High precision displacement sensing of monolithic piezoelectric disk resonators using a single-electron transistor

TL;DR

This paper demonstrates ultra-sensitive displacement detection of quartz disk resonators using a single-electron transistor, achieving measurements below 1E-13 meters and approaching quantum-limited sensitivity.

Contribution

It introduces the use of RF-SETs for detecting shear-mode oscillations in piezoelectric resonators with unprecedented sensitivity.

Findings

RF-SET provides highest sensitivity among methods tested

Displacement amplitudes below 1E-13 meters measured

Potential to reach quantum-limited detection of mechanical vibrations

Abstract

A single-electron transistor (SET) can be used as an extremely sensitive charge detector. Mechanical displacements can be converted into charge, and hence, SETs can become sensitive detectors of mechanical oscillations. For studying small-energy oscillations, an important approach to realize the mechanical resonators is to use piezoelectric materials. Besides coupling to traditional electric circuitry, the strain-generated piezoelectric charge allows for measuring ultrasmall oscillations via SET detection. Here, we explore the usage of SETs to detect the shear-mode oscillations of a 6-mm-diameter quartz disk resonator with a resonance frequency around 9 MHz. We measure the mechanical oscillations using either a conventional DC SET, or use the SET as a homodyne or heterodyne mixer, or finally, as a radio-frequency single-electron transistor (RF-SET). The RF-SET readout is shown to be the most sensitive method, allowing us to measure mechanical displacement amplitudes below 1E-13 m. We conclude that a detection based on a SET offers a potential to reach the sensitivity at the quantum limit of the mechanical vibrations.