Quantum Entropic Dynamics of a Trapped Ion in a Standing Wave

By performing a unitary transformation, we transform the Hamiltonian of the trapped ion in any position of standing wave to that of the normal Jaynes-Cummings model in ionic bare basis and we obtain a general evolution operator of the trapped ion system. We study the quantum entropic dynamics of the phonons and trapped ion.Our results show that, when the trapped ion is located at the node of standing wave, the quantum entropic dynamics of phonons and trapped ion are the same as the one of the field in the Jaynes-Cummings model. When the trapped ion deviates from the node of standing wave, the entropies of the phonons and ion keep their maximum value except at the initial stage, and the phonons and trapped ion become extremely entangled.