Stochastic Resonance And Chaos In Coupled Optomechanical Systems

Stochastic resonance and chaotic motion are two kinds of interesting nonlinear behaviors,which have wide application scope and prospect in physics.Stochastic resonance has been widely used in weak signal detection as it can take advantage of the unique mechanism of noise.Meanwhile,chaos has important applications in secure communication,neural network and weak signal detection because of its sensitivity to initial value and complexity of motion.In recent years,the two behaviors have also received extensive attention in optomechanical systems.Both chaos and stochastic resonance are worth studying for the extension of basic research on nonlinear behavior and the realization of signal detection or secure communication in optomechanics systems.In this thesis,stochastic resonance and chaos in coupled optomechanical systems are studied based on the richer nonlinearity of coupled systems.Firstly,we investigate the stochastic resonance effects in a coupled optomechanical system,one of the subsystems driving by a strong control field and optical coupled with another subsystem.The results show that,under the driving of a strong control field,the two mechanical oscillators can be in the same bistable area.Adding a periodic weak signal to the first subsystem,the stochastic resonance effect can be appeared in the two mechanical positions with the appropriate thermal noise.And a standard inverted U-curve emerges for the system signal-noise-ratio,which means the weak signal acting on the first subsystem can also be output enhanced in another subsystem.Moreover,the threshold of the periodic weak signal can be reduced significantly by adding an auxiliary periodic weak signal to another subsystem.Meanwhile,the beating-like effect can be occurred while the two weak signals have a small frequency difference.This work will provide some theoretical foundations for the detection of weak signals and non-localized detection in the optomechanical systems.Secondly,we study the chaotic motion in a whispering gallery mode coupled optomechanical system,consisting of two evanescently-coupled optomechanical subsystems.A period-doubling transition to chaos can be realized in a single whispering-gallery-mode cavity,which can be regarded as a chaotic oscillator.The results show that the strong coupling results in complete synchronization of subsystems.In the case of complete synchronization,adjusting the optical coupling can make the coupling optomechanical system reproduce the periodic-doubling transition to chaos in the subsystem.When the coupling strength is relatively weak,optical coupling can make the oscillation between the two subsystems coherently,in which case the coupled system dynamics enter a higher dimensional phase space,a quasiperiodic transition to chaos can be produced when the detuning coupling system is set properly.We use power spectrum,phase space,and Lyapunov exponentsto analyse in detail the transition from quasi-periodic motion to chaos,and show the quasi-periodic path diagram of the system to chaos completely.