Proposal for direct measurement of the Wigner function of a weak cavity field around the origin using resonant atoms

Abstract

We propose a scheme for the direct measurement of the Wigner function of a cavity field with no more than three photons around the origin. In the scheme the cavity field is first displaced by a small amount. Then a two-level atom is sent through the cavity. After a resonant interaction time the difference between the probabilities of the atom being in the ground and excited states is directly related to the Wigner function for the field state. The scheme can also be used for conditional generation of four-photon and six-photon states using two and three resonant atoms, respectively.