Controlling Excitations Inversion of a Cooper Pair Box Interacting with a Nanomechanical Resonator

We investigate the action of time dependent detunings upon the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator. The method employs the Jaynes-Cummings model with damping, assuming different decay rates of the Cooper pair box and various fixed and t-dependent detunings. It is shown that while the presence of damping plus constant detunings destroy the collapse/revival effects, convenient choices of time dependent detunings allow one to reconstruct such events in a perfect way. It is also shown that the mean excitation of the nanomechanical resonator is more robust against damping of the Cooper pair box for convenient values of t-dependent detunings.