  A design for an ultra-high Q photonic crystal nanocavity engineered to
interact with nitrogen-vacancy (NV) centers located near the surface of a
single crystal diamond sample is presented. The structure is based upon a
nanowire photonic crystal geometry, and consists of a patterned high refractive
index membrane, such as gallium phosphide (GaP), supported by a diamond
substrate. The nanocavity supports a mode with quality factor Q > 1.5 million
and mode volume V < 0.52 (\lambda/n_\text{GaP})^3, and promises to allow
Purcell enhanced collection of spontaneous emission from an NV located more
than 50 nm below the diamond surface. The nanowire photonic crystal waveguide
can be used to efficiently couple light into and out of the cavity, or as an
efficient broadband collector of NV phonon sideband emission. The proposed
structures can be fabricated using existing materials and processing
techniques.
