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

Optical cavities are one of the best ways to increase atom-light coupling and will be a key ingredient for future quantum technologies that rely on light-matter interfaces. We demonstrate that traveling-wave "ring" cavities can achieve a greatly reduced mode waist $w$, leading to larger atom-cavity coupling strength, relative to conventional standing-wave cavities for given mirror separation and stability. Additionally, ring cavities can achieve arbitrary transverse-mode spacing simultaneously with the large mode-waist reductions. Following these principles, we build a parabolic atom-ring cavity system 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 a factor of $35(5)$ times greater than what could be achieved with a near-confocal standing-wave cavity with the same mirror separation and finesse. By using parabolic mirrors, we eliminate astigmatism--which can otherwise preclude stable operation--and increase optical access to the atoms. Cavities based on these principles, with enhanced coupling and large mirror separation, will be particularly useful for achieving strong coupling with ions, Rydberg atoms, or other strongly interacting particles, which often have undesirable interactions with nearby surfaces.