Temperature and spin-state dependence of phonon-limited spin relaxation for nitrogen-vacancy centers in diamond

Phonon-induced relaxation of the nitrogen-vacancy (NV) center's ground-state electronic spin triplet places hard limits on its performance in many proposed quantum applications. We report experimental measurements of the relaxation rates on both the m_s=-1 ↔ m_s=+1 qutrit transition and the m_s=0 ↔ m_s=±1 qubit transition as functions of temperature from 5 to 475 K in high-purity samples, where relaxation is dominated by spin-phonon interactions. We determine the upper limits imposed on NV spin coherence by spin-phonon relaxation over the temperature range relevant for almost all NV applications, and discuss their implications. We analyze the processes responsible for the observed relaxation, finding that two-phonon Raman scattering of quasilocalized phonons with a range of energies surrounding a 72(2) meV vibrational resonance drives relaxation on the qutrit transition approximately twice as fast as on the qubit transition. In addition, we find that a T⁵ term contributes to the temperature dependence of the relaxation rates on both transitions with equal magnitude, suggesting that the current understanding of the role of acoustic phonons in NV spin-phonon relaxation is incomplete. Part of this work was performed under the auspices of US DOE by LLNL under Contract DE-AC52-07NA27344.