Single Color Center Spin Coherence revealed in Optically Detected Magnetic Resonance of an Ensemble of Silicon Vacancies in SiC

Abstract: We present a quantitative theory for simulating optically detected magnetic resonance (ODMR) measurements of optically-active spin centers using steady-state Lindblad equations. We apply the theory to an experimental ODMR spectrum associated with the negatively-charged silicon vacancy V2 center in 6H-SiC, showing that spin Hamiltonian parameters, optical transition rates, and even coherence times may be extracted, with values consistent with recent literature. Notably the $T_2$ spin coherence time is measurable, not just the $T_2^*$ dephasing time. Furthermore, we simulate the ODMR spectra of a V2 center in isotopically-purified 6H-SiC, and predict an order-of-magnitude narrowing of some, but not all spectral lines compared with natural abundance samples.