Quantitative analysis of the interaction between a dc SQUID and an integrated micromechanical doubly clamped cantilever

We provide simulations to quantitatively describe the interaction between a dc superconducting quantum interference device (SQUID) and an integrated doubly clamped cantilever. The simulations have been performed using the SQUID equations described by the resistively and capacitively shunted junction model coupled to the equation of motion of a damped harmonic oscillator. We have chosen to investigate an existing experimental configuration and have explored the motion of the cantilever configuration and the reaction of the SQUID as a function of the voltage flux $V(Φ)$ characteristics. We clearly observe the Lorentz force back-action interaction and demonstrate how a sharp transition state drives the system into a nonlinear-like regime and modulates the cantilever displacement amplitude, simply by tuning the SQUID parameters.