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

Strong squeezing and robust entanglement in cavity electromechanics