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Optical cavities are one of the best ways to increase atom-light coupling andwill be a key ingredient for future quantum technologies that rely onlight-matter interfaces. We demonstrate that traveling-wave "ring" cavities canachieve a greatly reduced mode waist $w$, leading to larger atom-cavitycoupling strength, relative to conventional standing-wave cavities for givenmirror separation and stability. Additionally, ring cavities can achievearbitrary transverse-mode spacing simultaneously with the large mode-waistreductions. Following these principles, we build a parabolic atom-ring cavitysystem that achieves strong collective coupling $NC = 15(1)$ between $N=10^3$Rb atoms and a ring cavity with a single-atom cooperativity $C$ that is afactor of $35(5)$ times greater than what could be achieved with anear-confocal standing-wave cavity with the same mirror separation and finesse.By using parabolic mirrors, we eliminate astigmatism--which can otherwisepreclude stable operation--and increase optical access to the atoms. Cavitiesbased on these principles, with enhanced coupling and large mirror separation,will be particularly useful for achieving strong coupling with ions, Rydbergatoms, or other strongly interacting particles, which often have undesirableinteractions with nearby surfaces.

30-Fold Increase in Atom-Cavity Coupling Using a Parabolic Ring Cavity