Controlling Statistical Properties of a Cooper Pair Box Interacting with a Nanomechanical Resonator

We investigate the quantum entropy, its power spectrum, and the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator, the first initially prepared in its excited state, the second prepared in a "cat"-state. The method uses the Jaynes-Cummings model with damping, with different decay rates of the Cooper pair box and distinct detuning conditions, including time dependent detunings. Concerning the entropy, it is found that the time dependent detuning turns the entanglement more stable in comparison with previous results in literature. With respect to the Cooper pair box excitation inversion, while the presence of detuning destroys the its collapses and revivals, it is shown that with a convenient time dependent detuning one recovers such events in a nice way.