Vortex patterns and energies in a rotating superfluid

Campbell, L.J.; Ziff, Robert M.

doi:10.1103/physrevb.20.1886

Cited by 185 publications

(170 citation statements)

References 8 publications

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“…5(d) and 5(e)]. As is well known in the study of rotating superfluid helium [34,35], the rotating drive pulls vortices into the rotation axis, while repulsive interaction between vortices tends to push them apart; this competition yields a vortex lattice whose vortex density depends on the rotation frequency. In the presence of dissipation, six vortices enter the condensate, eventually forming a vortex lattice.…”

Section: B Dynamics From a Non-vortex State To A Vortex Statementioning

confidence: 96%

Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate

2003

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We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by the quasiparticle projection method. A simple recurrence oscillation of surface mode populations is broken in the quadrupole resonance region that depends on the trap anisotropy, causing stochastization of the dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.

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Section: B Dynamics From a Non-vortex State To A Vortex Statementioning

confidence: 96%

Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate

2003

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“…The dynamical instability appears only for nine vortices in the ring with a central vortex, indicating the existence of other more stable states than this '9+ 1 ' configuration. Campbell and Ziff [5] studied the stationary vortex patterns in a uniform condensate, evaluating the corresponding free energy for numbers of vortices N v = 1 to 30 (they did not investigate the small-amplitude normal modes). According to their findings, the stable state with the lowest free energy for a system of ten vortices, has '4+4+2' vortices (three concentric rings; beginning from the outer-most ring); the '9+ 1 ' configuration has slightly higher free energy and is nearly stable, as opposed to stable.…”

Section: A Uniform Condensatementioning

confidence: 99%

“…Subsequently, Hess [4] studied the energy of various configurations analytically to determine the sequence of low-lying equilibrium states, and Campbell and Ziff [5] evaluated the energies numerically for larger numbers of vortices. After heroic efforts, Yarmchuk et al [6] photographed some stable vortex patterns in superfluid 4 He.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a single ring of vortices in two-dimensional trapped Bose-Einstein condensates

Kim

Fetter

2004

Phys. Rev. A

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The dynamics of a ring of vortices in two-dimensional Bose-Einstein condensates (with and without an additional vortex at the center) is studied for (1) a uniform condensate in a rigid cylinder and (2) a nonuniform trapped condensate in the Thomas-Fermi limit. The sequence of ground states (within these single-ring configurations) is determined as a function of the external rotation frequency by comparing the free energy of the various states. For each ground state, the Tkachenko-like excitations and the associated dynamical stability are analyzed.

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“…There the selection of the defects starts, because their further invasion into the condensate costs the energy and the angular momentum. As is well known in the study of rotating superfluid helium [14], the rotating drive pulls vortices into the rotation axis, while repulsive interaction tends to push them apart; this competition yields a vortex lattice whose vortex density depends on the rotation frequency. In our case, some vortices enter the condensate and form a lattice dependent on Ω, while excessive vortices are repelled and escape to the outside.…”

mentioning

confidence: 99%

Vortex lattice formation in a rotating Bose-Einstein condensate

2002

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We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation, and find that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The origin of the peculiar surface-mode excitations is identified to be phase fluctuations at the low-density surface regime. The obtained dependence of a distortion parameter on time and that on the driving frequency agree with the recent experiments by Madison et al. [Phys. Rev. Lett. 86, 4443 (2001)].PACS numbers: 03.75. Fi, 67.40.Db Quantized vortices have long been studied in superfluid 4 He as the topological defects characteristic of superfluidity [1,2]. However, the relatively high density and strong repulsive interaction complicate the theoretical treatments of the Bose-Einstein condensed liquid, and the healing length of the atomic scale makes the experimental visualization of the quantized vortices difficult. The recent achievement of Bose-Einstein condensation in trapped alkali-metal atomic gases at ultra low temperatures has stimulated intense experimental and theoretical activity. The atomic Bose-Einstein condensates(BECs) have the weak interaction because they are dilute gases, thus being free of the above difficulties that superfluid 4 He is subject to. Quantized vortices in the atomic BECs have recently been created experimentally by Matthews et al. By rotating an asymmetric trapping potential, Madison et al. at ENS succeeded in forming a quantized vortex in 87 Rb BEC for a stirring frequency that exceeds a critical value [4]. Vortex lattices were obtained for higher frequencies. The ENS group subsequently observed that vortex nucleation occurs via a dynamical instability of the condensate [6]. For a given modulation amplitude and stirring frequency, the steady state of the condensate was distorted to an elliptic cloud, stationary in the rotating frame, as predicted by Recati et al. [7]. An intrinsic dynamical instability [8] of the steady state transformed the elliptic state into a more axisymmetric state with vortices. However, the origin of that instability and how it leads to the formation of vortex lattices remains to be investigatedThe ENS group found that the minimum rotation frequency Ω nuc at which one vortex appears is 0.65ω ⊥ , where ω ⊥ is the transverse oscillation frequency of the cigar-shaped trapping potential, independent of the number of atoms or the longitudinal frequency ω z [9]. There is a discrepancy between the observations and the theoretical considerations based on the stationary solution of the Gross-Pitaevskii equation(GPE) [10,11]; Ω nuc is significantly larger than its equilibrium estimates.The present paper addresses these issues by numerically solving the GPE that governs the time evolution of the order parameter ψ(r, t):Here g = 4πh 2 a/m is the coupling constant, proportional to the 87 Rb scattering length a ≈5.77 nm. The high anisotropy of the cig...

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Vortex patterns and energies in a rotating superfluid

Cited by 185 publications

References 8 publications

Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate

Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate

Dynamics of a single ring of vortices in two-dimensional trapped Bose-Einstein condensates

Vortex lattice formation in a rotating Bose-Einstein condensate

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