Matrix diagonalization and exact solution of the k-photon Jaynes-Cummings model

Abstract

We study and exactly solve the two-photon and k-photon Jaynes-Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the $SU(2)$ group and let us diagonalize the Hamiltonian of these models by properly choosing the coherent state parameters of the transformation. Finally, we explicitly obtain the energy spectrum and eigenfunctions for each model.

arXiv comment12 pages

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Cited by in corpus (4)

• Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry
• A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties
• Berry phase of the Tavis-Cummings model with three modes of oscillation
• Exact solution of the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators