Decoherence of three-level systems: Application to nitrogen-vacancy centers in diamond near a surface

We study the dynamics of quantum three-level systems due to fast fluctuations of their environment (white noise). As an example, we model the decoherence and dephasing of nitrogen-vacancy (NV) centers in diamond that are positioned near a surface that gives rise to quickly fluctuating magnetic field noise, with and without the presence of a rf field that couples levels of the ground electronic state manifold. We use a simple quantum mechanical model that allows for analytical solutions. The model treats the NV three-level ground state in the presence of rapidly fluctuating magnetic fields that arise from the environment and result in decoherence, dephasing, and dissipation. We show that the magnetic field fluctuations can couple all the elements of the density matrix of the three-level system. Hence, all 9 eigenmodes may contribute to both population and coherence dynamics. We also discuss consequences for fitting experiments in which decoherence plays a role.