Double-quantum spin-relaxation limits to coherence of near-surface nitrogen-vacancy centers

We probe the relaxation dynamics of the full three-level spin system of near-surface nitrogen-vacancy (NV) centers in diamond to define a $T_{1}$ relaxation time that helps resolve the $T_{2} \leq 2T_{1}$ coherence limit of the NV's subset qubit superpositions. We find that double-quantum spin relaxation via electric field noise dominates $T_{1}$ of near-surface NVs at low applied magnetic fields. Furthermore, we differentiate $1/f^{\alpha}$ spectra of electric and magnetic field noise using a novel noise-spectroscopy technique, with broad applications in probing surface-induced decoherence at material interfaces.