Dynamic nuclear polarization mechanism in isolated NV-centers at high magnetic fields

Nitrogen vacancy centers in diamonds are promising spin-based quantum sensors and qubits. These optically addressable paramagnetic point defects have the potential to allow efficient dynamic nuclear polarization (DNP) under ambient conditions due to their large electron spin polarization and long spin coherence time. NV-based DNP studies have shown significant sensitivity enhancement of ¹³C nuclear magnetic resonance (NMR). In this work, we present an analytical theory using a density matrix and average Hamiltonian theory for NV-¹³C spin system under varying magnetic fields, internal interaction strengths, and microwave irradiation parameters. We use a reduced basis approach under selective excitation of a single quantum transition in NV-center electron spin levels to derive the expressions for the matching conditions, effective Hamiltonian and polarization transfer frequency. Our results provide insight into the optimal experimental conditions for efficient DNP and the impact of the internal interactions on the DNP performance. The theoretical predictions are verified using numerical simulations.