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arXiv:1007.3548 · Physical Review A

Kelvin-Tkachenko waves of few-vortex arrays in trapped Bose-Einstein condensates

Tapio Simula, K. Machida

Published Dec 27, 2010• 21 citations
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Abstract

We have calculated the low-lying elementary excitations of three-dimensional few-vortex arrays in trapped Bose-Einstein condensates. The number of different Kelvin-Tkachenko vortex wave branches found matches the number of vortices in the condensate. The lowest odd-parity modes exhibit superfluid gyroscopic vortex motion. Experimentally, these modes could be excited and observed individually or in connection with the formation and decay of quantum turbulence.

DOI
10.1103/physreva.82.063627

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We have calculated the low-lying elementary excitations of three-dimensional few-vortex arrays in trapped Bose-Einstein condensates. The number of different Kelvin-Tkachenko vortex wave branches found matches the number of vortices in the condensate. The lowest odd-parity modes exhibit superfluid gyroscopic vortex motion. Experimentally, these modes could be excited and observed individually or in connection with the formation and decay of quantum turbulence.
We have calculated collective-mode spectra for three-dimensional, rotating Bose-Einstein condensates in oblate harmonic traps using the microscopic Bogoliubov--de Gennes field theory. For condensates with Nv{N}_{v}Nv​ vortices, Nv{N}_{v}Nv​ Kelvin-Tkachenko-mode branches are obtained. The features of these modes are compared with those predicted by a classical point-vortex model. We have created movies to visualize the motion of the vortices corresponding to the Kelvin-Tkachenko waves.
We have theoretically investigated Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates. Counterrotating perturbation induces an elliptical instability to the initially straight vortex line, driven by a parametric resonance between a quadrupole mode and a pair of Kelvin modes of opposite momenta. Subsequently, Kelvin waves rapidly decay to longer wavelengths emitting sound waves in the process. We present a modified Kelvin wave dispersion relation for trapped superfluids and propose a simple method to excite Kelvin waves of specific wave number.
We investigate low-energy collective excitations in Bose-Einstein condensates (BECs) with a single-vortex line or many vortices by using the microscopic theory based on the Bogoliubov-Popov formalism. The paper is divided into the following two section: (i) We first study the damping process of the quadrupole modes in a three-dimensional cigar-shaped BEC. The selective excitation of such the modes occurs during the rotation of the condensate in the opposite or same direction relative to a vortex velocity field. The dramatic change of the damping process of these modes is explained by the linear response theory. It is proposed that Kelvin modes play a leading part in the decay process of the quadrupole excitation. These results are quantitatively compared with the recent experiment on 87 Rb by Bretin et al. [Phys. Rev. Lett. 90, 100403 (2003)]. (ii) In addition, the complete spectrum of the collective excitations in vortex-lattice states is obtained by solving the Bogoliubov-de Gennes equation in a two-dimensional disk-shaped BEC. We also discuss the frequency shift of totally symmetric and twofold symmetric Tkachenko modes.
We investigate two-dimensional turbulence in finite-temperature trapped Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematically explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and co-rotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov ${k}^{\ensuremath{-}5/3}$ power law over almost a decade of length or wave-number (kkk) scales. The kinetic energy spectrum of regime (C) exhibits a clear ${k}^{\ensuremath{-}3/2}$ power law associated with an inertial range for weak-wave turbulence and a ${k}^{\ensuremath{-}7/2}$ power law for high wave numbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.