  We study theoretically a radio frequency superconducting interference device
integrated with both a nanomechanical resonator and an LC one. By applying
adiabatic and rotating wave approximations, we obtain an effective Hamiltonian
that governs the dynamics of the mechanical and LC resonators. Nonlinear terms
in this Hamiltonian can be exploited for performing a quantum nondemolition
measurement of Fock states of the nanomechanical resonator. We address the
feasibility of experimental implementation and show that the nonlinear coupling
can be made sufficiently strong to allow the detection of discrete mechanical
Fock states.
