Quantum Nondemolition Measurement of Discrete Fock States of a   Nanomechanical Resonator
  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. 
Eyal Buks, Eran Arbel-Segev, Stav Zaitsev, Baleegh Abdo and M. P.   Blencowe