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

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