Monitoring the energy of a cavity by observing the emission of a repeatedly excited qubit

The number of excitations in a large quantum system (harmonic oscillator or qudit) can be measured in a quantum non demolition manner using a dispersively coupled qubit. It typically requires a series of qubit pulses that encode various binary questions about the photon number. Recently, a method based on the fluorescence measurement of a qubit driven by a train of identical pulses was introduced to track the photon number in a cavity, hence simplifying its monitoring and raising interesting questions about the measurement backaction of this scheme. A first realization with superconducting circuits demonstrated how the average number of photons could be measured in this way. Here we present an experiment that reaches single shot photocounting and number tracking owing to a cavity decay rate 4 orders of magnitude smaller than both the dispersive coupling rate and the qubit emission rate. An innovative notch filter and pogo-pin based galvanic contact makes possible these seemingly incompatible features. The qubit dynamics under the pulse train is characterized. We observe quantum jumps by monitoring the photon number via the qubit fluorescence as photons leave the cavity one at a time. Besides, we extract the measurement rate and induced dephasing rate and compare them to theoretical models. Our method could be applied to quantum error correction protocols on bosonic codes or qudits.