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Communications in Theoretical Physics

Atomic Interference Method for Direct Measurement of the Wigner Function of a Cavity Field

Zheng Shi-Biao

Published Aug 15, 2001• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/36/2/213

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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.
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.
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.
A scheme is proposed for the reconstruction of two-mode entangled states in cavity QED and ion traps. For a two-mode field we show that the Wigner function can be obtained by measuring the probability of a two-level atom being in ground states after resonant interaction with two classical fields and dispersive interaction with the two-mode cavity field displaced by resonant sources. For the two-dimensional motion of a trapped ion the Wigner function is obtained by measuring the probability of the ion in its ground electronic state after displacing the ion motion and then resonantly exciting the ion.
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.