Core-bound waves on a Gross-Pitaevskii vortex

TL;DR

This paper investigates the dispersion relations of core-bound excitations in a Gross-Pitaevskii vortex, revealing new families of waves and proposing a method for their experimental detection.

Contribution

It identifies and characterizes varicose and fluting core-bound waves in GP vortices, expanding understanding of vortex excitations beyond Kelvin waves.

Findings

Varicose and fluting waves have infinite core-bound branches below Bogoliubov dispersion.

Short-wavelength excitations behave as particles bound to the vortex.

Proposed spectroscopic protocol successfully detects varicose waves in simulations.

Abstract

We find the dispersion relations of two elusive families of core-bound excitations of the Gross-Pitaevskii (GP) vortex, varicose (axisymmetric) and fluting (quadrupole) waves. For wavelengths of order the healing length, these two families -- and the well-known Kelvin wave -- possess an infinite sequence of core-bound, vortex-specific branches whose energies lie below the Bogoliubov dispersion relation. In the short-wavelength limit, these excitations can be interpreted as particles radially bound to the vortex, which acts as a waveguide. In the long-wavelength limit, the fluting waves unbind from the core, the varicose waves reduce to phonons propagating along the vortex, and the fundamental Kelvin wave is the only core-bound vortex-specific excitation. Finally, we propose a realistic spectroscopic protocol for creating and detecting the varicose wave, which we test by direct numerical simulations of the GP equation.