Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates

Abstract

We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency $\omega$ on the chemical potential $\mu$, this is no longer true for a general potential $V(r)\propto r^p$. Our calculations suggest that for $p>2$, the precession frequency scales with $\mu$ as $\omega \sim {\mu }^{-2/p}$. This theoretical prediction is corroborated by numerical computations, both at the level of spectral (Bogolyubov-de Gennes) stability analysis by identifying the relevant precession mode dependence on $\mu$, but also through direct numerical computations of the vortex evolution in the large $\mu$, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the radius of an initially displaced from the center vortex is examined and the corresponding predictions are tested against numerical results.

9 pages, 5 figures

References in corpus (7)

• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Emergence of turbulence in an oscillating Bose-Einstein condensate
• Observation of Vortex Pinning in Bose-Einstein Condensates
• Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates
• Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates
• Experimental observation of the 'Tilting Mode' of an array of vortices in a dilute Bose-Einstein Condensate
• On Two-Component Dark-Bright Solitons in Three-dimensional Atomic Bose-Einstein Condensates