Quantum information in cavity quantum electrodynamics: logical gates, entanglement engineering and 'Schrödinger-cat states'.

In cavity-quantum-electrodynamics experiments, two-level Rydberg atoms and single-photon microwave fields can be seen as qubits. Quantum gates based on resonant and dispersive atom-field effects have been realized, which implement various kinds of conditional dynamics between these qubits. We have also studied the interaction between a single atom and coherent fields stored in the cavity. By progressively increasing the number of photons in these fields, we have explored various aspects of the quantum-classical boundary. We have realized a complementarity experiment demonstrating the continuous evolution of an apparatus from a quantum to a classical behaviour. We have also prepared 'Schrödinger-cat'-like states of the field made of a few photons, and observed their decoherence. We present a brief review of these experiments along with a proposal to study larger systems, i.e. coherent fields with more photons. Fundamental limits to the size of mesoscopic superpositions of field states in a cavity will be briefly discussed.