Many-Body Amplified Nonclassical Photon Emission in Cavity-Coupled Atomic Arrays

The generation of high-performance nonclassical light remains a cornerstone of quantum technologies, yet faces a fundamental trade-off between emission purity and brightness. Here, we demonstrate that cavity-mediated many-body spin-exchange interactions provide a route to overcome this constraint by collectively amplifying spectral anharmonicity. In a cavity-coupled atomic array with a programmable relative phase $\phi$, the resulting interference-interaction mechanism reshapes the dressed-state manifold and enables deterministic switching between distinct quantum emission regimes. For $\phi=0$, constructive interference yields high-purity single-photon emission with antibunching improved by four orders of magnitude while preserving strong photon flux. Conversely, for $\phi=\pi$, destructive interference creates a dark single-photon manifold, resonantly activating two-photon processes to produce bright and pure photon-pair bundles. Our work establishes interference-engineered many-body interactions as a scalable mechanism for on-demand quantum light generation and open a new avenue for harnessing collective many-body physics in quantum photonics.