Cavity quantum electrodynamics provide a very powerful way to measure light states with atoms or atoms states with light via quantum non-demolition measurements. We present an experiment where the transmission of a weak probe through a microwave cavity allows to measure the dispersive shift induced by Rydberg atoms. The system is quantitatively described by the dispersive Tavis-Cummings Hamiltonian which describes the coupling of a point-like ensemble of identical two-level atoms to a single resonator mode. We measured the dispersive shift scaling with the number of atoms and the detuning between the cavity resonance and the atomic transition. The dispersive shift measurement provides a non-destructive measurement of the atom number.
This constitutes a first step for our hybrid cavity quantum electrodynamics experiment. Indeed, we aim at coupling Rydberg atoms to superconducting qubits to take advantage of long coherence time and optical transition of the former, and strong coupling constant and scalability of the latter.