Master-equation-based model for infrared-based magnetometry with nitrogen-vacancy-centers-in-diamond cavities: A path to subpicotesla sensitivity at submillimeter scales

Our study aims to increase the spatial resolution of high-sensitivity magnetometry based on singlet-transition infrared (IR) absorption using nitrogen-vacancy ($\mathrm{N}$-$V$) centers in diamond in monolithic cavities, with potential applications in biomagnetic field detection. We develop a master-equation treatment of optically detected magnetic resonance, incorporating IR light saturation effects. This master equation provides the singlet population, which is then utilized to calculate the reflectivity and ultimately derive the magnetic field sensitivity taking into account photon and spin shot noise. We further show that our model is compatible with experiments of IR-based $\mathrm{N}$-$V$-center magnetometry. Through optimization in a high-parameter space, we uncover the potential to achieve sensitivities in the order of subpicotesla, even for submillimeter scales.