Theory of Low Magnetic Field Photoluminescence Spectra of Nitrogen-Vacancy Centers in Diamond*

At weak magnetic fields (<2 mT) the photoluminescence (PL) of nitrogen vacancy (NV) centers in diamond is reduced from resonant dipole-coupling between centers even in the absence of microwaves. A single-center hamiltonian coupled with a population model in the hyperfine and electronically excited states qualitatively matches experimental findings. The dipole interaction between centers is included phenomenologically as an increase in the intersystem crossing of degenerate electronically excited states. We compare the PL dependence on field magnitude and orientation, optical power and NV density between experiment and theory for both 14N and 15N -based vacancies. Our findings open up new possibilities for low-power all-optical NV magnetometers.