Nanomechanical parametric amplification and oscillation via electrostatic coupling to Cooper-pair box

Nanomechanical resonator coupled to a Cooper-pair box exhibits frequency modulation as a function of the gate voltage when the qubit is adiabatically tuned. We utilize this effect to demonstrate mechanical degenerate parametric amplification and oscillation. Gain above 30dB and self-oscillation is observed. This technique would provide an efficient way to enhance the force sensitivity in the measurement of coupled dynamics of nanomechanical resonanator modes and a solid state qubit.