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Acta Physica Sinica

Reconstructing the Wigner function of cavity fields with the micromaser

Zhi‐Ming Zhang, 上海交通大学物理系，上海 200240

Published Jan 1, 2004• 4 citations
Publisher

Abstract

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.

DOI
10.7498/aps.53.70

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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 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 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 propose a scheme for directly measuring the Wigner functions of cavity fields. The scheme is based on the Raman interaction between atoms and cavity fields. We find a simple and direct relation between the Wigner function and the atomic population difference. By suitably choosing the interaction time, we find that the Wigner function is just two times of the atomic population difference. Thus, one can obtain the Wigner function by measuring the atomic populations and calculating the population difference.
We suggest a quantum state reconstruction scheme. Our proposal is applicable to the field inside a microwave cavity as well as to the harmonic motion of a trapped atom. It will be shown that the inversion of two-level atoms after a resonant interaction with a coherently displaced quantum state is directly related to the Wigner characteristic function of the initial state. This method neither requires the preparation of atoms in a quantum superposition of the upper and lower energy levels nor heavy numerical processing of the measured data. We demonstrate the reconstruction scheme for the example of a Schr\"odinger-cat superposition state.
We suggest an iterative, maximum-likelihood–based, method to reconstruct the photon number distribution of the steady-state cavity field of a micromaser starting from the statistics of the atoms leaving the cavity after the interaction. The scheme is based on measuring the atomic populations of probe atoms for different interaction times and works effectively using a small number of atoms and a limited sampling of the interaction times. The method has been tested by numerically simulated experiments showing that it may be reliably used in any micromaser regime, leading to high-fidelity reconstructions for single-peaked distributions as well as for double-peaked ones and for trapping states.