Quantum simulation of Abelian Wu-Yang monopoles in spin-1/2 systems

TL;DR

This paper demonstrates how to simulate and analyze artificial magnetic monopoles in a driven superconducting qubit using Berry curvature and Chern number, revealing topological transitions and asymmetric quantum state behavior.

Contribution

It provides a combined analytical and numerical approach to simulate magnetic monopoles in spin-1/2 systems and explores their topological properties and transition asymmetries.

Findings

Degeneracy points act as sources or sinks of Berry curvature.

Topological transitions affect quantum state behavior asymmetrically.

Magnetic monopoles influence the geometry of eigenstates in parameter space.

Abstract

With the help of the Berry curvature and the first Chern number $($$\textit{C}_1$$)$, we both analytically and numerically investigate and thus simulate artificial magnetic monopoles formed in parameter space of the Hamiltonian of a driven superconducting qubit. The topological structure of a spin-1/2 system $($qubit$)$ can be captured by the distribution of Berry curvature, which describes the geometry of eigenstates of the Hamiltonian. Degeneracy points in parameter space act as sources $($$\textit{C}_1$ = $1$$)$ or sinks $($$\textit{C}_1$ = $-1$$)$ of the magnetic field. We note that the strength of the magnetic field $($described by Berry curvature$)$ has an apparent impact on the quantum states during the process of topological transition. It exhibits an unusual property that the transition of the quantum states is asymmetric when the degenerate point passes from outside to inside and again outside the manifold spanned by system parameters. Our results also pave the way to explore intriguing properties of magnetic monopoles in other spin-1/2 systems.