Splitting Instability of a Multiply Charged Vortex in a Bose-Einstein Condensate

TL;DR

This paper investigates how multiply charged vortices in Bose-Einstein condensates split into singly charged vortices, revealing the role of unstable modes and confirming findings through numerical simulations.

Contribution

It identifies the unstable modes responsible for vortex splitting and links the vortex configuration to the angular momentum of negative-energy modes.

Findings

Unstable complex eigenmodes cause vortex splitting.

Negative-energy modes influence the vortex configuration.

Numerical simulations confirm the theoretical analysis.

Abstract

We consider the splitting mechanism of a multiply charged vortex into singly charged vortices in a Bose-Einstein condensate confined in a harmonic potential at zero temperature. The Bogoliubov equations support unstable modes with complex eigenfrequencies (CE modes), which cause the splitting instability without the influence of thermal atoms. The investigation of the excitation spectra shows that the negative-energy (NE) mode plays an important role in the appearance of the CE modes. The configuration of vortices in splitting is determined by the angular momentum of the associated NE mode. This structure has also been confirmed by the numerical simulation of the time-dependent Gross-Pitaevskii equation.