Noise color and asymmetry in stochastic resonance with silicon nanomechanical resonators

Stochastic resonance (SR) with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for SR, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a $1/f$ spectrum. As a result, improved understanding of the effects of noise color is necessary in maximizing device performance. Here, we report measurements of SR in a silicon nanomechanical resonator using $1/f$ noise and exponentially correlated Ornstein-Uhlenbeck noise. Power spectral densities and residence time distributions provide insight into asymmetry of the bistable amplitude states, and evidence suggests that $1/f^{\alpha }$ spectra with increasing noise exponent $\alpha $ may lead to increasing asymmetry in the system, reducing the achievable signal-to-noise ratio. Furthermore, we explore the effects of correlation time $\tau $ on SR with the use of exponentially correlated noise. We find monotonic suppression of the spectral amplification as the correlation time increases.