We study theoretically a radio frequency superconducting interference device integrated with a nanomechanical resonator and an LC resonator. 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.
Buks, E.; Segev, E.; Zaitsev, S.; Abdo, B.; and Blencowe, M. P., "Quantum Nondemolition Measurement of Discrete Fock States of a Nanomechanical Resonator" (2008). Open Dartmouth: Faculty Open Access Articles. 840.