arXiv subjects

Raoni S. N. Moreira

Publications and source records attributed to Raoni S. N. Moreira.

4 recordsLinked to original sources

arXiv2026

Deep squeezing or cooling the fluctuations of a parametric resonator using feedback

Here we analyze ways to achieve deep subthreshold parametric squeezing or cooling of a single degree-of-freedom parametric resonator enhanced by a lock-in amplifier feedback loop. Due to the feedback, the dynamics of the parametric resonator becomes more complex and a Hopf bifurcation at the instability threshold can occur. Initially, we calculate the phase-dependent gain of parametric amplification with feedback of an added ac signal. In one approach, we obtain the amplification gain approximately using two independent approaches: the averaging method and the harmonic balance method. We also obtain this gain more exactly using Floquet theory and Green's functions methods. The Hopf bifurcation was predicted by the harmonic balance method and by Floquet theory, but not by the averaging method. In our analysis of fluctuations, we Fourier analyze the response of the parametric resonator with feedback to an added white noise. We were able to calculate, in addition to the noise spectral density, the squeezing of fluctuations in this resonator with feedback. Very strong squeezing or cooling can occur. Deamplification and cooling occur near the Hopf bifurcation, whereas squeezing occurs near a saddle-node bifurcation.

quant-ph↗

arXiv2024

Deep noise squeezing in parametrically driven resonators

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.

physics.app-ph↗

arXiv2021

Stochastic resonance and amplification in the ac driven Duffing oscillator with added noise

Stochastic resonance (SR) is a coherence enhancement effect due to noise that occurs in periodically-driven nonlinear dynamical systems. A very broad range of physical and biological systems present this effect such as climate change, neurons, neural networks, lasers, SQUIDS, and tunnel diodes, among many others. Early theoretical models of SR dealt only with overdamped bistable oscillators. Here, we propose a simple model that accounts for SR in an underdamped driven Duffing oscillator with added white noise. Furthermore, we develop a theoretical method to predict the effect of white noise on the pump, signal, and idler responses of a Duffing amplifier. We also calculate the power spectral density of the response of the Duffing amplifier. This approach may prove to be useful for assessing the robustness of acoustic, phononic, or mechanical frequency-comb generation to the presence of noise.

nlin.PS↗

arXiv2011

Signal to noise ratio in parametrically-driven oscillators

Here we report a theoretical model based on Green's 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.

cond-mat.stat-mech↗