Quantum information in cavity quantum electrodynamics: logical gates, entanglement engineering and ‘Schrödinger–cat states’

Abstract
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.