Experimental Observation of Tensor Monopoles with a Superconducting Qudit

Abstract

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 3D and Yang monopole in 5D, 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 three-fold 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.

arXiv comment6+6 pages, 4+4 figures; version accepted for publication in PRL

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• Higher Gauge Theory
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• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model
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• Second Euler number in four dimensional synthetic matter
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• Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers
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