Quantum Signatures Of Nonlinear Motion In Multimode Cavity Optomechanical Systems

To find the quantum signatures of classical nonlinear dynamics is one of the most fundamental problems in nonlinear physics.We study this problem based on cavity optomechanical systems from the perspective of quantum entanglement.The most typical cavity optomechanical system is formed by the interaction of an optical resonator with a mechanical oscillator.In this system,the optical field in the cavity generates radiation pressure on the mechanical vibrator,and the vibrator starts to vibrate back and forth,which in turn affects the eigenfrequency of the cavity and the distribution of the optical field in the cavity.This effective,dynamic nonlinear coupling is a brief description of the physical mechanism of the cavity optomechanical system.By adjusting the system parameters,the system may exhibit various types of nonlinear dynamics and different quantum entanglement characteristics.In this thesis,based on a cavity optomechanical phonon laser system,we study the entanglement characteristics of the system's stable fixed point and limit cycle behaviors.We use the logarithmic negativity to calculate the quantum entanglement.Our calculations show that the quantum entanglement of the stable fixed points does not change with time,but the quantum entanglement of the limit cycles exhibit periodic oscillations with time,and its oscillation frequency is the same as the vibration frequency of the mechanical vibrator.We also studied the quantum characteristics of the classical transition from stable fixed point to limit cycle.Numerical calculations show that the quantum entanglement on the boundary line remains constant,and its value corresponds to the maximum quantum entanglement reached by the stable fixed point.In addition,the quantum entanglement at the boundary line has strong robustness to thermal noise.These properties can be used to characterize this particular classical transition behavior.