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Recent technological advancements have enabled strong light-matterinteraction in highly dissipative cavity-emitter systems. However, in thesesystems, which are well described by the Tavis-Cummings model, the considerableloss rates render the realization of many desirable nonlinear effects, such assaturation and photon blockade, problematic. Here we present another effectoccurring within the Tavis-Cummings model: a nonlinear response of the cavityfor resonant external driving of intermediate strength, which makes use oflarge cavity dissipation rates. In this regime, $(N+1)$-photon processesdominate when the cavity couples to $N$ emitters. We explore and characterizethis effect in detail, and provide a picture of how the effect occurs due todestructive interference between the emitter ensemble and the external drive.We find that a central condition for the observed effect is largecooperativity, i.e., the product of the cavity and emitter decay rates is muchsmaller than the collective cavity-emitter interaction strength squared.Importantly, this condition does not require strong coupling. We also find ananalytical expression for the critical drive strength at which the effectappears. Our results have potential for quantum state engineering, e.g., photonfiltering, and could be used for the characterization of cavity-emitter systemswhere the number of emitters is unknown. In particular, our results open theway for investigations of unique quantum-optics applications in a variety ofplatforms that neither require high-quality cavities nor strong coupling.

Unconventional saturation effects at intermediate drive in a lossy cavity coupled to few emitters