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Nondestructive photon counting in waveguide QED

Number-resolving single-photon detectors represent a key technology for a host of quantum optics protocols, but despite significant efforts, state-of-the-art devices are limited to few photons. In contrast, state-dependent atom counting in arrays can be done with extremely high fidelity up to hundreds of atoms. In waveguide QED, the problem of photon counting can be reduced to atom counting, if the photonic state is mapped to an atomic one. We show that this can be achieved by engineering a second decay channel of an excited atom to a metastable state. Our scheme is robust to disorder and finite Purcell factors, and its fidelity increases with atom number. We further show that if the initial atomic state is a symmetric Dicke state, dissipation engineering can be used to implement a nondestructive photon number measurement, in which the incident state is re-emitted into the waveguide unchanged. Our results readily generalize to related platforms, including superconducting qubits.