Strong squeezing and robust entanglement in cavity electromechanics

We investigate nonlinear effects in an electromechanical system consisting of a superconducting charge qubit coupled to transmission line resonator and a nanomechanical oscillator, which in turn is coupled to another transmission line resonator. The nonlinearities induced by the superconducting qubit and the optomechanical coupling play an important role in creating optomechanical entanglement as well as the squeezing of the transmitted microwave field. We show that strong squeezing of the microwave field and robust optomechanical entanglement can be achieved in the presence of moderate thermal decoherence of the mechanical mode. We also discuss the effect of the coupling of the superconducting qubit to the nanomechanical oscillator on the bistability behaviour of the mean photon number.