Spin-1 Topological Monopoles in Parameter Space of Ultracold Atoms

TL;DR

This paper proposes a method to realize and study three types of spin-1 topological monopoles in ultracold atoms, revealing their geometric properties, topological phase transitions, and experimental measurability, advancing topological quantum matter research.

Contribution

It introduces a scheme to create and analyze spin-1 topological monopoles in ultracold atoms, expanding beyond previous monopole types and enabling experimental exploration.

Findings

Different monopole charges exhibit distinct Berry curvature fields.

Topological phase transitions involve the emergence of spin vortices.

Berry curvature and monopole charge can be determined from dynamical effects.

Abstract

Magnetic monopole, a hypothetical elementary particle with isolated magnetic pole, is crucial for the quantization of electric charge. In recent years, analogues of magnetic monopoles, represented by topological defects in parameter spaces, have been studied in a wide range of physical systems. These works mainly focused on Abelian Dirac monopoles in spin-1/2 or non-Abelian Yang monopoles in spin-3/2 systems. Here we propose to realize three types of spin-1 topological monopoles and study their geometric properties using the parameter space formed by three hyperfine states of ultracold atoms coupled by radio-frequency fields. These spin-1 monopoles, characterized by different monopole charges, possess distinct Berry curvature fields and spin textures, which are directly measurable in experiments. The topological phase transitions between different monopoles are accompanied by the emergence of spin "vortex", and can be intuitively visualized using Majorana's stellar representation. We show how to determine the Berry curvature, hence the geometric phase and monopole charge from dynamical effects. Our scheme provides a simple and highly tunable platform for observing and manipulating spin-1 topological monopoles, paving the way for exploring new topological quantum matter.