Scheme for direct measurement of the Wigner characteristic function in cavity QED

We propose a simple scheme for the reconstruction of the single-mode cavity field by considering the resonant atom-cavity interaction in the presence of a strong classical field. With the aid of the strong classical field, it is easy to realize the displacement operator for the cavity field correlated to the internal state of the atom. It is shown that the measurement of the population of the lower internal state directly yields the Wigner characteristic function of the cavity field.