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Modern Physics Letters B

RECONSTRUCTING THE WIGNER FUNCTION OF FIELD-MODES IN TWO SPATIALLY-SEPARATED CAVITIES

Chun-Hua Yuan, Zhi‐Ming Zhang

Published Oct 10, 2004• 1 citation
Publisher

Abstract

We suggest a scheme for reconstructing the Wigner function of two-mode fields. The scheme is based on the interaction between a Λ-type three-level atom and two field-modes in spatially-separated cavities. The two field-modes are displaced with two classical coherent fields and the atom passes through the two cavities successively. We find that there is a simple relation between the Wigner function of the cavity fields and the atomic populations. Therefore, we can reconstruct the Wigner function of cavity fields by measuring the atomic populations in the micromaser experiments.

DOI
10.1142/s0217984904007748

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We suggest a scheme for reconstructing the Wigner function of two-mode fields. The scheme is based on the interaction between a Λ-type three-level atom and two field-modes in spatially-separated cavities. The two field-modes are displaced with two classical coherent fields and the atom passes through the two cavities successively. We find that there is a simple relation between the Wigner function of the cavity fields and the atomic populations. Therefore, we can reconstruct the Wigner function of cavity fields by measuring the atomic populations in the micromaser experiments.
We propose a scheme for the reconstruction of a cavity field state. In the scheme the cavity field is first displaced by a microwave source, and then couples with a three-level Λ-type atom in a Raman manner. After an appropriate interaction time the measurement of the difference between the probabilities of the atom being in two ground states directly yields the Wigner function for the field state. The scheme can be easily generalized to measure the Wigner function of an entangled state of two spatially separated single-mode cavities.
A scheme for reconstructing the Wigner function of cavity fields is proposed, and this scheme can be realized with the micromaser. We find that there is a simple relation between the Wigner function of cavity fields and the atomic populations. Therefore, we can reconstruct the Wigner function of cavity fields by measuring the atomic populations in the micromaser experiments. We test our theory with the one-photon Fock state and the Schr?dinger cat state, and find that the results are rather good.
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.
We suggest a scheme to reconstruct a two-mode entangled state in cavity QED by using the interaction of a V-configuration three-level atom and by driving the cavity field. After the atomic interaction with the cavity fields, the probability of the atom being in its initial ground state is found to be directly related to the two-mode Wigner characteristic function. The Wigner function and the four-dimensional density-matrix elements can be obtained for the two-mode entangled field by simple transformations. We consider both the cases where two entangled modes are prepared in one cavity or in two spatially separated cavities.
We propose a scheme for the reconstruction of a cavity field state. In the scheme the cavity field is first displaced by a microwave source, and then is placed in front of one slit of the two-slit apparatus. Ground state atoms pass through the apparatus, hitting upon the screen far away from the two-slit apparatus. The atom-field interaction is dispersive. The contrast of interference fringes is directly related to the Wigner function for the field state. The scheme can be easily generalized to measure the Wigner function of an entangled state of two spatially separated single-mode cavities.