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--Pérot cavity whose optically-characterized single-atom cooperativity reaches $η_{\mathrm{cav}}=125\pm13$. Atom-cavity transmission spectra of trapped atoms yield an effective spectroscopic cooperativity $η_{\mathrm{spec}}=106\pm 3$, providing an in-situ verification of strong coupling in the integrated platform. In this integrated system, we achieve a state-measurement fidelity of $99.925^{+15}_{-18}\%$ for a single atom with a 4-$μ$s readout time. We also demonstrate simultaneous coupling of up to 21 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 $2~Å$. 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.