  The millimeter wave (mm-wave) frequency band provides exciting prospects for
quantum science and devices, since many high-fidelity quantum emitters,
including Rydberg atoms, molecules and silicon vacancies, exhibit resonances
near 100 GHz. High-Q resonators at these frequencies would give access to
strong interactions between emitters and single photons, leading to rich and
unexplored quantum phenomena at temperatures above 1K. We report a 3D mm-wave
cavity with a measured single-photon internal quality factor of $3 \times
10^{7}$ and mode volume of $0.14 \times \lambda^3$ at $98.2$ GHz, sufficient to
reach strong coupling in a Rydberg cavity QED system. An in-situ piezo
tunability of $18$ MHz facilitates coupling to specific atomic transitions. Our
unique, seamless and optically accessible resonator design is enabled by the
realization that intersections of 3D waveguides support tightly confined bound
states below the waveguide cutoff frequency. Harnessing the features of our
cavity design, we realize a hybrid mm-wave and optical cavity, designed for
interconversion and entanglement of mm-wave and optical photons using Rydberg
atoms.
