Sensing Coherent Nuclear Spin Dynamics with an Ensemble of Paramagnetic Nitrogen Spins

The unpolarized spin environment surrounding a central spin qubit is typically considered as an incoherent source of dephasing, however, precise characterization and control of the spin bath can yield a resource for storing and sensing with quantum states. In this work, we use nitrogen-vacancy (NV) centers in diamond to measure the coherence of optically dark paramagnetic nitrogen defects (P1 centers) and detect coherent interactions between the P1 centers and a local bath of ${}^{13}\mathrm{C}$ nuclear spins. The dipolar coupling between the P1 centers and ${}^{13}\mathrm{C}$ nuclear spins is identified by signature periodic collapses and revivals in the P1 spin coherence signal. We then demonstrate, using a range of dynamical decoupling protocols, that the probing NV centers and the P1 spins are coupled to independent ensembles of ${}^{13}\mathrm{C}$ nuclear spins. Our work illustrates how the optically dark P1 spins can be used to extract information from their local environment and offers new insight into the interactions within a many-body system.