  We present the design and fabrication of nanobeam photonic crystal cavities
in single crystal diamond for applications in cavity quantum electrodynamics.
First, we describe three-dimensional finite-difference time-domain simulations
of a high quality factor (Q ~ 10^6) and small mode volume (V ~ 0.5
({\lambda}/n)^3) device whose cavity resonance corresponds to the zero-phonon
transition (637nm) of the Nitrogen-Vacancy (NV) color center in diamond. This
high Q/V structure, which would allow for strong light-matter interaction, is
achieved by gradually tapering the size of the photonic crystal holes between
the defect center and mirror regions of the nanobeam. Next, we demonstrate two
different focused ion beam (FIB) fabrication strategies to generate thin
diamond membranes and nanobeam photonic crystal resonators from a bulk crystal.
These approaches include a diamond crystal "side-milling" procedure as well as
an application of the "lift-off" technique used in TEM sample preparation.
Finally, we discuss certain aspects of the FIB fabrication routine that are a
challenge to the realization of the high-Q/V designs.
