A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion

TL;DR

This paper generalizes the Jaynes-Cummings model to include relativistic effects, deriving its energy spectrum and eigenfunctions, and applies it to relativistic parametric amplification and quantum simulation of a trapped ion.

Contribution

It introduces a unified framework for the Jaynes-Cummings model incorporating relativistic effects and connects it to practical quantum systems.

Findings

Derived the energy spectrum and eigenfunctions of the generalized model.

Linked the model to relativistic parametric amplification.

Applied the model to simulate a single trapped ion.

Abstract

We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional har- monic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.