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

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.