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

TL;DR

The paper presents a scalable cavity array microscope (CAM) that delivers hundreds of degenerate, tightly focused cavities by routing light through a 2D microlens array and demagnifying telescopes, enabling parallel interfacing with large neutral-atom arrays. Core results include >600 cavities with an array-averaged finesse of 114(17) and a field of view sufficient to host ~615 cavities, with 537 cavities degenerate within the readout linewidth; these figures are limited by optical losses and field curvature. The authors analyze misalignments, aberrations, and Gouy-phase effects that degrade degeneracy, and demonstrate methods to compensate using precise longitudinal/transverse positioning and Zernike decomposition to diagnose nm-scale aberrations. They outline a clear pathway to tens of thousands of cavities with higher finesse, predicting high information bandwidths and GHz-scale entangling rates, while maintaining large atom-surface separations to mitigate surface-charge decoherence. Overall, the CAM offers a highly scalable, high-cooperativity platform for parallel quantum networking, fast mid-circuit readout, and explorations of hybrid atom-photon Hamiltonians, with practical routes to dramatically larger arrays and improved performance.

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.

Figures (16)

• Figure 1: Summary of results.a. The cavity array microscope (CAM) is an optical imaging system that generates a 2D array of independent, simultaneously resonant optical cavities with wavelength-scale mode waists and mode spacings. b. Cavity transmission for hundreds of simultaneously driven individual cavity modes. c, d. We demonstrate a cavity array microscope with >600 cavities and an array-averaged finesse of 114(17). When the outcoupling is optimized for collection efficiency (Sup. \ref{['SI:collection']}), 537 cavities are degenerate to within the cavity linewidth, indicated by red lines on color bar. The dashed black circle indicates the field of view of the intra-cavity optics, beyond which field curvature inhibits stability (Sec. \ref{['sec:fov']}). The degeneracy of the CAM is interferometrically sensitive to nanometer-scale variations in optical path lengths between cavities due to misalignments, aberrations, stresses, and surface irregularity of various optics. e. The number of achievable cavities can be increased through simple modifications to the intra-cavity optics. By doubling the density of the microlens array (MLA) and leveraging a wider field of view microscope objective, the CAM could support tens of thousands of cavities at high cooperativity. f. We compare the CAM to other state-of-the-art, neutral atom array-compatible resonator geometries on the axes of bandwidth (fastest possible readout/entanglement speed), distance of atoms from dielectric surfaces, and cooperativity. Grey shading is a guide to the eye for distances at which surface charges are potentially deleterious to Rydberg excitation ocola2025control. Stars: cavity array microscopes shaw2025cavarray, Squares: nanophotonic cavities dhordjevic2021entanglement, Triangles: fiber and micro-mirror cavities grinkemeyer2025errording2025highfinesse, Circles: macro-mirror cavities shadmany2025cavitydeist2022midhu2025siteliu2023realizationhartung2024quantumnetwork.
• Figure 2: Experimental setup. Our experimental realization of the cavity array microscope (CAM) contains both off-the-shelf and custom optical elements. A spatial light modulator (SLM) is used to couple serially into each cavity in the array. The central cavity can be separately driven using light detuned by 80 MHz relative to the SLM path, enabling characterization of the relative degeneracy of different cavities to less than the cavity linewidth. All cavities are read out using a shared avalanche photodiode. Lower panels: Paraxial stability diagrams for the central cavity, plotting the smallest waist and round trip Gouy phase ($\phi_{rt}$) as a function of displacements of each optic from its optimal telescopic position. The stability of all cavities in the array can be approximated by a paraxial model of the central "on-axis" cavity. The aspheric lens is the most sensitive optic, with its stability region spanning only 11 $\upmu$m of longitudinal displacement.
• Figure 3: Cavity mode waista. The two 4f telescopes of the CAM have the action of the identity on an incoming ray (in the ABCD matrix formalism), which means that the CAM can be reduced to an effective two mirror cavity consisting of the planar end mirror and a curved micro-mirror array. b. In this effective cavity picture, the mode size at the micro-mirror array (and MLA) increases monotonically as $\Delta d_{Mirror}$ is swept from zero to $f_{\textrm{MLA}}$. c. Asphere stability diagrams at three values of $\Delta d_{\textrm{Mirror}}$, illustrating that $\Delta d_{\textrm{Mirror}}$ fixes the maximum size of the cavity mode waist (as the asphere separation is varied). At zero asphere defocus (dashed line), the mode waist is exactly equal to $w_{\textrm{MLA}}/M$.
• Figure 4: Field of View.a, b. Both (a) the field of view— plotted as an array of cavity finesses— and (b, top) the stability of cavities at a given radial displacement from the central cavity are sensitive to micron-scale longitudinal displacements of the two aspheres. Radially averaged finesse measurements are used as a proxy for assessing the corresponding stability regions, with lines connecting points to guide to the eye. We work at a displacement that simultaneously maximizes both number of stable cavities (b, middle) and the array-averaged finesse (b, bottom); with further optics development, we anticipate substantial gains in the achievable field of view. c. The field curvature of the asphere (top) produces a radially dependent, quadratic focal shift which translates the asphere stability regions as a function of radial cavity index, limiting the field of view. (inset) We visualize this curvature by ray tracing tilted plane waves through a single pass of the aspheric lens. (bottom) Experimental (circles), and numerically calculated (stars, see Sup. \ref{['SI:RayTracing']})) stability diagram shifts align with the expected focal shift from the asphere field curvature (multiplied 4 for the number of asphere passes per cavity round trip), while numerical calculations using ideal lenses (triangles) exhibit no shift. We attribute the small discrepancy between the experimental data and the numerics to quadratic misalignment aberrations, such as defocus, which add to or subtract from the intrinsic field curvature. Red lines indicate the radial index and stability shift corresponding to the maximum field of view.
• Figure 5: Degeneracy characterization.a. The degeneracy of the CAM is sensitive to perturbations that change the relative round-trip optical path length of the individual cavities in the array. Such perturbations can, for instance, arise from misalignments of various intra-cavity optics, or from imperfections of their surfaces, such as stress or form-error of the end mirrors. b. To characterize these effects, we measure the fractional detuning $\Delta_m$ of each cavity (blue) relative to the central cavity (red). c. Transverse misalignment of the spherical lens produces a linear gradient of detunings across the array, while d. a mechanically stressed end-mirror produces astigmatism across the array. We distinguish these effects by decomposing the map of detunings into a sum of Zernike polynomials (with one site Gaussian smoothing applied on the data), allowing quantitative evaluation of aberrations, order-by-order.