Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates

Abstract

In the present work, motivated by numerous recent experimental developments we revisit the dynamics of a single vortex ring in anisotropic harmonic traps. At the theoretical level, we start from a general Lagrangian dynamically capturing the evolution of a vortex ring and not only consider its spectrum of linearized excitations, but also explore the full nonlinear dynamical evolution of the ring as a vortical filament. The theory predicts that the ring is stable for $1\le \lambda \le 2$, where $\lambda ={\omega }_z/{\omega }_r$ is the ratio of the trapping frequencies along the $z$ and $r$ axes, i.e., for spherical to slightly oblate condensates. We compare this prediction with direct numerical simulations of the full 3D Gross-Pitaevskii equation (GPE) capturing the linearization spectrum of the ring for different values of the chemical potential and as a function of the anisotropy parameter $\lambda$. We identify this result as being only asymptotically valid as the chemical potential $\mu \to \infty$, revealing how the stability interval narrows and, in particular, its upper bound decreases for finite $\mu$. Finally, we compare at the dynamical level the results of the GPE with the ones effectively capturing the ring dynamics, revealing the unstable evolution for different values of $\lambda$, as well as the good agreement between the two.

Corrected citation, 10 pages and many fun figures

References in corpus (6)

• Emergence of a Turbulent Cascade in a Quantum Gas
• Characterization of reconnecting vortices in superfluid helium
• Bending-wave Instability of a Vortex Ring in a Trapped Bose-Einstein Condensate
• Scattering and leapfrogging of vortex rings in a superfluid
• Large-scale superfluid vortex rings at nonzero temperatures
• Parametric instability of oscillations of a vortex ring in a $z$-periodic Bose-Einstein condensate and the recurrence to starting state

Cited by in corpus (14)

• Instabilities of vortex-ring-bright soliton in trapped binary 3D Bose-Einstein condensates
• Three-dimensional numerical simulation of long-lived quantum vortex knots and links in a trapped Bose-Einstein condensate
• Quasi-stable quantum vortex knots and links in anisotropic harmonically trapped Bose-Einstein condensates
• Instabilities of a Filled Vortex in a Two-Component Bose-Einstein Condensate
• Bubbles with attached quantum vortices in trapped binary Bose-Einstein condensates
• Collective oscillations of a Bose-Einstein condensate induced by a vortex ring
• Symmetry-breaking instability of leapfrogging vortex rings in a Bose-Einstein condensate
• Dynamics of interacting dark soliton stripes
• Nonlinearity and Topology
• Discrete vortices on spatially nonuniform two-dimensional electric networks
• Vortex knots on three-dimensional lattices of nonlinear oscillators coupled by space-varying links
• Dynamical Instability of 3d Stationary and Traveling Planar Dark Solitons
• Discrete Vortices in Systems of Coupled Nonlinear Oscillators: Numerical Results for an Electric Model
• Discrete Vortex Filaments on Arrays of Coupled Oscillators in the Nonlinear Resonant Mode