  Photon-mediated interactions between quantum systems are essential for
realizing quantum networks and scalable quantum information processing. We
demonstrate such interactions between pairs of silicon-vacancy (SiV) color
centers strongly coupled to a diamond nanophotonic cavity. When the optical
transitions of the two color centers are tuned into resonance, the coupling to
the common cavity mode results in a coherent interaction between them, leading
to spectrally-resolved superradiant and subradiant states. We use the
electronic spin degrees of freedom of the SiV centers to control these
optically-mediated interactions. Our experiments pave the way for
implementation of cavity-mediated quantum gates between spin qubits and for
realization of scalable quantum network nodes.
