We report a high-finesse bow-tie cavity designed for atomic physics experiments with Rydberg atom arrays. The cavity has a finesse of 51,000 and a waist of 7.1
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μ m at the cesium D2 line (852 nm). With these parameters, the cavity is expected to induce strong coupling between a single atom and a single photon, corresponding to a cooperativity per traveling mode of 35 at the cavity waist. To trap and image atoms, the cavity setup utilizes two in-vacuum aspheric lenses with a numerical aperture (NA ) of 0.35 and is capable of housingNA = 0.5 microscope objectives. In addition, the large atom-mirror distance (cm) provides good optical access and minimizes stray electric fields at the position of the atoms. This cavity setup can operate in tandem with a Rydberg array platform, creating a fully connected system for quantum simulation and computation.