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

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

doi:10.1038/s41467-022-28223-w

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.

Highlights

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
Acoustic resonators operating in the super high frequency range are being aggressively pursued for quantum information, where they are used for quantum state generation[3,4], as well as state transfer and entanglement between qubits[5]
There are a number of challenges in operating these interferometers in the super high frequency range, including electromagnetic interference (EMI) from external microwave communications signals, strong cross-coupling between excitation and measurement signals, and high signal attenuation in cables

Summary

Introduction

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. The most widely used approach for measuring vibrations in micromechanical resonators is optical scanning interferometry with a continuous-wave (CW) laser, which provides noncontact, high-resolution, phase-sensitive mapping of the vibration profile[12,13,14,15,16,17,18,19,20] This has included homodyne[12,13,14,15] and heterodyne[16,17,18,19,20] configurations using different interferometer geometries, such as Michelson[12,13,16,17,18,19,20], Mach–Zehnder[14], and Sagnac[15], and have been used to characterize the frequency responses and mode shapes of radio frequency (RF) resonators under coherent sinusoidal excitation. Other issues with pumpprobe measurements include high pump power, high probe power, and long measurement times due to the use of a scanning delay-line to capture the dynamic response

Methods

Results

Conclusion