Abstract: In this paper, we introduce a flexible model for the control and measurement of NAMRs (nanomechanical resonators). We obtain the free Hamiltonian of the dc-SQUID (direct current superconducting quantum interference device) and the interaction Hamiltonian between these two NAMRs and the dc-SQUID by introducing the annihilation and creation operators under the rotating wave approximation. We can treat the mode of the dc-SQUID as a classical field. In the Heisenberg picture, the generation of two-mode squeezed states of two nanomechanical resonators is shown by their collective coordinate and momentum operators.

Key words: squeezed state, two-mode, mechanical resonator