Super-rolloff electron tunneling transduction of nanomechanical motion using frequency downmixing

Electron tunneling transduction has high sensitivity for detecting the motion of nanomechanical devices, but the relatively low detection bandwidth of a few 10's of kHz has limited its development. Here we demonstrate a novel downmixing transduction scheme which eliminates the detection bandwidth problem of electron tunneling transduction. With this technique, the high frequency vibration modes ($\sim $ 1 MHz) of a MEMS doubly clamped beam are measured. This measurement is 2 orders of magnitude above the electronic bandwidth of our readout circuitry with no fundamental limitation anticipated up to microwave frequencies. The displacement sensitivity is 40 fm/Hz$^{1/2}$ comparable to state-of-the-art low finesse free-space optical interferometry. The back-action force induced by the STM tip on the MEMS device is also explored and is shown to have a small effect on the measurement resonance frequency, causing slight resonance frequency shifts of order 1{\%}.