Super and Sub-Radiance in a Tunable Spacing Quantum Gas Microscope*

Quantum gas microscopy permits the study of cooperative optical effects in a regime qualitiativly distinct from what is traditionally realized in optical cavities and bulk gases. Here we explore super and sub-radiance beyond the Dicke limit via a tunable-spacing quantum gas microscope of erbium atoms. Our tightly spaced 266nm optical lattice, along with erbium's narrow 841nm transition, results in a favorable spacing-to-wavelength ratio for observing collective emission. We measure super and sub-radiance by tracking the excited state population of atoms undergoing decay and observe that super-radiance scales with system size in systems much larger than the light's native 841nm length scale. Sweeping the spacing-to-wavelength ratio reveals geometric resonances that result in revivals of super-radiance. Our microscope's single-site resolution reveals ferromagnetic spatial correlations through super-radiant emission and antiferromagnetic correlations in deeply sub-radiant regimes. Unlike in all-to-all interacting systems that are restricted to the Dicke manifold, our system moves throughout the angular momentum manifold as it decays. We measure the magnetization in our experiment to track the dynamics of this decay and map out the trajectory of finite-inversion preparations through the Hilbert space. This work paves the way for future work in studying cooperative effects in ordered atomic arrays with applications in engineering photonic states for quantum communication and dissapative generation of exotic quantum states.