Solid-state electron spin lifetime limited by phononic vacuum modes

Longitudinal relaxation is the process by which an excited spin ensemble decays into its thermal equilibrium with the environment. In solid-state spin systems, relaxation into the phonon bath usually dominates over the coupling to the electromagnetic vacuum(1-9). In the quantum limit, the spin lifetime is determined by phononic vacuum fluctuations(10). However, this limit was not observed in previous studies due to thermal phonon contributions(11-13) or phonon-bottleneck processes(10,14,15). Here we use a dispersive detection scheme(16,17) based on cavity quantum electrodynamics(18-21) to observe this quantum limit of spin relaxation of the negatively charged nitrogen vacancy (NV-) centre(22) in diamond. Diamond possesses high thermal conductivity even at low temperatures(23), which eliminates phonon-bottleneck processes. We observe exceptionally long longitudinal relaxation times T-1 of up to 8 h. To understand the fundamental mechanism of spin-phonon coupling in this system we develop a theoretical model and calculate the relaxation time ab initio. The calculations confirm that the low phononic density of states at the NV-transition frequency enables the spin polarization to survive over macroscopic timescales.