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Acta Physica Sinica

EXACT SOLUTION OF JAYNES-CUMMINGS MODEL UNDER ROTATIONLESS WAVE APPROXIMATION USING-COHERENT-STATE REPRESENTATION

FANG XI-MING, Feng Mang, SHI LEI, Kelin Gao, Xiwen Zhu, 中国科学院武汉物理与数学研究所波谱与原子分子物理国家重点实验室

Published Jan 1, 1997• 0 citations
Publisher

Abstract

In this paper, a new approach of exact solution of Jaynes-Cummings model under rotationless wave approximation is proposed. The Jaynes-Cummings models of two-level system and three-level system have been investigated. Compared to some other approximate approaches, this approach can give not only an analytic exact solution, which agrees with others results but also a restraint condition, which is usefull for practical experiment.

DOI
10.7498/aps.46.2160

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In this paper, a new approach of exact solution of Jaynes-Cummings model under rotationless wave approximation is proposed. The Jaynes-Cummings models of two-level system and three-level system have been investigated. Compared to some other approximate approaches, this approach can give not only an analytic exact solution, which agrees with others results but also a restraint condition, which is usefull for practical experiment.
An accurate method to solve the Jaynes—Cummings (J—C) Hamiltonian has been investigated here. The phenomenon of atomic collapse and revival predicted by Jaynes—Cummings model is demonstrated. Solutions are consistent with the precious such as using the operator method. Furthermore, the Jaynes—Cummings Hamiltonian including the anti-rotating term is also solved precisely using this accurate way so that results agree with experiments better. Essences of the anti-rotating term are revealed. We discuss the relations of the phenomenon of atomic collapse and revival with the average photons number, the light field phase angle, the resonant frequency, and the size of coupling constant. The discussions may make one select suitable conditions to carry out experiment well and study the virtual light field effect on cavity quantum electrodynamics.
By utilizing the property of the supersymmetric structure in the two-level multiphoton Jaynes-Cummings model, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators. We obtain the exact solutions of the time-dependent Schrödinger equation which describes the time-dependent supersymmetric two-level three-photon Jaynes-Cummings model (TLTJCM) by using the invariant-related unitary transformation formulation. The case under the adiabatic approximation is also discussed. Keywords: Supersymmetric Jaynes-Cummings model; exact solutions; invariant theory; geometric phase factor; adiabatic approximation