A photonic crystal nanocavity with a Quality (Q) factor of 2.3 x 10^5, a mode volume of 0.55($lambda/n$)^3, and an operating wavelength of 637 nm is designed in a silicon nitride (SiN_x) ridge waveguide with refractive index of 2.0. The effect on the cavity Q factor and mode volume of single diamond nanocrystals of various sizes and locations embedded in the center and on top of the nanocavity is simulated, demonstrating that Q > 2 x 10^5 is achievable for realistic parameters. An analysis of the figures of merit for cavity quantum electrodynamics reveals that strong coupling between an embedded diamond nitrogen-vacancy center and the cavity mode is achievable for a range of cavity dimensions.
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