  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.
