Multiplexed photon number measurement of a cavity using the fluorescence of a coupled qubit.*

Measuring the photon number of an electromagnetic mode in a quantum nondemolition manner is instrumental to control the quantum state of a cavity, detect photon emission or measure work. In the microwave domain it can be done using the dispersive coupling between the cavity of interest and a coupled Rydberg atom or superconducting circuit. This method has been used successfully to count up to about a dozen photons, to realize Quantum Zeno dynamics experiments, or count photon number parity. Yet this technique has constraints on the measurement time. In particular it increases with the maximal number of photons. In this contribution, we present a technique that avoids this constraint by using the resonant fluorescence of a qubit coupled to the resonator of interest and a multiplexing measurement of the fluorescence field. We show an experiment where an independent quantum state tomography can be performed on the resonator to compare the result of the conventional method to this new technique.