Experimental Observation of Tensor Monopoles with a Superconducting Qudit

Monopoles play a center role in gauge theories and topological matter. There are two fundamental types of monopoles in physics: vector monopoles and tensor monopoles. Examples of vector monopoles include the Dirac monopole in three dimensions and Yang monopole in five dimensions, which have been extensively studied and observed in condensed matter or artificial systems. However, tensor monopoles are less studied, and their observation has not been reported. Here we experimentally construct a tunable spin-1 Hamiltonian to generate a tensor monopole and then measure its unique features with superconducting quantum circuits. The energy structure of a 4D Weyl-like Hamiltonian with threefold degenerate points acting as tensor monopoles is imaged. Through quantum-metric measurements, we report the first experiment that measures the Dixmier-Douady invariant, the topological charge of the tensor monopole. Moreover, we observe topological phase transitions characterized by the topological Dixmier-Douady invariant, rather than the Chern numbers as used for conventional monopoles in odd-dimensional spaces.

Automated summary

Monopoles are important in physics, with two fundamental types: vector monopoles and tensor monopoles. While vector monopoles have been extensively studied and observed in condensed matter, tensor monopoles are less studied and their observation has not been reported yet. Through experimental methods, the energy structure of a 4D Weyl-like Hamiltonian with tensor monopoles has been imaged, and the first experiment measuring Dixmier-Douady invariant for tensor monopoles has been reported. The observation of topological phase transitions characterized by the Dixmier-Douady invariant is a significant finding in this study.