tend to zero as ϵϵϵ or faster. We demonstrate that the standard classical hydrodynamics approach fails to reproduce this low frequency mode, because it does not contain the discrete structure of the vortex lattice.
We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities Omega where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency sqrt[6]Omega in the rotating frame, irrespective of the mode multipolarity m, as well as a class of low energy modes with frequency proportional to |m|/Omega. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.