Controlling Atom Array in an Ultra-high-cooperativity Optical Cavity

Neutral-atom array and cavity quantum electrodynamics offer complementary strengths for quantum science: scalable, reconfigurable qubit architectures and strong coherent light-matter coupling. Combining them in a single platform requires an optical cavity with simultaneously high cooperativity, sufficient mode volume to accommodate atom array, and ample side optical access for atom trapping, imaging, cooling, and rearrangement, a combination that is challenging to achieve. Here we realize an atomic array integrated with a millimeter-scale Fabry--P\'erot cavity whose optically-characterized single-atom cooperativity reaches $\eta_{\mathrm{cav}}=125\pm13$. Atom-cavity transmission spectra of trapped atoms yield an effective spectroscopic cooperativity $\eta_{\mathrm{spec}}=112.3\pm3.3$, providing an in-situ verification of strong coupling in the integrated platform, and we demonstrate simultaneous coupling of up to 16 individually trapped atoms to the antinode of the cavity mode. The key technical advance is a two-step mirror-fabrication method combining precision mechanical shaping and carbon-dioxide laser polishing, which produces concave fused-silica mirrors with sub-millimeter radii of curvature and residual roughness below 2 \r{A}. Our results establish a regime of cavity-integrated atomic array that simultaneously provides high cooperativity, large mode volume, and flexible manipulation of individual atoms, opening opportunities for cavity-assisted quantum state readout and long-range entanglement-engineering in atom-array platforms.