Theoretical analysis and experimental measurement of 14N nuclear spin polarization in nitrogen-vacancy centers in diamond

We investigated the dependence of 14 N nuclear spin polarization of the nitrogen-vacancy (NV) center on the magnitude (0-1100 G) and orientation of the magnetic field, experimentally using optically detected magnetic resonance and theoretically using the Lindblad equation for the density matrix to model the expected 14 N nuclear spin polarization. The mechanisms of 14 N nuclear spin polarization in magnetic field regions away from ground and excited level anticrossing points are explained through the analysis of the interactions of the hyperfine components. We found that in magnetic field regions, where hyperfine mixing is weak, nuclear spin polarization occurs as a result of several thousands of excitation-relaxation cycles. Results show that when the magnetic field is parallel to the NV axis, the polarization profile is mainly determined by the mixing of the excited-state hyperfine components and the mixing of the hyperfine components of the electron spin 𝑚𝑠=1 manifold. In addition, an in-depth explanation of the magnetic field transverse component sensitivity around the ground-state level anticrossing has been offered based on hyperfine level mixing analysis and Hamiltonian simulations.