Signal-to-noise ratio in parametrically driven oscillators

Abstract

We report a theoretical model based on Green's functions and averaging techniques that gives analytical estimates to the signal-to-noise ratio (SNR) near the first parametric instability zone in parametrically driven oscillators in the presence of added ac drive and added thermal noise. The signal term is given by the response of the parametrically driven oscillator to the added ac drive, while the noise term has two different measures: one is dc and the other is ac. The dc measure of noise is given by a time average of the statistically averaged fluctuations of the displacement from equilibrium in the parametric oscillator due to thermal noise. The ac measure of noise is given by the amplitude of the statistically averaged fluctuations at the frequency of the parametric pump. We observe a strong dependence of the SNR on the phase between the external drive and the parametric pump. For some range of the phase there is a high SNR, while for other values of phase the SNR remains flat or decreases with increasing pump amplitude. Very good agreement between analytical estimates and numerical results is achieved.