Kinetic inductive mechano-electric transduction for nano-scale force sensing

We use the principles of cavity opto-mechanics to design a resonant mechanical force sensor for atomic force microscopy. The sensor is based on a new type of electro-mechanical coupling, dual to traditional capacitive coupling, whereby the motion of a cantilever induces surface strain that causes a change in the kinetic inductance of a superconducting nanowire. The cavity is realized by a compact microwave plasma mode with an equivalent LC circuit involving the nanowire's kinetic inductance. The device is fully co-planar and we show how to transform the cavity impedance for optimal coupling to the transmission line and readout circuit. For the device presented here, we estimate the bare Kinetic Inductive Mechano-Electric Coupling (KIMEC) rate $g_0/2\pi$ in the range 3 Hz to 10 Hz. We demonstrate phase-sensitive detection of cantilever motion using a multifrequency pumping and measurement scheme.