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

摘要

We introduce two generalizations of the Jaynes-Cummings (JC) model for twomodes of oscillation. The first model is formed by two Jaynes-Cummingsinteractions, while the second model is written as a simultaneousJaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some ofits properties and obtain the energy spectrum and eigenfunctions of thesemodels by using the tilting transformation and the Perelomov number coherentstates of the two-dimensional harmonic oscillator. Moreover, as physicalapplications, we connect these new models with two important and noveltyproblems: The relativistic non-degenerate parametric amplifier and therelativistic problem of two coupled oscillators.