Vortex graphs as N-omers and CP(N-1) Skyrmions in N-component Bose-Einstein condensates

TL;DR

This paper constructs and classifies stable vortex N-omers in multi-component Bose-Einstein condensates, revealing their description as CP(N-1) skyrmions and analyzing their size dependence on Rabi coupling.

Contribution

It introduces a comprehensive classification of vortex N-omers using graph theory and links them to CP(N-1) skyrmions in symmetric coupling conditions.

Findings

All possible N-omers for N=2,3,4 are classified and constructed.

N-omers are described as CP(N-1) skyrmions under symmetric couplings.

Size of skyrmions depends on the Rabi coupling.

Abstract

Stable vortex N-omers are constructed in coherently coupled N-component Bose-Einstein condensates. We classify all possible N-omers in terms of the mathematical graph theory and numerically construct all graphs for N=2,3,4. We also find that N-omers are well described as CP(N-1) skyrmions when inter-component and intra-component couplings are U(N) symmetric, and we evaluate their size dependence on the Rabi coupling.