Tunable 3D Photonic Crystal Cavity for Coherent Coupling between Microwave Fields and Solid State Spins*

We present a theory and experiment of a three dimensional (3D) photonic crystal (PhC) cavity for the control of microwave fields with ultra-low loss. The cavity consists of an engineered defect in a woodpile photonic crystal made of low-loss alumina rods. We measure a large complete bandgap of 13% of the center frequency and a cavity quality factor exceeding 22,000. The architecture allows for easy mechanical tuning of the cavity and waveguide. Our design has a variety of applications including the coherent coupling of microwave photons with electron and nuclear spins in solids.