Proposal for Direct Measurement of the Wigner Function of a Cavity Field via Raman Coupling

We propose a scheme for the reconstruction of a cavity field state. In the scheme the cavity field is first displaced by a microwave source, and then couples with a three-level A-type atom in a Raman manner. After an appropriate interaction time the measurement of the difference between the probabilities of the atom being in two ground states directly yields the Wigner function for the field state. The scheme can be easily generalized to measure the Wigner function of an entangled state of two spatially separated single-mode cavities.