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 “Schrödinger-cat” state. The method employs the Jaynes–Cummings model with damping, with different decay rates of the Cooper pair box and different ranges of detuning, going from resonant to off-resonant cases, 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 the literature. With respect to the Cooper pair box excitation inversion, while the presence of detuning destroys the collapses and revivals, it is shown that convenient time dependent detunings recover such effects in a nice way.