Experimental evidence of vibrational resonance in a multistable system

Vibrational resonance in bichromatically excited diatomic molecules in a shifted molecular potential

For bichromatically excited diatomic molecules modeled in a shifted Tietz-Wei molecular potential, we demonstrate the occurrence of vibrational resonance (VR) when a saddle-node (SN) bifurcation takes place and its nonoccurrence in the absence of an SN bifurcation. We have examined the VR phenomenon and its connection with SN bifurcation for eight diatomic molecules, namely, H_{2}, N_{2}, Cl_{2}, I_{2}, O_{2}, HF, CO, and NO, consisting of homogeneous, heterogenous, and halogen molecules. We demonstrate that each of them vibrates at a distinct resonant frequency but with a spread in frequency. The high-frequency amplitude at which VR occurs corresponds to the SN-bifurcation point. We validate our analytic results by numerical simulations and show that the homonuclear halogens respond only weakly to bichromatic fields, which may perhaps be linked to their absence of SN bifurcation.

Ultrasensitive vibrational resonance induced by small disturbances

We have found two kinds of ultrasensitive vibrational resonance in coupled nonlinear systems. It is particularly worth pointing out that this ultrasensitive vibrational resonance is transient behavior caused by transient chaos. Considering a long-term response, the system will transform from transient chaos to a periodic response. The pattern of vibrational resonance will also transform from ultrasensitive vibrational resonance to conventional vibrational resonance. This article focuses on the transient ultrasensitive vibrational resonance phenomenon. It is induced by a small disturbance of the high-frequency excitation and the initial simulation conditions, respectively. The damping coefficient and the coupling strength are the key factors to induce the ultrasensitive vibrational resonance. By increasing these two parameters, the vibrational resonance pattern can be transformed from ultrasensitive vibrational resonance to conventional vibrational resonance. The reason for different vibrational resonance patterns to occur lies in the state of the system response. The response usually presents transient chaotic behavior when the ultrasensitive vibrational resonance appears and the plot of the response amplitude vs the controlled parameters shows a highly fractalized pattern. When the response is periodic or doubly periodic, it usually corresponds to the conventional vibrational resonance. The ultrasensitive vibrational resonance not only occurs at the excitation frequency, but it also occurs at some more nonlinear frequency components. The ultrasensitive vibrational resonance as transient behavior and the transformation of vibrational resonance patterns are new phenomena in coupled nonlinear systems.

Dynamically induced conformation depending on excited normal modes of fast oscillation

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given potential energy function depending on the bending angle, but also by fast motion of the springs which constructs the effective potential. A conformation corresponding with a local minimum of the effective potential is hence called the dynamically induced conformation. We develop a theory to derive the effective potential using multiple-scale analysis and the averaging method. A remarkable consequence is that the effective potential depends on the excited normal modes of the springs and amount of the spring energy. Efficiency of the obtained effective potential is numerically verified.

Vibrational Resonance Amplification in a Thermo-Optic Optomechanical Nanocavity

Vibrational resonance is a generic phenomenon found in many different bistable systems whereby a weak low-frequency signal is amplified by use of an additional nonresonant high-frequency modulation. The realization of weak signal enhancement in integrated nonlinear optical nanocavities is of great interest for nanophotonic applications where optical signals may be of low power. Here, we report experimental observation of vibrational resonance in a thermo-optically bistable photonic crystal optomechanical resonator with an amplification up to +16 dB. The characterization of the bistability can interestingly be done using a mechanical resonance of the membrane, which is submitted to a strong thermoelastic coupling with the cavity.

Amplification of optical signals in a bistable vertical-cavity surface-emitting laser by vibrational resonance

The paper presents the results of the experimental study of an application of the phenomenon of vibrational resonance (VR) for enhancement of the response of a bistable vertical-cavity surface-emitting laser (VCSEL) to the effect of optical modulating signals. Specifically, two different cases were investigated: (a) the control of all-optical switching caused by a modulated orthogonal optical injection from another VCSEL and (b) the amplification of autodyne signals from a vibrating diffusely reflecting surface in the self-mixing optical interferometry. It is experimentally demonstrated that an application of the phenomenon of VR in both cases studied leads to a strong amplification of the input optical signals by a factor from 10 to 200 depending on the experimental conditions with respect to the initial values. The effect of the asymmetry of a bistable potential on the amplification factor was also studied. The results obtained can be used to improve all-optical switchings for application in communication systems and enhancement of autodyne signals in self-mixing optical interferometry. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Vibrational resonances in driven oscillators with position-dependent mass

The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM). We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework for determining the response amplitude of PDM systems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximize the efficiency of devices being operated in VR modes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.

Entropic vibrational resonance

We demonstrate the existence of vibrational resonance associated with the presence of an uneven boundary. When the motion of a Brownian particle is confined in a region with an uneven boundary, constrained to a double cavity, a high-frequency signal may produce a peak in the spectral power amplification of the other low-frequency signal and therefore to the appearance of the vibrational resonance phenomenon. The mechanism of vibrational resonance in constrained boundaries is different from that in energetic potentials and is termed entropic vibrational resonance (EVR). The EVR can be observed even if the bias force is absent in any direction. Through careful analysis, we clarify two types of mechanisms of the EVR. The one mechanism is ascribed to the transition from a bistable system to a monostable system, and the other corresponds to the match between the escape rate and the natural frequency of the low-frequency signal. Our work merges the vibrational resonance with an uneven boundary, thus extending the scope of the vibrational resonance and shedding new light on the concept of resonance.

Quantum vibrational resonance in a dual-frequency-driven Tietz-Hua quantum well

We investigate the response of a quantum particle in the Tietz-Hua quantum potential driven by biharmonic fields: a low-frequency force and a very high frequency force. The response is characterized by the occurrence of a maximum in the first-order transition probability amplitude |s|^{2} under the influence of the applied fields. It is shown that in the absence of the high-frequency component of the applied fields, |s|^{2} shows a distinct sequence of resonances, whereas an increase in the amplitude of the high-frequency field induces minima in |s|^{2}. However, the |s|^{2} maximum occurs in the low-frequency regime where it may be considered otherwise weak in the presence of a single harmonic force.

A microscopic Kapitza pendulum

Pyotr Kapitza studied in 1951 the unusual equilibrium features of a rigid pendulum when its point of suspension is under a high-frequency vertical vibration. A sufficiently fast vibration makes the top position stable, putting the pendulum in an inverted orientation that seemingly defies gravity. Kapitza’s analytical method, based on an asymptotic separation of fast and slow variables yielding a renormalized potential, has found application in many diverse areas. Here we study Kapitza’s pendulum going beyond its typical idealizations, by explicitly considering its finite stiffness and the dissipative interaction with the surrounding medium, and using similar theoretical methods as Kapitza. The pendulum is realized at the micrometre scale using a colloidal particle suspended in water and trapped by optical tweezers. Though the strong dissipation present at this scale prevents the inverted pendulum regime, new ones appear in which the equilibrium positions are displaced to the side, and with transitions between them determined either by the driving frequency or the friction coefficient. These new regimes could be exploited in applications aimed at particle separation at small scales.

Vibrational resonance in an inhomogeneous medium with periodic dissipation

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

Analysis of vibrational resonance in bi-harmonically driven plasma

The phenomenon of vibrational resonance (VR) is examined and analyzed in a bi-harmonically driven two-fluid plasma model with nonlinear dissipation. An equation for the slow oscillations of the system is analytically derived in terms of the parameters of the fast signal using the method of direct separation of motion. The presence of a high frequency externally applied electric field is found to significantly modify the system's dynamics, and consequently, induce VR. The origin of the VR in the plasma model has been identified, not only from the effective plasma potential but also from the contributions of the effective nonlinear dissipation. Beside several dynamical changes, including multiple symmetry-breaking bifurcations, attractor escapes, and reversed period-doubling bifurcations, numerical simulations also revealed the occurrence of single and double resonances induced by symmetry breaking bifurcations.

Vibrational higher-order resonances in an overdamped bistable system with biharmonic excitation

Experimental evidence of vibrational higher-order resonances in a bistable vertical-cavity surface-emitting laser driven by two harmonic signals with very different frequencies is reported. The phenomenon shows up in a parameter space (the dc current, the amplitude of the high-frequency signal) as well-defined structures with multiple local maxima at higher harmonics of the low-frequency signal. Such structures appear due to a strong suppression of higher harmonics for certain values of the high-frequency amplitude and the dc current. Complexity of the structures and the total number of the local maxima depend on the harmonic order k. The behavior of nonlinear distortion factor is also studied. The experimental results are in a good agreement with the numerical results which were obtained in the model of the bistable overdamped oscillator with biharmonic excitation.