Quantum-state measurement of two-mode entangled field-state in a high-Q cavity

We propose a scheme for the measurement of a two-mode entangled field-state in a high-Q cavity. The scheme utilizes the momentum distribution spectrum in the Raman-Nath regime of a three-level atom in V configuration. Due to the two modes of the electromagnetic field the atom may have x interactions with mode A, and y interactions with mode B, causing a complex momentum distribution. The momentum distribution of the atom after interaction with the quantized cavity fields contains the information of the field photon statistics. We reconstruct the joint photon statistics of the entangled field with the help of recorded momentum spectrum. We also propose to reconstruct the Wigner function of a two-mode entangled field state by injecting two coherent states resonant to each mode into the cavity and then measuring the joint photon statistics of the displaced field.