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Register a new userSignal to noise ratio in parametrically-driven oscillators
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Added by
Adriano de Albuquerque Batista
Publication date
2011
fields
Physics
and research's language is
English
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Here we report a theoretical model based on Greens functions and averaging techniques that gives ana- lytical 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 dif- ferent 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 position of 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.
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In this paper we report a theoretical model based on Green functions, Floquet theory and averaging techniques up to second order that describes the dynamics of parametrically-driven oscillators with added thermal noise. Quantitative estimates for heating and quadrature thermal noise squeezing near and below the transition line of the first parametric instability zone of the oscillator are given. Furthermore, we give an intuitive explanation as to why heating and thermal squeezing occur. For small amplitudes of the parametric pump the Floquet multipliers are complex conjugate of each other with a constant magnitude. As the pump amplitude is increased past a threshold value in the stable zone near the first parametric instability, the two Floquet multipliers become real and have different magnitudes. This creates two different effective dissipation rates (one smaller and the other larger than the real dissipation rate) along the stable manifolds of the first-return Poincare map. We also show that the statistical average of the input power due to thermal noise is constant and independent of the pump amplitude and frequency. The combination of these effects cause most of heating and thermal squeezing. Very good agreement between analytical and numerical estimates of the thermal fluctuations is achieved.
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