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Journal of Chengdu University of Information Technology

Solution to super-Jaynes-Cummings model using invariant method

Yu Wan‐Lun

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Since the super-Jaynes-Cummings(SJC) model possesses a super symmetricstructure aninvariant can be constructedfromthe super-symmetric generators by work-inginthe subspace with particular eigenvalues of the conserved super-symmetric genera-tor N.Therefore based on the invariant theory the eigenspectrum,the eigenstates andthe ti me-evolving operator for the SJC model with the Grassman valued coupling con-stant can be easily derived.

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Since the super-Jaynes-Cummings(SJC) model possesses a super symmetricstructure aninvariant can be constructedfromthe super-symmetric generators by work-inginthe subspace with particular eigenvalues of the conserved super-symmetric genera-tor N.Therefore based on the invariant theory the eigenspectrum,the eigenstates andthe ti me-evolving operator for the SJC model with the Grassman valued coupling con-stant can be easily derived.
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