  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.
