# Efficient Mapping and Tracking the Properties of Micromechanical Resonators Using Phase-Lock Loops with Closely-Spaced Frequencies

## TL;DR

This paper introduces a fast and efficient method to track and map the properties of tiny mechanical resonators using phase-locked loops with closely spaced frequencies.

## Contribution

The novel approach uses three phase-locked tones to monitor mechanical properties without repeated frequency sweeps.

## Key findings

- The method enables rapid tracking of frequency shift, linewidth, and nonlinearity in mechanical resonators.
- It eliminates the need for traditional frequency sweeps, improving efficiency in monitoring MEMS and NEMS devices.
- The technique allows spatial mapping of resonator properties using closely spaced drive frequencies.

## Abstract

Studying the dynamical behavior of micro- and nano-mechanical systems (MEMSs and NEMSs) is essential in various fields from nonlinear dynamics to quantum technologies. Hence, it is important 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 appropriately selecting three closely spaced drive frequencies and using phase-locked loops. This technique tracks changes in the system quickly and efficiently, without the need for repeated frequency sweeps of the oscillator response, simply by employing three phase-locked tones.