We propose a scheme for generating squeezed states of nanomechanical resonator in a solid state circuit system which consists of a nanomechanical resonator, a superconducting Cooper-pair box, and a superconducting transmission line resonator. The nonlinear interaction between the nanomechanical resonator and superconducting transmission line resonator can be implemented by setting the external biased flux of the Cooper-pair box at some special values. The squeezed states of the nanomechanical resonator can be generated by degenerate three-wave mixing and the Cooper-pair box plays the role of “nonlinear medium” in the squeezing process.
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