How single-photon nonlinearity is quenched with multiple quantum emitters: Quantum Zeno effect in collective interactions with $\Lambda$-level atoms

Single-photon nonlinearity, namely the change in the response of the system as the result of the interaction with a single photon, is generally considered an inherent property of a single quantum emitter. Understanding the dependence of the nonlinearity on the number of emitters is important both fundamentally and practically, as strong light-matter coupling is more readily achieved through collective interactions than with a single emitter. Here, we theoretically consider a system that explores the transition from a single to multiple emitters with a $\Lambda$-level scheme. We show that the single-photon nonlinearity indeed vanishes with the number of emitters. Interestingly, the mechanism behind this behavior is the quantum Zeno effect, manifested in the slowdown of the photon-controlled dynamics.