Abstract : We observe that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-Q cavity. The field is split into two components whose phases differ by an angle inversely proportional to the square root of the average photon number. The field and the atomic dipole are phase-entangled. These manifestations of photon graininess vanish at the classical limit. This experiment opens the way to studies of large Schrödinger cat states at the quantum-classical boundary.