Geometry-driven splitting dynamics of a triply quantized vortex in a ring-shaped condensate

TL;DR

This study investigates how the geometry of a ring-shaped Bose-Einstein condensate influences the splitting dynamics of a triply quantized vortex, revealing geometry-dependent pathways and patterns of vortex decay.

Contribution

It provides a combined numerical and analytical analysis showing how trap anisotropy controls vortex splitting pathways and final vortex arrangements.

Findings

Vortex splits along the trap's long axis to minimize energy.

Initial quantum fluctuations delay splitting and suppress transient patterns.

Stronger nonlinear interactions accelerate vortex splitting.

Abstract

We study the splitting dynamics of a triply quantized vortex (TQV) confined in a ring-shaped Bose-Einstein condensate under a weakly elliptical harmonic trap. Using full 3D simulations in cylindrical coordinates, combined with a semi-analytical energy analysis, we show that the vortex preferentially splits along the long axis of the trap, a direction that minimizes the kinetic-energy cost relative to the initial TQV state. Systematic parameter scans reveal that initial quantum fluctuations increase the splitting time and suppress the transient three-core pattern observed in noise-free simulations, whereas stronger nonlinear interactions accelerate the splitting. When the trap is nearly isotropic, the unstable Bogoliubov modes are dominated by both azimuthal quantum number $l_q=3$ and $l_q=2$; this leads to a dynamical sequence where three daughter vortices first form a triangular arrangement, later evolving into a linear chain. For stronger anisotropy, geometric coupling selectively enhances the $l_q=2$ mode, making it the sole dominant channel and resulting directly in linear vortex alignment -- a clear signature of geometry-induced mode competition explained through combined energy-based and Bogoliubov stability analysis. Our results provide a quantitative picture of how trap geometry can steer the instability pathway, splitting time, and final pattern of a multiply quantized vortex, offering a route toward geometry-controlled vortex engineering.