Reconstruction of non-classical states of light in cavity quantum electrodynamics/Complete reconstruction of non-classical cavity fields states in cavity quantum electrodynamics

Our cavity Quantum Electrodynamics experiment consists of two simple and well controlled systems interacting in the strong coupling regime: two-level atoms and a single mode of the electromagnetic field. The use of superconducting mirrors allows to trap a microwave field in a cavity for times up to a tenth of a second. In order to probe and to manipulate the trapped field, we use Rubidium atoms excited in a circular Rydberg state. They cross one by one the cavity detuned with respect to their transition. The atoms thus behave as small atomic clocks whose rate is affected by the presence of photons inside the mode through the light shift effect. We measure the small modifications of the atomic superposition's phase after the atoms have crossed the cavity by means of a Ramsey interferometry technique, allowing us to count the number of trapped photons. Slightly modifying this method, one can reconstruct the full density matrix of the state. We applied this technique to several non-classical states of the field: Fock states with a well determined number of photons, and Schroedinger's cat states, which are quantum superpositions of two classical fields with different phases. By repeating the reconstruction scheme for several delays after preparation, we are able to record a step-by-step movie of the time evolution of the state. The evolution of the Schroedinger's cat state under the effect of decoherence sheds new light on the problem of quantum measurement and the quantum to classical boundary. (author)