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[Submitted on 19 Oct 2022]

Overview: Rydberg arrays fuse the collective behavior of ordered atomic arrangements with the controllability and optical nonlinearity of Rydberg systems, yielding a powerful platform for realizing photonic many-body physics. As an application of this platform, we propose a protocol for quantum non-destructive (QND) photon counting. Our protocol includes photon storage in the Rydberg array, an observation phase consisting of a series of Rabi flops to Rydberg states and measurements, and retrieval of stored photons. Rabi frequencies experience a collective enhancement of $\sqrt{n}$. where $n$ is the number of photons stored in the array. Projectively measuring the presence or absence of Rydberg excitation after some oscillations is therefore a weak measure of the photon number. We show that photon-counting protocols can be used to extract Fock states from arbitrary pure or mixed initial states and perform photonic state identification. Experimentally confirm that the protocol works even in the presence of realistic noise.