In this paper, we derive a f-deformed Hamiltonian for the anti-Jaynes-Cummings (AJC) model, using a trapped ion technology. We show that f-deformed Dirac oscillator is a mathematical description of the anti-Jaynes-Cummings model in a nonlinear Kerr-like medium. We prove that one can simulate the Zitterbewegung effect in the f-deformed version of the anti-Jaynes-Cummings model. We also study the non-relativistic limit of the f-deformed Dirac oscillator and interpret the Zitterbewegung effect in this limit with quantum optic interferometers.
