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arXiv:1110.5757 · Physical Review E

Vortex knots in a Bose-Einstein condensate

Davide Proment, Miguel Onorato, Carlo F. Barenghi

Published Mar 19, 2012• 96 citations
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Abstract

We present a method for numerically building a vortex knot state in the superfluid wave function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and shape preservation of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: for smaller ratio, the knot travels faster. Finally, we show how vortex knots break up into vortex rings.

DOI
10.1103/physreve.85.036306

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We present a method for numerically building a vortex knot state in the superfluid wave function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and shape preservation of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: for smaller ratio, the knot travels faster. Finally, we show how vortex knots break up into vortex rings.
We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics relating the topological parameter to its translational velocity and characteristic size. We also investigate the breaking mechanisms of non shape-preserving torus knots confirming an evidence of universal decaying behaviour previously observed.
We examine the static and dynamic properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics, relating the topological parameter to its translational velocity and characteristic size. We also investigate the breaking mechanisms of non shapepreserving torus knots, confirming an evidence of universal decaying behaviour previously observed.
© Published under licence by IOP Publishing Ltd. We examine the static and dynamic properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics, relating the topological parameter to its translational velocity and characteristic size. We also investigate the breaking mechanisms of non shapepreserving torus knots, confirming an evidence of universal decaying behaviour previously observed.
We study vortex ring solutions of the Gross-Pitaevskii equation for Bose-Einstein condensates confined in toroidal traps. Analogously to the Feynman-Onsager ansatz for a single vortex line, we assume a condensate wavefunction that describes a quantized vortex ring. This leads to a modified Gross-Pitaevskii equation that incorporates vortex ring solutions. By numerically solving this equation, we have obtained the density profiles and the vortex core structure. We have also calculated the nucleation energy of a vortex ring, and have analyzed its dependence on the ring position. Finally, a qualitative description of the vortex ring dynamics is presented.
The dynamics of the simplest vortex knots, “unknots,” and torus links in an atomic Bose condensate at zero temperature in an anisotropic harmonic trap has been simulated numerically within the three-dimensional Gross–Pitaevskii equation. It has been found that such quasistationary rotating vortex structures exist for a very long time in wide ranges of the parameters of the system. This new result is qualitatively consistent with a previous prediction based on a simplified one-dimensional model approximately describing the motion of knotted vortex filaments.