# Cubic singularities in binary linear electromechanical oscillators

## TL;DR

This paper demonstrates the realization of cubic singularities in a coupled binary electromechanical system without nonlinearities, enabling enhanced response and controllability for advanced sensing and computing applications.

## Contribution

It introduces a novel method to achieve cubic singularities through phase tomography in a linear coupled system, avoiding complex nonlinear tuning.

## Key findings

- Realization of cubic singularities in a linear system
- Enhanced cubic-root response to frequency perturbations
- Voltage-controlled nonreciprocity demonstrated

## Abstract

Singularities arise in diverse disciplines and play a key role in both exploring fundamental laws of physics and making highly-sensitive sensors. Higher-order (>3) singularities, with further improved performance, however, usually require exquisite tuning of multiple (>3) coupled degrees of freedom or nonlinear control, thus severely limiting their applications in practice. Here we propose theoretically and confirm using mechanics experiments that, cubic singularities can be realized in a coupled binary system without any nonlinearity, only by observing the phase tomography of the driven response. By steering the cubic phase-tomographic singularities in an electrostatically-tunable micromechanical system, enhanced cubic-root response to frequency perturbation and voltage-controlled nonreciprocity are demonstrated. Our work opens up a new phase-tomographic method for interacted-system research and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with a wide range of applications including precision metrology, portable nonreciprocal devices, and on-chip mechanical computing.