Experimental Observation of Tensor Monopoles with a Superconducting Qudit

  1. Xinsheng Tan,
  2. Dan-Wei Zhang,
  3. Danyu Li,
  4. Xiaopei Yang,
  5. Shuqing Song,
  6. Zhikun Han,
  7. Yuqian Dong,
  8. Dong Lan,
  9. Hui Yan,
  10. Shi-Liang Zhu,
  11. and Yang Yu
Monopoles play a center role in gauge theories and topological matter. Examples of 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 in 4D 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.
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