Studies On The Quantum Entanglement Properties Of Instability Boundary In Optomechanical Systems

Cavity optomechanical systems are formed by the coupling of mechanical oscillators and optical cavities through radiation pressure force.The coupling between these two is nonlinear,which makes the system contain rich nonlinear dynamic behaviors.When the temperature goes down sufficiently low,various quantum effects of the system will show up,therefore,optomechanical systems are very suitable for studying the corresponding relationship between classical nonlinear dynamic behavior and quantum properties.Based on the two-dimensional stability phase diagram of a three-mode cavity optomechanical system,it has been found that the entanglement on the instability boundary line remains unchanged when the stable fixed points transform into limit cycles.In order to find the condition under which the boundary entanglement remains unchanged and explain the mechanism of this phenomenon,further research is done in this thesis by combining the three-mode and the two-mode cavity optomechanical systems.In order to find the condition under which the boundary entanglement remains con-stant,we discuss the influence of various parameters on boundary entanglement.It is found that the necessary condition for boundary entanglement to remain unchanged is that the frequency difference between the two optical supermodes and the mechanical frequency equal to each other,and the boundary entanglement is proportional to the de-cay rate of the mechanical oscillator,independent of the single-photon optomechanical coupling strength and the frequency of the mechanical oscillator.Further,we try to un-derstand why the boundary entanglement is constant based on a simpler two-mode system.With the help of analytical calculation,we have studied the boundary entanglement of the system in the whole detuning region,and found that the phenomenon that boundary en-tanglement remains unchanged only shows up in the weak mechanical dissipation region.In addition,the influence of various parameters on boundary entanglement in the weak mechanical dissipation region is discussed,and it is found that the parameter dependence is quite similar with that of the three-mode system,indicating that the two-mode system fully captures the main characteristics of the three-mode system.At the same time,we find that the invariant behavior of boundary entanglement is actually the slowly chang-ing behavior of the boundary entanglement function.The most important thing is that this almost invariant boundary entanglement is a common phenomenon in the process of parameter down-conversion under the condition of weak mechanical dissipation.The phenomenon of boundary entanglement being constant is interesting as a quantum prop-erty of threshold in optomechanical phonon lasers and may have potential value in related applications based on boundary quantum properties.