Multimode Oscillator Research Articles

Temperature evolution of frequency and anharmonic phonon loss for multi-mode epitaxial HBARs

This Letter reports measured cryogenic temperature trends for over 300 longitudinal phonon modes spanning >10 GHz in an epitaxial GaN/NbN/SiC high overtone bulk acoustic resonator (epi-HBAR). We present temperature profiles from 7.2 K to 200 K for the mode frequency (f), the quality factor (Q), the figure of merit (f×Q), and the phonon loss or attenuation coefficient (α). We show that for all m phonon modes, fmT follows an identical parabolic trend, with a zero-slope turnover temperature of 35 K. Thus, the epi-HBAR comb spectrum can be considered an ensemble of modes with the same temperature dependencies, potentially enabling the design of precise multi-mode temperature-stable RF oscillators and clocks operating at GHz frequencies. Using temperature trends for (f×Q)m and αm, we provide strong evidence that the epi-HBARs are fundamentally limited by anharmonic phonon scattering in the materials that make up the epi-HBAR. Crucially, we unambiguously demonstrate the evolution of this anharmonic phonon scattering from the low frequency Akhiezer scattering regime αm∝T1 to the high frequency Landau–Rumer scattering regime αm∝T4, using hundreds of phonon modes in the same device. Finally, we show that at extremely low temperatures, other emergent loss mechanisms overshadow anharmonic phonon scattering. This finding motivates further investigation into the root causes of these limiting mechanisms for precision RF signal processing, quantum acoustodynamics, and other applications that require extremely low loss micromechanical devices.

The role of vibronic modes in formation of red antenna states of cyanobacterial PSI.

Cyanobacterial photosystem I (PSI) constitutes monomeric and trimeric pigment-protein complexes whose optical properties are marked by the presence of long-wavelength absorption bands. In spite of numerous experimental studies, the nature of these bands is still under debate and requires intensive theoretical analysis. Collecting together the data of linear spectroscopy and single-molecule spectroscopy (SMS) of PSI from Arthrospira platensis, we performed quantum modeling of the optical response based on molecular exciton theory (ET) and the multimode Brownian oscillator model (MBOM). Applying MBOM, the spectra of the red antenna state were calculated considering a particular for each red state adjustment of the low-frequency vibronic modes. Within the framework of our PSI exciton model it was shown that the coupling energy between antenna chlorophylls cannot be a factor of the red states formation, thus the long-wavelength bands are calculated without attribution to so-called antenna red chlorophylls. By the fitting of Huang-Rhys factors and frequencies for the lowest vibronic modes, we were able to reproduce the effects of strong and weak electron-phonon coupling experimentally observed in SMS spectra of red antenna states. Based on our theoretical calculations and also analysis of existing crystal structures of cyanobacterial PSI, we assumed that long-wavelength Chls can be localized in the peripheral protein subunits containing one or two pigment molecules.

Probability Representation of Quantum Mechanics and the Quantizer—Dequantizer Formalism

A review of the approach where the states of quantum systems are identified with fair probability distributions is presented. The quantizer–dequantizer operators used to construct the invertible map of the density operators onto the probability distributions are applied to obtain the kinetic equations for probability distributions identified with the quantum system states. For qubit states, the von Neumann evolution equation for the density operator is explicitly given in the form of kinetic equation for the probability distribution. Simplest tomographic probability distributions describing the states of multimode quantum oscillator are constructed.

Optimizing the Multimode Brownian Oscillator Model for the Optical Response of Carotenoids in Solution by Fine Tuning of Differential Evolution

During last twenty years, the Differential evolution algorithm (DE) has proved to be one of the powerful methods to solve minimization problems for multidimensional functions. Being a member of the family of evolutionary optimization algorithms, its main principle is based upon the concepts of natural selection and mutation. In this study, we test the potential of DE to find a proper set of parameters for the multimode Brownian oscillator model, which was then used to simulate absorption lineshapes of carotenoid molecules in solution: spheroidene and spheroidenone. This theory assumes that the correlation function of a particular electronic state of the carotenoid is calculated using the semiclassical spectral density function. Considering our previous studies on photosynthetic pigments, we employed several DE strategies to do fitting of the carotenoid experimental spectra. We found that simulated absorption spectra are very sensitive to several parameters that characterize carotenoid vibronic modes, namely, Huang–Rhys factors. Fine tuning of DE crossover parameter (Cr) and the scaling factor (F) provided acceptable convergence of the algorithm. It appears that to get good convergence of DE, a certain spectral range of carotenoid absorption from 400 to 600 nm must be chosen. This fact can be explained by the limitations of the applied theory, which simply does not predict properly the carotenoid absorption at higher frequencies.

Multimode Self-Oscillating Vesicle Transformers.

Engineering synthetic materials that mimic the complex rhythmic oscillatory behavior of living cells is a fundamental challenge in science and technology. Up to now, the reported synthetic model system still cannot compete with nature in oscillatory modes and amplitudes. Presented here is a novel alternating copolymer vesicle that exhibits drastic and multimode shape oscillations in real time, which are controlled by polymer concentrations and driven by the Belousov-Zhabotinsky oscillatory reaction, including swelling/deswelling, twisting/detwisting, stretching/shrinking, fusion/fission, and multiple division. Some of them, especially the fission oscillation, have not been observed before. In addition, the oscillation magnitude with regard to diameter is much larger than that of previously reported self-oscillating vesicles. Such a self-oscillating vesicle transformer would extend the complexity and capacity of membrane deformations in synthetic systems, approaching those of natural cells.

Multimode Self‐Oscillating Vesicle Transformers

AbstractEngineering synthetic materials that mimic the complex rhythmic oscillatory behavior of living cells is a fundamental challenge in science and technology. Up to now, the reported synthetic model system still cannot compete with nature in oscillatory modes and amplitudes. Presented here is a novel alternating copolymer vesicle that exhibits drastic and multimode shape oscillations in real time, which are controlled by polymer concentrations and driven by the Belousov—Zhabotinsky oscillatory reaction, including swelling/deswelling, twisting/detwisting, stretching/shrinking, fusion/fission, and multiple division. Some of them, especially the fission oscillation, have not been observed before. In addition, the oscillation magnitude with regard to diameter is much larger than that of previously reported self‐oscillating vesicles. Such a self‐oscillating vesicle transformer would extend the complexity and capacity of membrane deformations in synthetic systems, approaching those of natural cells.

Optoelectronic parametric oscillator

Oscillators are one of the key elements in various applications as a signal source to generate periodic oscillations. Among them, an optical parametric oscillator (OPO) is a driven harmonic oscillator based on parametric frequency conversion in an optical cavity, which has been widely investigated as a coherent light source with an extremely wide wavelength tuning range. However, steady oscillation in an OPO is confined by the cavity delay, which leads to difficulty in frequency tuning, and the frequency tuning is discrete with the minimum tuning step determined by the cavity delay. Here, we propose and demonstrate a counterpart of an OPO in the optoelectronic domain, i.e., an optoelectronic parametric oscillator (OEPO) based on parametric frequency conversion in an optoelectronic cavity to generate microwave signals. Owing to the unique energy-transition process in the optoelectronic cavity, the phase evolution in the OEPO is not linear, leading to steady single-mode oscillation or multimode oscillation that is not bounded by the cavity delay. Furthermore, the multimode oscillation in the OEPO is stable and easy to realize owing to the phase control of the parametric frequency-conversion process in the optoelectronic cavity, while stable multimode oscillation is difficult to achieve in conventional oscillators such as an optoelectronic oscillator (OEO) or an OPO due to the mode-hopping and mode-competition effect. The proposed OEPO has great potential in applications such as microwave signal generation, oscillator-based computation, and radio-frequency phase-stable transfer.

Advanced Alicki–Fannes–Winter method for energy-constrained quantum systems and its use

We describe an universal method for quantitative continuity analysis of entropic characteristics of energy-constrained quantum systems and channels. It gives asymptotically tight continuity bounds for basic characteristics of quantum systems of wide class (including multi-mode quantum oscillators) and channels between such systems under the energy constraint. The main application of the proposed method is the advanced version of the uniform finite-dimensional approximation theorem for basic capacities of energy-constrained quantum channels.

Retraction: "Transition between multimode oscillations in a loaded hair bundle" [Chaos 29, 083135 (2019)

First Page

Effect of asymmetric intermodal gain suppression on dynamics of multimode semiconductor lasers

This paper introduces a theoretical study on the influence of intermodal asymmetric gain suppression (AGS) on dynamics and output of multimode semiconductor lasers. The study includes comprehensive and intensive simulations of the dynamics of 21-oscillating longitudinal modes taking account of the self- and cross-modal gain suppression mechanisms. AGS is varied in terms of a pre-defined parameter, Hc, that combines the linewidth enhancement factor and differential gain as controlling parameters of AGS. We classify laser oscillation into four types, namely, single mode oscillation (SMO), symmetric steady-state multimode oscillation (SSMMO), asymmetric steady-state multimode oscillation (ASMMO) and hopping multimode oscillation (HMMO) depending on the values of Hc and injection current. We allocate the operating regime of each of these classes over a mapping diagram of Hc versus current. SMO is attained when the current increases beyond the threshold and Hc has small values. Jumping of the oscillating mode on the long-wavelength side is noticed by increasing Hc. When Hc increases and violates AGS, HMMO is induced among a number of modes, and asymmetric output spectra are obtained. In this case the mode-hopping frequency ranges between 36 and 392 MHz and the hopping modes are anti-correlated with correlation coefficient exceeding – 0.25.

Measurement-based Feedback Control of Linear Quantum Stochastic Systems with Quadratic-Exponential Criteria

This paper is concerned with a risk-sensitive optimal control problem for a feedback connection of a quantum plant with a measurement-based classical controller. The plant is a multimode open quantum harmonic oscillator driven by a multichannel quantum Wiener process, and the controller is a linear time invariant system governed by a stochastic differential equation. The control objective is to stabilize the closed-loop system and minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential functional (QEF) which penalizes the plant variables and the controller output. We combine a frequency-domain representation of the QEF growth rate, obtained recently, with variational techniques and establish first-order necessary conditions of optimality for the state-space matrices of the controller.

A new mechanistic study of a second generation TADF material based on the path integral approach incorporating Herzberg–Teller and Duschinsky rotation effects

Quantitative predictions of the photophysical processes for a next generation thermally activated delayed fluorescence molecule are calculated by considering the Herzberg–Teller and the Duschinsky rotation effects within a multimode harmonic oscillator model.

Spatiotemporal self-similar fiber laser

In this Letter, we demonstrate, to the best of our knowledge, the first spatiotemporally mode-locked fiber laser with self-similar pulse evolution. The multimode fiber oscillator generates parabolic amplifier similaritons at 1030 nm with 90 mW average power, 2.3 ps duration, and 37.9 MHz repetition rate. Remarkably, we observe experimentally a near-Gaussian beam quality (M^2<1.4) at the output of the highly multimode fiber. The output pulses are compressed to 192 fs via an external grating compressor. Numerical simulations are performed to investigate the cavity dynamics which confirm experimental observations of self-similar pulse propagation. The reported results open a new direction to investigate new types of pulse besides beam shaping and nonlinear dynamics in spatiotemporal mode-locked fiber lasers.

Selection of the Oscillation Mode in Multi-Mode Oscillators by Initializing the Cavity Signal

We demonstrate a new method to select the oscillation mode in multi-mode oscillators with an instantaneous gain saturation. The method is based on initializing the cavity signal by feeding into the cavity an external signal for a duration that can be as short as the cavity delay. After the external signal is turned off, the steady state oscillation mode is exactly determined by the frequency of the external signal. By changing the external signal frequency, any specific mode can be selected over a broad continuous operating frequency region, which can be wider than the full width at half maximum (FWHM) bandwidth of the cavity filter. The method is not based on injection-locking effect and therefore the frequency of the external signal can be arbitrary chosen in a broad operating bandwidth, and it is not limited by the narrow locking range of the oscillator. When the frequency difference between the external signal and the central frequency of the filter is small, in comparison with the filter FWHM bandwidth, the selected mode is the mode with the nearest frequency to that of the external signal. However, as this frequency difference is increased, the selected mode is slightly shifted toward the filter central frequency. These results were experimentally demonstrated in an optoelectronic oscillator (OEO) and were compared to a comprehensive numerical simulation. A good quantitative agreement between theory and experiments were obtained. A fundamental limit on the minimum duration, which is required to initialize the cavity signal is given.

Transition between multimode oscillations in a loaded hair bundle.

In this paper, we study the dynamics of an autonomous system for a hair bundle subject to mechanical load. We demonstrated the spontaneous oscillations that arise owing to interactions between the linear stiffness and the adapting stiffness. It is found that by varying the linear stiffness, the system can induce a weakly chaotic attractor in a certain region where the stable periodic orbit is infinitely close to a parabolic curve composed of unstable equilibrium points. By altering the adapting stiffness associated with the calcium concentration, the system is able to trigger the transition from the bistable resting state, through a pair of symmetric Hopf bifurcation, into the bistable limit cycle, even to the chaotic attractor. At a negative adapting stiffness, the system exhibits a double-scroll chaotic attractor. According to the method of qualitative theory of fast-slow decomposition, the trajectory of a double-scroll chaotic attractor in the whole system depends upon the symmetric fold/fold bifurcation in a fast system. Furthermore, the control of the adapting stiffness in the improved system with two slow variables can trigger a new transition from the bistable resting state into the chaotic attractor, even to the hyperchaotic attractor by observing the Lyapunov exponent.

Upper Bounds for the Holevo Information Quantity and Their Use

We present a family of easily computable upper bounds for the Holevo (information) quantity of an ensemble of quantum states depending on a reference state (as a free parameter). These upper bounds are obtained by combining probabilistic and metric characteristics of the ensemble. We show that an appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many cases improve the estimates existing in the literature. We also present an upper bound for the Holevo quantity of a generalized ensemble of quantum states with finite average energy depending on the metric divergence of an ensemble. In the case of a multi-mode quantum oscillator, this upper bound is tight for large energy. Upper bounds for the Holevo capacity of finite-dimensional quantum channels depending on metric characteristics of the channel output are obtained.

Measurement and modeling of electrowetting lens oscillations using digital holographic interferometry and Bessel and Legendre polynomial functions.

The function of electrowetting liquid lenses is expanding beyond tunable focal length lensing. Recently, single and multi-mode oscillations on the meniscus profile of two non-miscible liquids have been used for optical phase modulation and fast focal length sweeping. To achieve a user-defined phase modulation, a prediction model of oscillation patterns and amplitudes is needed. We present digital holographic interferometry (DHI) measurements of oscillation patterns and amplitudes on a 5.8mm aperture lens up to 160 Hz, including frequency responses from 26-100 Hz. We discuss using Bessel function and Legendre polynomial models for oscillations on a conical frustum shaped electrowetting lens.

Analysis of multimodal stochastic oscillations in a biochemical reaction model

В работе изучается динамика двумерной биохимической модели Голдбетера под действием случайных возмущений. Модель описывает ферментативную реакцию с нелинейной рециркуляцией продукта в субстрат. Мы исследовали параметрические зоны, где система обнаруживает явление бистабильности - сосуществование двух аттракторов. В системе возможны следующие случаи бистабильности: сосуществование двух периодических режимов, представленных устойчивыми предельными циклами, либо сосуществование устойчивого равновесия и предельного цикла. Зоны притяжения аттракторов разделены неустойчивым предельным циклом, играющим роль сепаратрисы. С помощью прямого численного моделирования поведения системы продемонстрированы индуцированные шумом переходы стохастических траекторий между детерминированными аттракторами, приводящие к появлению мультимодальных осцилляций. Показано, как воздействие случайного шума на систему меняет частотные и амплитудные характеристики колебательных режимов.

Bichaoticity induced by inherent birhythmicity during the oscillatory electrodissolution of silicon.

The electrodissolution of p-type silicon in a fluoride-containing electrolyte is a prominent electrochemical oscillator with a still unknown oscillation mechanism. In this article, we present a study of its dynamical states occurring in a wide range of the applied voltage-external resistance parameter plane. We provide evidence that the system possesses inherent birhythmicity, and thus at least two distinct feedback loops promoting oscillatory behavior. The two parameter regions in which the different limit cycles exist are separated by a band in which the dynamics exhibit bistability between two branches with different multimode oscillations. Following the states along one path through this bistable region, one observes that each branch undergoes a different transition to chaos, namely, a period doubling cascade and a quasiperiodic route with a torus-breakdown, respectively, making Si electrodissolution one of the few experimental systems exhibiting bichaoticity.

Complex oscillation modes in the Belousov-Zhabotinsky reaction by weak diffusive coupling.

We study the diffusive coupling of oscillating or excitable Belousov-Zhabotinsky reaction units arranged in a square lattice array and show that for certain sizes of the units and for certain distances between the units, complex oscillation modes of individual spots occur, which manifest themselves in multi-periodic, amplitude-modulated, and multi-mode oscillations. This experimental finding can be reproduced in simulations of the FitzHugh-Nagumo model mimicking the experimental setup, suggesting that it is a generic phenomenon in systems of coupled excitable units such as excitable cell tissues or coupled oscillators such as neurons. Further analysis let us conclude that the complex oscillation modes occur close to the transition from quiescent to coupling-induced oscillations states if this transition is taking place at weak coupling strength.