Nobel Lecture: Controlling photons in a box and exploring the quantum to classical boundary

Microwave photons trapped in a superconducting cavity constitute an ideal system to realize some of the thought experiments imagined by the founding fathers of quantum physics. The interaction of these trapped photons with Rydberg atoms crossing the cavity illustrates fundamental aspects of measurement theory. The experiments performed with this ``photon box'' at Ecole Normale Sup\'erieure (ENS) belong to the domain of quantum optics called ``cavity quantum electrodynamics.'' We have realized the nondestructive counting of photons, the recording of field quantum jumps, the preparation and reconstruction of ``Schr\"odinger cat'' states of radiation and the study of their decoherence, which provides a striking…