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 theentropy 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.
We employ a more realistic treatment to investigate the entropy and the excitation-inversion of a coupled system that consists of a nanomechanical resonator and a superconducting Cooperpair box. The procedure uses the Buck-Sukumar model in the microwave domain, considers the nanoresonator with a time dependent frequency and both subsystems in the presence of losses. Interesting results were found for the temporal evolutions of the entropy of each subsystem and of the excitation-inversion in the Cooper pair box. A comparison was also performed about which of these two subsystems is more sensitive to the presence of losses. The results suggest that appropriate choices of the involved time dependent parameters allow us to monitor these two features of the subsystems and may offer potential applications, e.g., in the generation of nonclassical states, quantum communication, quantum lithography.