Stability, degeneracy, and scalability of a 600-site cavity array microscope

Abstract: Optical cavities are a foundational technology for controlling light-matter interactions. While interfacing a single cavity to either an atom or ensemble has become a standard tool, the advent of single atom control in large atomic arrays has spurred interest in a new frontier of ``many-cavity QED,'' featuring many independent resonators capable of separately addressing individual quantum emitters. In this fast-evolving landscape, the cavity array microscope was recently introduced -- employing free space intra-cavity optics to engineer a two-dimensional array of tightly spaced cavity TEM$_{00}$ modes with wavelength-scale waists, ideally suited for interfacing with atom arrays. Here we realize the next-generation of this architecture, achieving hundreds of degenerate cavity modes with improved, uniform finesse, and explore the technical features of the system which will enable further scalability. In particular, we study imperfections, including optical aberrations, field of view constraints, array non-degeneracies, and losses from optical elements. We identify the sensitivity to these various vectors and exposit the control knobs and techniques necessary to align and operate the system in a stable manner. Ultimately, we lay out a pathway towards operation with tens of thousands of independent cavities while maintaining compatibility with existing atom arrays, paving the way to myriad applications including highly parallelized remote entanglement generation, fast and non-destructive mid-circuit readout, and the implementation of hybrid atom-photon Hamiltonians.