arXiv subjects

Adriano A. Batista

Publications and source records attributed to Adriano A. Batista.

13 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↗

arXiv2025

Feedback-enhanced squeezing or cooling of fluctuations in a parametric resonator

Here we analyse ways to achieve deep subthreshold parametric squeezing of fluctuations beyond the $-6$~dB limit of single degree-of-freedom parametric resonators. One way of accomplishing this is via a lock-in amplifier feedback loop. Initially, we calculate the phase-dependent parametric amplification with feedback of an added ac signal. In one approach, we use the averaging method to obtain the amplification gain, while in the second approach, we obtain the ac response of the parametric amplifier with feedback using the harmonic balance method. In this latter approach, the feedback is proportional to an integral term that emulates the cosine quadrature output of a lock-in amplifier multiplied by a sine at the same tone of the lock-in. We find that the gain obtained via these two methods are the same whenever the integration time span of the integral is a multiple of the tone period. When this is not the case, we can obtain considerable deamplification. Finally, we analyse the response of the parametric resonator with feedback, described by this integro-differential model, to an added white noise in the frequency domain. Using this model we were able to calculate, in addition to squeezing, the noise spectral density in this resonator with feedback. Very strong squeezing or cooling can be obtained.

physics.app-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↗

arXiv2024

Amplification in parametrically-driven resonators near instability based on Floquet theory and Green's functions

Here we use Floquet theory to calculate the response of parametrically-driven time-periodic systems near the onset of parametric instability to an added external ac signal or white noise. We provide new estimates, based on the Green's function method, for the response of the system in the frequency domain. Furthermore, we write novel expressions for the power and the noise spectral densities. We validate our theoretical results by comparing our predictions for the specific cases of a single degree of freedom parametric amplifier and of the parametric amplifier coupled to a harmonic oscillator with the numerical integration results and with analytical approximate results obtained via the averaging method up to second order.

nlin.CD↗

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↗

arXiv2020

An epidemiological compartmental model with automated parameter estimation and forecasting of the spread of COVID-19 with analysis of data from Germany and Brazil

In this work, we adapt the epidemiological SIR model to study the evolution of the dissemination of COVID-19 in Germany and Brazil (nationally, in the State of Paraiba, and in the City of Campina Grande). We prove the well posedness and the continuous dependence of the model dynamics on its parameters. We also propose a simple probabilistic method for the evolution of the active cases that is instrumental for the automatic estimation of parameters of the epidemiological model. We obtained statistical estimates of the active cases based the probabilistic method and on the confirmed cases data. From this estimated time series we obtained a time-dependent contagion rate, which reflects a lower or higher adherence to social distancing by the involved populations. By also analysing the data on daily deaths, we obtained the daily lethality and recovery rates. We then integrate the equations of motion of the model using these time-dependent parameters. We validate our epidemiological model by fitting the official data of confirmed, recovered, death, and active cases due to the pandemic with the theoretical predictions. We obtained very good fits of the data with this method. The automated procedure developed here could be used for basically any population with a minimum of extra work. Finally, we also propose and validate a forecasting method based on Markov chains for the evolution of the epidemiological data for up to two weeks.

q-bio.PE↗

arXiv2020

Frequency-comb response of a parametrically-driven Duffing oscillator to a small added ac excitation

Here we present a one-degree-of-freedom model of a nonlinear parametrically-driven resonator in the presence of a small added ac signal that has spectral responses similar to a frequency comb. The proposed nonlinear resonator has a spread spectrum response with a series of narrow peaks that are equally spaced in frequency. The system displays this behavior most strongly after a symmetry-breaking bifurcation at the onset of parametric instability. We further show that the added ac signal can suppress the transition to parametric instability in the nonlinear oscillator. We also show that the averaging method is able to capture the essential dynamics involved.

nlin.PS↗

arXiv2015

Gain and noise spectral density in an electronic parametric amplifier with added white noise

In this paper, we discuss the behavior of a linear classical parametric amplifier (PA) in the presence of white noise and give theoretical estimates of the noise spectral density based on approximate Green's functions obtained by using averaging techniques. Furthermore, we give analytical estimates for parametric amplification bandwidth of the amplifier and for the noisy precursors to instability. To validate our theory we compare the analytical results with experimental data obtained in an analog circuit. We describe the implementation details and the setup used in the experimental study of the amplifier. Near the threshold to the first parametric instability, and in degenerate-mode amplification, the PA achieved very high gains in a very narrow bandwidth centered on its resonance frequency. In quasi-degenerate mode amplification, we obtained lower values of gain, but with a wider bandwidth that is tunable. The experimental data were accurately described by the predictions of the model. Moreover, we noticed spectral components in the output signal of the amplifier which are due to noise precursors of instability. The position, width, and magnitude of these components are in agreement with the noise spectral density obtained by the theory proposed here.

physics.class-ph↗

arXiv2015

Rabi oscillations in two-level systems beyond the rotating-wave approximation

Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLS's). By going beyond the rotating-wave approximation, especifically to second-order in perturbation, we obtain the Bloch-Siegert shift of the TLS resonant frequency, in which the resonant frequency increases with the driving field amplitude. This frequency shift implies that short resonant $π$-pulses in which the Rabi frequency is approximately 40\% or higher of the transition frequency do not achieve complete inversion in TLS's. Hence, guided by analytical results based on the averaging technique, we propose two methods for obtaining population inversions in the TLS driven by short $π$-pulses: one with chirping and the other with pulse shaping and near resonance blue-shifted detuning. Both methods minimize dephasing due to the Bloch-Siegert shift, reduce the dependance of the excitation of the TLS on the pulse phase, and are very effective in achieving complete population inversions.

quant-ph↗

arXiv2012

Heating and thermal squeezing in parametrically-driven oscillators with added noise

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.

cond-mat.stat-mech↗

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↗

arXiv2006

Mixing, ergodicity and slow relaxation phenomena

Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation-dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.

cond-mat.stat-mech↗

arXiv2001

A Hopf bifurcation with a strong incommensurate frequency response in quantum wells

The behavior of delta-doped wide quantum well heterostructures in the presence of intense far-infrared radiation is studied using semiconductor Bloch equations. A quantum well is designed where one can either obtain a strong subharmonic (period-doubling) or a strong incommensurate (Hopf) frequency response by varying the sheet density and field strength. These strong responses are easily attainable with current quantum well technology and the field amplitudes and frequencies of the drive are well within the range of the free electron laser.

cond-mat.mes-hall↗