Superconducting inductive displacement detection of a microcantilever

We demonstrate a superconducting inductive technique to measure the displacement of a micromechanical resonator. In our scheme, a type I superconducting microsphere is attached to the free end of a microcantilever and approached to the loop of a dc Superconducting Quantum Interference Device (SQUID) microsusceptometer. A local magnetic field as low as 100 $\mu$T, generated by a field coil concentric to the SQUID, enables detection of the cantilever thermomechanical noise at $4.2$ K. The magnetomechanical coupling and the magnetic spring are in good agreement with image method calculations assuming pure Meissner effect. These measurements are relevant to recent proposals of quantum magnetomechanics experiments based on levitating superconducting microparticles.