Controlling properties of a hybrid Cooper pair box interacting with a nanomechanical resonator in the presence of Kerr nonlinearities and losses

We consider the Jaynes-Cummings model describing the interaction of a Cooper pair box (CPB) and a nanoresonator (NR) in the presence of a Kerr medium and losses The evolution of the entropy of both subsystems and the CPB population inversion were calculated numerically. It is found that these properties increase when the NR frequency is time-dependent, even in the presence of losses; the effect is very sensitive to detuning and disappears in the resonant regime. The roles played by the losses affecting the CPB and the NR are also compared.