Dispersive readout of a high-Q encapsulated micromechanical resonator

TL;DR

This paper demonstrates a room-temperature dispersive microwave readout method for encapsulated bulk micromechanical resonators, achieving improved displacement sensitivity and enabling future cryogenic thermomechanical noise studies.

Contribution

The authors introduce a dispersive coupling technique for high-Q encapsulated micromechanical resonators using standard components, enhancing displacement measurement resolution.

Findings

Achieved a displacement resolution of 522 fm/√Hz.

Demonstrated room-temperature operation with commercially available components.

Enabled potential for cryogenic thermomechanical noise characterization.

Abstract

Encapsulated bulk mode microresonators in the megahertz range are used in commercial timekeeping and sensing applications but their performance is limited by the current state of the art of readout methods. We demonstrate a readout using dispersive coupling between a high-Q encapsulated bulk mode micromechanical resonator and a lumped element microwave resonator that is implemented with commercially available components and standard printed circuit board fabrication methods and operates at room temperature and pressure. A frequency domain measurement of the microwave readout system yields a displacement resolution of $522 \, \mathrm{fm/\sqrt{Hz}}$, which demonstrates an improvement over the state of the art of displacement measurement in bulk-mode encapsulated microresonators. This approach can be readily implemented in cryogenic measurements, allowing for future work characterizing the thermomechanical noise of encapsulated bulk mode resonators at cryogenic temperatures.