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 T₁ 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.