Deep noise squeezing in parametrically driven resonators

Abstract: Here we investigate white noise squeezing in the frequency domain of classical parametrically-driven resonators with added noise. We use Green's functions to analyse the response of resonators to added noise. In one approach, we obtain the Green's function approximately using the first-order averaging method, while in the second approach, exactly, using Floquet theory. We characterize the noise squeezing by calculating the statistical properties of the real and imaginary parts of the Fourier transform of the resonators response to added noise. In a single parametric resonator, due to correlation, the squeezing limit of $-6$~dB can be reached even with detuning at the instability threshold in a single parametrically-driven resonator. We also applied our techniques to investigate squeezing in a dynamical system consisting a parametric resonator linearly coupled to a harmonic resonator. In this system, we were able to observe deep squeezing at around $-40$~dB in one of the quadratures of the harmonic resonator response. We noticed that this occurs near a Hopf bifurcation to parametric instability, which is only possible when the dynamics of the coupled resonators cannot be decomposed into normal modes. Finally, we also showed that our analysis of squeezing based on Floquet theory can be applied to multiple coupled resonators with parametric modulation and multiple noise inputs.