Frequency stabilization of self-sustained oscillations in a sideband-driven electromechanical resonator

TL;DR

This paper introduces a method to stabilize the frequency of self-sustained oscillations in micro- and nanomechanical resonators by controlling phase fluctuations through a two-mode system, enhancing vibration stability across broad frequencies.

Contribution

The study demonstrates a novel phase stabilization technique for self-sustained oscillations in electromechanical resonators using inter-mode control and phase anti-correlation.

Findings

Phase fluctuations can be significantly reduced in both high and low frequency modes.

Phase control is achieved through pump phase adjustments, independent of pump amplitude and frequency.

The method enables stable vibrations over a broad frequency range via parametric downconversion.

Abstract

We present a method to stabilize the frequency of self-sustained vibrations in micro- and nanomechanical resonators. The method refers to a two-mode system with the vibrations at significantly different frequencies. The signal from one mode is used to control the other mode. In the experiment, self-sustained oscillations of micromechanical modes are excited by pumping at the blue-detuned sideband of the higher-frequency mode. Phase fluctuations of the two modes show near perfect anti-correlation. They can be compensated in either one of the modes by a stepwise change of the pump phase. The phase change of the controlled mode is proportional to the pump phase change, with the proportionality constant independent of the pump amplitude and frequency. This finding allows us to stabilize the phase of one mode against phase diffusion using the measured phase of the other mode. We demonstrate that phase fluctuations of either the high or low frequency mode can be significantly reduced. The results open new opportunities in generating stable vibrations in a broad frequency range via parametric downconversion in nonlinear resonators.