Measuring the Wigner Functions of Two-Mode Cavity Fields and Testing the Bell’s Inequalities

We propose a scheme for measuring the Wigner function of a two mode cavity field. The scheme bases on the interaction between the two-mode cavity field and three-level atoms. We find a simple relation between the Wigner function and the atomic population. One can obtain the Wigner function by measuring the atomic population with a micromaser-like experiment and doing a numerical integral. By using the two-mode Wigner function one can obtain the Clauser--Horne combination and test the Bell's inequalities. We test our equations with a two-mode entanglement state and the results are rather good.