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Chern numbers are gaining traction as they characterize topological phases invarious physical systems. However, the resilience of the system topology toexternal perturbations makes it challenging to experimentally investigatetransitions between different phases. In this study, we demonstrate thetransitions of Chern number from 0 to 3, synthesized in an electronic-nuclearspin system associated with the nitrogen-vacancy (NV) centre in diamond. TheChern number is characterized by the number of degeneracies enclosed in acontrol Hamiltonian parameter sphere. The topological transitions betweendifferent phases are depicted by varying the radius and offset of the sphere.We show that the measured topological phase diagram is not only consistent withthe numerical calculations but can also be mapped onto an interactingthree-qubit system. The NV system may also allow access to even higher Chernnumbers, which can be applied to exploring exotic topology or topologicalquantum information.

Controllable tunability of a Chern number within the electronic-nuclear spin system in diamond