Nonlinear exceptional points boost phase-shift sensing in silicon micromechanical resonators
Phys. Rev. Applied 25, 034039 – Published 11 March, 2026
DOI: https://doi.org/10.1103/qwql-lbqw
Abstract
Sensors based on silicon micromechanical resonators play an important part in many aspects of daily life, such as motion sensors in mobile phones and navigation sensors in automobiles. Traditionally, a very small perturbation of the resonators induces a linear frequency shift with a scaling factor of about 0.5. Recently, an exceptional point that occurs in parity-time (PT)-symmetric systems featuring gain and loss has been utilized to amplify the response of the systems to perturbation. However, the frequency shift related to the perturbation displays a scaling factor considerably less than 1, which somewhat offsets the square-root singularity of the response in systems with linear gain, and the cube-root singularity of the response in systems with nonlinear gain. Meanwhile, asymmetric perturbations in systems with linear gain result in a spectrum broadening, while systems with nonlinear gain exhibit a reduced dynamic range of measurements. Here we theoretically and experimentally show that the phase difference between loss and gain resonators in PT-symmetric silicon micromechanical resonators with nonlinear gain follows a cube-root dependence on perturbation over a broad range of measurements, with a scaling factor substantially greater than 1. By using voltage-induced perturbations in PT-symmetric silicon micromechanical resonators with nonlinear gain, we demonstrate that the sensitivity, as characterized by the phase difference, is amplified by several orders of magnitude compared with that defined by the frequency shift. These findings set the stage for the development of highly sensitive silicon resonant sensors.
