Femtometer-amplitude imaging of coherent super high frequency vibrations in micromechanical resonators

Lei Shao; Vikrant J Gokhale; Bo Peng; Penghui Song; Jingjie Cheng; Justin Kuo; Amit Lal; Wen-Ming Zhang; Jason J Gorman

doi:10.1038/s41467-022-28223-w

Femtometer-amplitude imaging of coherent super high frequency vibrations in micromechanical resonators

Nat Commun. 2022 Feb 4;13(1):694. doi: 10.1038/s41467-022-28223-w.

Authors

Lei Shao^{1

2}, Vikrant J Gokhale^{3

4}, Bo Peng^{5

6}, Penghui Song^{5

6}, Jingjie Cheng⁷, Justin Kuo⁸, Amit Lal⁸, Wen-Ming Zhang^{5

6}, Jason J Gorman⁹

Affiliations

¹ National Institute of Standards and Technology, Gaithersburg, MD, USA. lei.shao@sjtu.edu.cn.
² University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, China. lei.shao@sjtu.edu.cn.
³ National Institute of Standards and Technology, Gaithersburg, MD, USA.
⁴ U.S. Naval Research Laboratory, Washington, DC, USA.
⁵ School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China.
⁶ State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, China.
⁷ University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, China.
⁸ School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA.
⁹ National Institute of Standards and Technology, Gaithersburg, MD, USA. gorman@nist.gov.

Abstract

Dynamic measurement of femtometer-displacement vibrations in mechanical resonators at microwave frequencies is critical for a number of emerging high-impact technologies including 5G wireless communications and quantum state generation, storage, and transfer. However, the resolution of continuous-wave laser interferometry, the method most commonly used for imaging vibration wavefields, has been limited to vibration amplitudes just below a picometer at several gigahertz. This is insufficient for these technologies since vibration amplitudes precipitously decrease for increasing frequency. Here we present a stroboscopic optical sampling approach for the transduction of coherent super high frequency vibrations. Phase-sensitive absolute displacement detection with a noise floor of 55 fm/√Hz for frequencies up to 12 GHz is demonstrated, achieving higher bandwidth and significantly lower noise floor simultaneously compared to previous work. An acoustic microresonator with resonances above 10 GHz and displacements smaller than 70 fm is measured using the presented method to reveal complex mode superposition, dispersion, and anisotropic propagation.