Measuring Entanglement between Two Cavities Quantum Electrodynamics

We propose a new experimental setup of the Mach-Zendher interferometer for the three levels Rydberg atoms. The three levels Rydberg atomic systems are interacted with two entangled cavities quantum electrodynamics. In our proposal the state of incoming atoms and entangled cavities (C1 and C2) are denoted by |g> and a |0, 1> + b |1, 0>, respectively. The amount of entanglement is measured by the imaginary parameters a, b. We have |a|=|b|=1/√2 for maximum entanglement, a = 1, b = 0 (or a = 0, b = 1) for no entanglement and otherwise partially entanglement states. One of the cavities is placed in clockwise path of interferometer and the other one is placed in counter-clockwise path. In each path two cavities are sandwiching Ci (i = 1, 2) that Ri (i = 1, 2 or i = 3, 4) are identical low Q cavities. In this case, the Rydberg atoms interact classically with the resonance cavities Ri and quantum mechanically with the out of resonance cavities Ci. For a specific phase difference in Ri cavities, the entangled parameters are involved in the outgoing state of atom. It is shown that the measurement of the state of individual outgoing atoms give us the entanglement parameters a, b as well as the phase difference between two paths. Furthermore, the result is given in terms of the value of the Wigner function at the origin.