Origin and evolution of the multiply-quantised vortex instability

TL;DR

This paper investigates the origin and evolution of multiply-quantized vortex instabilities in quantum fluids, revealing a superradiant bound state mechanism and novel non-linear behaviors that suggest possible vortex pair metastability.

Contribution

It identifies the superradiant bound state as the cause of vortex instability and uncovers non-linear vortex dynamics that challenge previous expectations about vortex separation.

Findings

Superradiant bound state causes vortex instability.

Vortex pairs exhibit modulated separation without entering a two-defect regime.

Potential formation of metastable vortex pairs under certain conditions.

Abstract

We show that the dynamical instability of quantum vortices with more than a single quantum of angular momentum results from a superradiant bound state inside the vortex core. Our conclusion is supported by an analytic WKB calculation and numerical simulations of both linearised and fully non-linear equations of motion for a doubly-quantised vortex at the centre of a circular bucket trap. In the late stage of the instability, we reveal a striking novel behaviour of the system in the non-linear regime. Contrary to expectation, in the absence of dissipation the system never enters the regime of two well-separated phase defects described by Hamiltonian vortex dynamics. Instead, the separation between the two defects undergoes modulations which never exceed a few healing lengths, in which compressible kinetic energy and incompressible kinetic energy are exchanged. This suggests that, under the right conditions, pairs of vortices may be able to form meta-stable bound states.