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. Although the dependence on the number of emitters is well understood for the case of two-level systems, deterministic operations such as single-photon switching or photon-atom gates inherently require more complex level structures. Here, we theoretically consider single-photon switching in ensembles of emitters with a Λ-level scheme and show that the switching efficiency vanishes with the number of emitters. Interestingly, the mechanism behind this behavior is the quantum Zeno effect, manifested in a slowdown of the photon-controlled dynamics of the atomic ground states.
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