  Precise knowledge of a quantum system's 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.
