Higher-order singularities in phase-tracked electromechanical oscillators

Xin Zhou (), Xingjing Ren, Dingbang Xiao, Jianqi Zhang, Ran Huang, Zhipeng Li, Xiaopeng Sun, Xuezhong Wu (), Cheng-Wei Qiu, Franco Nori () and Hui Jing ()
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Xin Zhou: College of Intelligence Science and Technology, NUDT
Xingjing Ren: College of Intelligence Science and Technology, NUDT
Dingbang Xiao: College of Intelligence Science and Technology, NUDT
Jianqi Zhang: Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences
Ran Huang: Cluster for Pioneering Research, RIKEN
Zhipeng Li: National University of Singapore
Xiaopeng Sun: College of Intelligence Science and Technology, NUDT
Xuezhong Wu: College of Intelligence Science and Technology, NUDT
Cheng-Wei Qiu: National University of Singapore
Franco Nori: Cluster for Pioneering Research, RIKEN
Hui Jing: Hunan Normal University

Nature Communications, 2023, vol. 14, issue 1, 1-9

Abstract: Abstract Singularities ubiquitously exist in different fields and play a pivotal role in probing the fundamental laws of physics and developing highly sensitive sensors. Nevertheless, achieving higher-order (≥3) singularities, which exhibit superior performance, typically necessitates meticulous tuning of multiple (≥3) coupled degrees of freedom or additional introduction of nonlinear potential energies. Here we propose theoretically and confirm using mechanics experiments, the existence of an unexplored cusp singularity in the phase-tracked (PhT) steady states of a pair of coherently coupled mechanical modes without the need for multiple (≥3) coupled modes or nonlinear potential energies. By manipulating the PhT singularities in an electrostatically tunable micromechanical system, we demonstrate an enhanced cubic-root response to frequency perturbations. This study introduces a new phase-tracking method for studying interacting systems and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with potential applications in precision metrology, portable nonreciprocal devices, and on-chip mechanical computing.

Date: 2023
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DOI: 10.1038/s41467-023-43708-y

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