State-dependent phonon-limited spin relaxation of nitrogen-vacancy centers

Understanding the limits to the spin coherence of the nitrogen-vacancy (NV) center in diamond is vital to realizing the full potential of this quantum system. We show that relaxation on the vertical bar m(s) = -1 > <-> vertical bar m(s) = +1 > transition occurs approximately twice as fast as relaxation on the vertical bar m(s) = 0 <-> vertical bar m(s) = +/- 1 > transitions under ambient conditions in native NVs in high-purity bulk diamond. The rates we observe are independent of NV concentration over four orders of magnitude, indicating they are limited by spin-phonon interactions. We find that the maximum theoretically achievable coherence time for an NV at 295 K is limited to 6.8(2) ms. Finally, we present a theoretical analysis of our results that suggests Orbach-like relaxation from quasilocalized phonons or contributions due to higher-order terms in the spin-phonon Hamiltonian are the dominant mechanism behind vertical bar m(s) = -1 > <-> vertical bar m(s) = +1 > relaxation, motivating future measurements of the temperature dependence of this relaxation rate.