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

## TL;DR

This paper introduces two new two-mode generalizations of the Jaynes-Cummings model, analyzing their properties, energy spectra, and eigenfunctions, and connecting them to relativistic quantum systems.

## Contribution

It presents novel two-mode JC and AJC models, deriving their spectra and linking them to relativistic quantum systems, expanding the theoretical framework.

## Key findings

- Derived energy spectra and eigenfunctions for the new models
- Connected the models to relativistic parametric amplification
- Linked the models to coupled relativistic oscillators

## 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.