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

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.

💡 Research Summary

This paper investigates the decay of a triply quantized vortex (TQV, winding number S = 3) embedded in a toroidal Bose‑Einstein condensate when the condensate is released into a weakly elliptical harmonic trap. Using full three‑dimensional Gross‑Pitaevskii simulations performed in cylindrical coordinates, the authors explore how trap anisotropy, interaction strength, and initial quantum fluctuations determine the instability pathway, the splitting time, and the final vortex configuration.

The initial state is a ring‑shaped ^87Rb condensate (N ≈ 10⁵ atoms) with outer radius ≈ 12 µm and a central hole ≈ 6.5 µm, prepared in a harmonic trap (ω_r0 = 2π × 47 Hz, ω_z = 2π × 238 Hz) together with a blue‑detuned plug beam that creates the toroidal geometry. A phase imprint or rotation generates a TQV along the symmetry axis. After adiabatically removing the plug, the condensate is transferred to a harmonic trap with radial frequencies ω_x and ω_y, defining an ellipticity parameter η = (ω_x² − ω_y²)/ω_x² that is varied from 0 (isotropic) to 1 (strongly elongated).

The dynamics obey the 3D Gross‑Pitaevskii equation iħ∂_tΨ =