Driven nonlinear nanomechanical resonators as digital signal detectors

TL;DR

This paper explores how driven nonlinear nanomechanical resonators can serve as sensitive digital signal detectors by exploiting their bistability and phase-dependent amplitude response, with analytical insights into error rates near critical points.

Contribution

It introduces a novel use of driven nonlinear resonators as digital bifurcation amplifiers and provides analytical methods to analyze their error rates near the critical threshold.

Findings

Resonators exhibit phase-dependent bistability useful for digital detection.

Operation near the critical point lowers the signal threshold.

Analytical techniques predict error rates close to the bifurcation threshold.

Abstract

Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes binary information, a signal at the same frequency increases or decreases the force amplitude. The resulting force amplitude can be outside the range of bistability. The values of the mode amplitude differ significantly on the opposite sides of the bistability region. Therefore the mode amplitude is very sensitive to the signal phase. This suggests using a driven mode as a bi-directional bifurcation amplifier, which switches in the opposite directions depending on the signal phase and provides an essentially digital output. We study the operation of the amplifier near the critical point where the width of the bistability region goes to zero and thus the threshold of the signal amplitude is low. We also develop an analytical technique and study the error rate near the threshold. The results apply to a broad range of currently studied systems and extend to micromechanical systems and nonlinear electromagnetic cavities.