  We propose a scheme for generating squeezed states in solid state circuits
consisting of a nanomechanical resonator (NMR), a superconducting Cooper-pair
box (CPB) and a superconducting transmission line resonator (STLR). The
nonlinear interaction between the NMR and the STLR can be implemented by
setting the external biased flux of the CPB at certain values. The interaction
Hamiltonian between the NMR and the STLR is derived by performing Fr$\rm\ddot
o$hlich transformation on the total Hamiltonian of the combined system. Just by
adiabatically keeping the CPB at the ground state, we get the standard
parametric down-conversion Hamiltonian. The CPB plays the role of ``nonlinear
media", and the squeezed states of the NMR can be easily generated in a manner
similar to the three-wave mixing in quantum optics. This is the three-wave
mixing in a solid-state circuit.
