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High-Precision Displacement Sensing of Monolithic Piezoelectric Disk Resonators Using a Single-Electron Transistor

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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 \(10^{-13}\) 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.

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Acknowledgements

This work was supported by the Academy of Finland (contract 250280, CoE LTQ, 275245), the European Research Council (615755-CAVITYQPD), the Centre for Quantum Engineering at Aalto University, and the Finnish Cultural Foundation (Central Fund 00160903). The work benefited from the facilities at the OtaNano—Micronova Nanofabrication Center and at the Low Temperature Laboratory.

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Authors and Affiliations

  1. Interdisciplinary Center of Quantum Information, National University of Defense Technology, Changsha, 410073, China

    J. Li

  2. Department of Applied Physics, Aalto University, P.O. Box 15100, 00076, Aalto, Finland

    J. T. Santos & M. A. Sillanpää

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  1. J. Li
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  3. M. A. Sillanpää
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Correspondence to J. Li.

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Li, J., Santos, J.T. & Sillanpää, M.A. High-Precision Displacement Sensing of Monolithic Piezoelectric Disk Resonators Using a Single-Electron Transistor. J Low Temp Phys 191, 316–329 (2018). https://doi.org/10.1007/s10909-018-1862-y

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