Revealing tensor monopoles through quantum-metric measurements

TL;DR

This paper proposes a method to create and detect tensor monopoles in four-dimensional parameter spaces using quantum-metric measurements in a three-level atomic system, advancing topological state exploration.

Contribution

It introduces a realistic three-band model and measurement technique for tensor monopoles, extending topological physics into four dimensions.

Findings

Tensor monopoles can be generated in a three-level atomic system.

Quantum metric measurements can reveal the topological charge of tensor monopoles.

The proposed method provides a feasible way to explore exotic topological objects.

Abstract

Monopoles are intriguing topological objects, which play a central role in gauge theories and topological states of matter. While conventional monopoles are found in odd-dimensional flat spaces, such as the Dirac monopole in three dimensions and the non-Abelian Yang monopole in five dimensions, more exotic objects were predicted to exist in even dimensions. This is the case of "tensor monopoles", which are associated with generalized (tensor) gauge fields, and which can be defined in four dimensional flat spaces. In this work, we investigate the possibility of creating and measuring such a tensor monopole, by introducing a realistic three-band model defined over a four-dimensional parameter space. Our probing method is based on the observation that the topological charge of this tensor monopole, which we relate to a generalized Berry curvature, can be directly extracted from the quantum metric. We propose a realistic three-level atomic system, where tensor monopoles could be generated and revealed through quantum-metric measurements.