Frequency Stability of Graphene Nonlinear Parametric Oscillator

TL;DR

This paper shows that graphene parametric oscillators operating in a nonlinear regime can achieve better short-term frequency stability than traditional Duffing oscillators, due to nonlinear damping reducing phase noise.

Contribution

It introduces the use of phase-locked loop operation in graphene parametric oscillators to enhance frequency stability through nonlinear damping effects.

Findings

Parametric oscillations exhibit lower Allan deviation than Duffing oscillations at the same amplitude.

Nonlinear damping suppresses amplitude-to-frequency noise conversion.

A theoretical model confirms nonlinear damping as key to phase noise reduction.

Abstract

High-frequency stability is crucial for the performance of graphene resonators in sensing and timekeeping applications. However, the extreme miniaturization and high mechanical compliance that make graphene attractive also render it highly susceptible to nonlinearities, degrading frequency stability. Here, we demonstrate that graphene parametric oscillators provide an alternative nonlinear operating regime, where short-term frequency stability can be enhanced despite strong nonlinearity. By operating graphene resonators in a phase-locked loop (PLL), we experimentally demonstrate that parametric oscillations in the post-bifurcation regime achieve lower Allan deviation at fast integration times than Duffing oscillations at identical amplitudes. This improvement originates from strong nonlinear damping inherent to parametric oscillators, which suppresses amplitude-to-frequency noise conversion at large amplitudes. A minimal theoretical model captures observed phase diffusion and identifies nonlinear damping as the dominant mechanism governing phase noise reduction. These results highlight the role of nonlinear dissipation in enabling precision sensing beyond conventional limits of graphene oscillators.