Above-Unity Coherent Cooperativity of Tin-Vacancy Centers in Diamond Photonic Crystal Cavities

The tin-vacancy center in diamond (SnV) has emerged as a compelling building block for realizing next-generation quantum networks thanks to its excellent optical and spin properties. Coupling to photonic crystal cavities (PCCs) promises to further enhance the SnV light-matter interface and unlock a diverse range of entanglement generation protocols. Recent pioneering experiments showing Purcell enhancement of SnV centers in PCCs underscore this potential. However, optical coupling that is coherent - the key ingredient for use in quantum protocols - has so far remained elusive. Here, we demonstrate above-unity coherent cooperativity of SnV centers embedded in photonic crystal cavities. We fabricate free-standing PCCs using a quasi-isotropic undercut. Across two samples, we conduct room-temperature characterizations, measuring resonances for 327 cavities, with an average quality factor exceeding $Q = 1.0(3) \times 10^4$. Two cavity-coupled emitters are examined in detail, exhibiting quality factors up to $Q = 25.4(4) \times 10^3$ and Purcell-reduced lifetimes corresponding to cooperativities up to $C = 20.6(11)$. Furthermore, the single SnVs are observed to strongly modulate the cavity transmission with an extinction contrast up to $98.8(4) \%$ on resonance. Finally, SnV linewidth measurements reveal above-unity coherent cooperativities in both devices, with the highest value being $C_\mathrm{coh} = 8.3(12)$. These results open the door to using cavity-coupled SnV centers as efficient, coherent light-matter interfaces for future quantum networks.