Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models

Abstract

We introduce two generalizations of the Jaynes-Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes-Cummings interactions, while the second model is written as a simultaneous Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novelty problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.

16 pages

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• Matrix diagonalization and exact solution of the k-photon Jaynes-Cummings model
• Algebraic approach to the Tavis-Cummings model with three modes of oscillation
• Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry
• $Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry
• Modular Operators and Entanglement in Supersymmetric Quantum Mechanics
• 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