# Direct and parametric synchronization of a graphene self-oscillator

## TL;DR

This paper demonstrates the synchronization of a graphene nanomechanical oscillator to an external reference signal, revealing phase resonance behavior and modeling it with a nonlinear differential equation.

## Contribution

It introduces a method to achieve and analyze synchronization in a graphene oscillator using photothermal feedback and external laser modulation.

## Key findings

- Synchronization regimes depend on detuning and signal strength.
- Phase resonance exhibits a power-law dependence on locking signal.
- The behavior is modeled with a forced nonlinear oscillator equation.

## Abstract

We explore the dynamics of a graphene nanomechanical oscillator coupled to a reference oscillator. Circular graphene drums are forced into self-oscillation, at a frequency fosc, by means of photothermal feedback induced by illuminating the drum with a continuous-wave red laser beam. Synchronization to a reference signal, at a frequency fsync, is achieved by shining a power-modulated blue laser onto the structure. We investigate two regimes of synchronization as a function of both detuning and signal strength for direct (fsync = fosc) and parametric locking (fsync = 2fosc). We detect a regime of phase resonance, where the phase of the oscillator behaves as an underdamped second-order system, with the natural frequency of the phase resonance showing a clear power-law dependence on the locking signal strength. The phase resonance is qualitatively reproduced using a forced van der Pol-Duffing-Mathieu equation.