Decoherence, Wigner functions, and the classical limit of quantum mechanics in cavity QED

Recent experiments in cavity QED have allowed the monitoring of the decoherence process, which is at the heart of the quantum theory of measurement and plays an essential role in the classical limit of quantum mechanics. It is shown here that the technique of Ramsey interferometry, central to those experiments, may be used to determine completely the quantum state of an electromagnetic field in a cavity. This new method, which allows the direct measurement of the Wigner function of the field, is a useful tool for probing the quantum-classical transition and, in particular, the decoherence of superpositions of distinguishable coherent states of the electromagnetic field in the cavity. It is also shown that the realization of a controlled-not gate within the framework of cavity QED is a special case of this proposal, and is related to the measurement of the Wigner function of a one-photon state.