Efficient mapping and tracking the properties of micromechanical resonators using phase-lock loops with closely-spaced frequencies

Studying the dynamical behavior of micro- and nano-mechanical systems (MEMS and NEMS) is essential in various fields from nonlinear dynamics to quantum technologies. Hence, it is important to be able to precisely monitor the mechanical properties of MEMS and NEMS devices. In this work, we show how to track and spatially map various properties of a mechanical resonator, such as frequency shift, linewidth, and nonlinearity, by aptly choosing three closely-spaced drive frequencies and using phase-locked loops. This technique tracks changes in the system faster and more efficiently, without the need for repeated frequency sweeps of the oscillator response, simply by employing three phase-locked tones.