  The nitrogen-vacancy center in diamond, owing to its optically addressable
and long-lived electronic spin, is an attractive resource for the generation of
remote entangled states. However, the center's low native fraction of coherent
photon emission, $\sim$3\%, strongly reduces the achievable spin-photon
entanglement rates. Here, we couple a nitrogen-vacancy center with a narrow
extrinsically broadened linewidth (\unit[159]{MHz}), hosted in a micron-thin
membrane, to the mode of an open optical microcavity. The resulting Purcell
factor of $\sim$1.8 increases the fraction of zero-phonon line photons to above
44\%, leading to coherent photon emission rates exceeding four times the state
of the art under non-resonant excitation. Bolstered by the enhancement provided
by the cavity, we for the first time measure resonance fluorescence without any
temporal filtering with $>$10 signal-to-laser background ratio. Our microcavity
platform would increase spin-spin entanglement success probabilities by more
than an order of magnitude compared to existing implementations. Selective
enhancement of the center's zero-phonon transitions could furthermore unlock
efficient application of quantum optics techniques such as wave-packet shaping
or all-optical spin manipulation.
