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arXiv:1303.0947 · Physical Review A

Collective dynamics of vortices in trapped Bose-Einstein condensates

Tapio Simula

Published Feb 27, 2013• 21 citations
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Abstract

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 ${N}_{v}$ vortices, ${N}_{v}$ 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.

DOI
10.1103/physreva.87.023630

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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 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.
The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates by solving the Bogoliubov-de Gennes equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both approaches allows one to unambiguously identify every observed mode.
We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes, and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable (`anomalous') mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex. We consider the effect of thermal quasiparticles on vortex normal modes as well as possible mechanisms for vortex dissipation. Vortex states in mixtures and spinor condensates are also discussed.