  The simple resonant Rabi oscillation of a two-level system in a single-mode
coherent field reveals complex features at the mesoscopic scale, with
oscillation collapses and revivals. Using slow circular Rydberg atoms
interacting with a superconducting microwave cavity, we explore this phenomenon
in an unprecedented range of interaction times and photon numbers. We
demonstrate the efficient production of `cat' states, quantum superposition of
coherent components with nearly opposite phases and sizes in the range of few
tens of photons. We measure cuts of their Wigner functions revealing their
quantum coherence and observe their fast decoherence. This experiment opens
promising perspectives for the rapid generation and manipulation of
non-classical states in cavity and circuit Quantum Electrodynamics.
