Cross-relaxation studies with optically detected magnetic resonances in nitrogen-vacancy centers in diamond in an external magnetic field

In this paper cross-relaxation between nitrogen-vacancy (NV) centers and substitutional nitrogen in a diamond crystal was studied. It was demonstrated that optically detected magnetic resonance signals (ODMR) can be used to measure these signals successfully. The ODMR were detected at axial magnetic field values around 51.2~mT in a diamond sample with a relatively high (200~ppm) nitrogen concentration. We observed transitions that involve magnetic sublevels that are split by the hyperfine interaction. Microwaves in the frequency ranges from 1.3 GHz to 1.6 GHz ($m_S=0\longrightarrow m_S=-1$ NV transitions) and from 4.1 to 4.6 GHz ($m_S=0\longrightarrow m_S=+1$ NV transitions) were used. To understand the cross-relaxation process in more detail and, as a result, reproduce measured signals more accurately, a model was developed that describes the microwave-initiated transitions between hyperfine levels of the NV center that are undergoing anti-crossing and are strongly mixed in the applied magnetic field. Additionally, we simulated the extent to which the microwave radiation used to induce ODMR in the NV center also induced transitions in the substitutional nitrogen via cross-relaxation. The improved understanding of the NV processes in the presence of a magnetic field will be useful for designing NV-diamond-based devices for a wide range of applications from implementation of q-bits to hyperpolarization of large molecules to various quantum technological applications such as field sensors.