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arXiv:cond-mat/0307130 · Physical Review Letters

Giant Vortex Lattice Deformations in Rapidly Rotating Bose-Einstein Condensates

Tapio Simula, A. A. Penckwitt, R. J. Ballagh

Published Feb 10, 2004• 49 citations
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Abstract

We have performed numerical simulations of giant vortex structures in rapidly rotating Bose-Einstein condensates within the Gross-Pitaevskii formalism. We reproduce the qualitative features, such as oscillation of the giant vortex core area, formation of toroidal density hole, and the precession of giant vortices, observed in the recent experiment [Phys. Rev. Lett., ()]]. We provide a mechanism which quantitatively explains the observed core oscillation phenomenon. We demonstrate the clear distinction between the mechanism of atom removal and a repulsive pinning potential in creating giant vortices. In addition, we have been able to simulate the transverse Tkachenko vortex lattice vibrations.

DOI
10.1103/physrevlett.92.060401

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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)].
We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped Bose-Einstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The simulations reveal previously unknown dynamical features of the vortex nucleation process, in which the condensate undergoes a strongly turbulent stage and the penetrating vortex lines vibrate rapidly. The vibrations arise from spontaneous excitation of Kelvin waves on the protovortices during a surface wave instability, caused by an inhomogeneity of the condensate density along the elongated axial direction.
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We present a mean-field theory numerical study of Tkachenko waves of a vortex lattice in trapped atomic Bose-Einstein condenstates. Our results show remarkable qualitative and quantitative agreement with recent experiments at the Joint Institute for Laboratory Astrophysics. We extend our calculations beyond the conditions of the experiment, probing deeper into the incompressible regime where we find excellent agreement with analytical results. In addition, bulk excitations observed in the experiment are discussed.