We propose a set-up where a classical field interacts via a two-level atom with a quantized field in a resonator. Due to entanglement we can reconstruct all available information about the field by measuring the momentum distribution of the atom.
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.
A method for the reconstruction of photon statistics and even the Wigner function of a quantized cavity field state is proposed. The method is based on the measurement of momentum distribution of two-level atoms in the Raman–Nath regime. Both the cases of resonant and off-resonant atom–field interaction are considered. The Wigner function is reconstructed by displacing the photon statistics of the cavity field. This reconstruction method is straightforward and does not need much mathematical manipulation of experimental data.