Quantum optics in different representations of the algebra of canonical commutation relations (I): Unexpected properties of Rabi oscillations -- theory and experiment

We discuss the Jaynes-Cummings model in different representations of the algebra of canonical commutation relations. The first conclusion is that all the irreducible representations lead to equivalent physical predictions. However, the reducible representation recently introduced as a candidate for `QED without infinities' leads to new effects. We analyze from this perspective the experiments on Rabi oscillations performed by the Kastler-Brossel Laboratory group from Paris. Surprisingly, the results seem to support the reducible representation approach. We also discuss possibilities of more definitive tests of the new formalism.