Collective coherent and dissipative dynamics of two quantum emitters in a nanophotonic cavity.

Interactions between two quantum emitters are a key ingredient for quantum networks. We demonstrate photon-mediated interactions in a platform consisting of two negatively-charged silicon-vacancy (SiV) color centers in diamond coupled with high cooperativity (C$\sim$20) to a nanophotonic cavity. We access cavity-coupled spin-selective optical transitions to initialize and read the SiV spin in a single shot with 96{\%} fidelity. When the optical transitions of the two SiV centers are near-resonant, the coupling of each SiV center to the cavity mode results in a cavity-mediated interaction between the two SiVs. This interaction hybridizes the two-SiV states into collective bright and dark states. Tuning of the magnetic field allows us to control the strength of this effect and observe a direct optical interaction between two SiV spin states. Thus, SiV centers which also have a long spin coherence of 10 ms may form building blocks for future quantum networks.