  An efficient atom-photon-interface is a key requirement for the integration
of solid-state emitters such as color centers in diamond into quantum
technology applications. Just like other solid state emitters, however, their
emission into free space is severely limited due to the high refractive index
of the bulk host crystal. In this work, we present a planar optical antenna
based on two silver mirrors coated on a thin single crystal diamond membrane,
forming a planar Fabry-P\'erot cavity that improves the photon extraction from
single tin vacancy (SnV) centers as well as their coupling to an excitation
laser. Upon numerical optimization of the structure, we find theoretical
enhancements in the collectible photon rate by a factor of 60 as compared to
the bulk case. As a proof-of-principle demonstration, we fabricate single
crystal diamond membranes with sub-$\mu$m thickness and create SnV centers by
ion implantation. Employing off-resonant excitation, we show a 6-fold
enhancement of the collectible photon rate, yielding up to half a million
photons per second from a single SnV center. At the same time, we observe a
significant reduction of the required excitation power in accordance with
theory, demonstrating the functionality of the cavity as an optical antenna.
Due to its planar design, the antenna simultaneously provides similar
enhancements for a large number of emitters inside the membrane. Furthermore,
the monolithic structure provides high mechanical stability and
straightforwardly enables operation under cryogenic conditions as required in
most spin-photon interface implementations.
