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Acta Physica Sinica

ANALYTIC SOLUTIONS FOR COHERENT THREE-LEVEL J-C MODEL

Xiao-shen Li, Yue-nan Peng, (1)江西师范大学物理系; (2)南京大学物理系

Published Jan 1, 1986• 0 citations
Publisher

Abstract

The interaction of a three-level atom initially in the common upper state with two initially coherent fields is investigated. Approximate analytic solutions for mean atomic level occupations and photon numbers are given, which exhibit collapse, revival and initial oscillation period explicitly. These are compared with the results of numerical, calculation, they agree satifactorily.

DOI
10.7498/aps.35.115

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Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
The interaction of a three-level atom initially in the common upper state with two initially coherent fields is investigated. Approximate analytic solutions for mean atomic level occupations and photon numbers are given, which exhibit collapse, revival and initial oscillation period explicitly. These are compared with the results of numerical, calculation, they agree satifactorily.
The quantum-statistical model for a three-level atom interacting with two radiation fields is studied. The mean atomic occupations and photon numbers are obtained under different initial conditions of one coherent field and one chaotic field or both chaotic or coherent fields, with the atom in upper or lower states. Through numerical summation, it is shown that the effects of coherent sources and chaotic sources are different even for low intensities. Meanwhile the effects of detuning on this interaction are discussed.
Recent interest in the collapse and revival of Rabi oscillations in the Jaynes-Cummings model was stimulated by a paper in 1980 by Eberly et al.1 These authors presented an analytic expression for the inversion of a two-level atom interacting with a single mode of the radiation field taken to be initially in a coherent state. Their analytic expression agreed well with a numerical evaluation of the standard summation formula for the inversion. Since the publication of this analytic result various discussions of its proof have appeared. Existing versions of the proof all convert the summation formula into an integral and evaluate this integral using the method of stationary phase.2 This approach is mathematically intricate and leaves one with little physical intuition for the approximations that are made. I offer an alternative proof, which, in compact form, takes only a few lines. The proof is built up in a series of approximations based on an expansion of the troublesome square root (n) in the Jaynes-Cummings summation formula in a Taylor series about the mean photon number: n=n¯[1+12n−n¯n¯−18(n−n¯n¯)2+…]. The analytical expression of Eberly ef al. is recovered using standard sums and integrals and this Taylor expansion to second order.