High-cooperativity coupling and spin-resolved extinction of tin-vacancy centers in a diamond-like microcavity

The tin-vacancy (SnV) center in diamond is a promising spin-photon interface for quantum networks, combining favorable optical properties with spin coherence above 1K. Unfolding the full potential requires cavity enhancement to increase photon-emitter coupling efficiency. Here, we demonstrate cavity-enhanced light-matter coupling of SnV centers in a fully tunable Fabry-P\'erot microcavity operating at temperatures down to 1K with in-situ magnetic field control. We access the diamond-like regime of hybrid cavity modes through integration of low-roughness diamond membranes, where the field is concentrated inside the diamond and Purcell enhancement is maximized. Diamond-like modes deliver a more than two-fold increase in the effective Purcell factor over air-like modes, reaching $C_0 = 4.1(1)$ compared to $C_0 = 1.85(5)$ in the air-like case, while simultaneously relaxing mechanical stability requirements. Resonant probing reveals coherent cavity-emitter coupling with 96% extinction contrast and a coherent cooperativity of $C = 4.0(14)$. By applying a magnetic field, we further achieve spin-resolved cavity extinction, observing spin-selective optical transitions with a contrast of ${\cal C}_{\rm spin} = 0.91$. These results establish SnV centers in diamond coupled to open Fabry-P\'erot microcavities as a promising platform for efficient spin-photon interfaces.