Precise knowledge of a quantum systems Hamiltonian is a critical pre-requisite for its use in many quantum information technologies. Here, we report a method for the precise characterization of the non-secular part of the excited-state Hamiltonian of an electronic-nuclear spin system in diamond. The method relies on the investigation of the dynamic nuclear polarization mediated by the electronic spin, which is currently exploited as a primary tool for initializing nuclear qubits and performing enhanced nuclear magnetic resonance. By measuring the temporal evolution of the population of the ground-state hyperfine levels of a nitrogen-vacancy center, we obtain the first direct estimation of the excited-state transverse hyperfine coupling between its electronic and nitrogen nuclear spin. Our method could also be applied to other electron-nuclear spin systems, such as those related to defects in silicon carbide.
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