Study On Common Quantum Features Across The Instability Boundary In Optomechanical System

The cavity optomechanical system is composed of the optical resonant cavity and the mechanical vibrator coupled by radiation pressure,whose interaction can produce many interesting nonlinear phenomena.When the system is driven by the blue-detuned laser to reach the threshold of the instability boundary,the mechanical vibrator will produce self-sustained oscillation.In the region near the instability boundary,the system is highly sensitive to external disturbances due to strong nonlinear response,which is beneficial to amplify some physical effects or improve the sensing accuracy.As the ground state cooling technology of the vibrator develops,the system enters into the quantum region,and this highly sensitive property is expected to be applied to quantum sensing and other fields.Therefore,it is necessary to study the quantum properties of the system across the instability boundary.In this paper,based on the stability phase diagram,the common quantum features of the system along different parameter paths across the instability boundary under the strong coupling condition have been studied by numerically solving the Lindblad quantum master equation.According to the steady-state Wigner distribution characteristics of the mechanical vibrator,every parameter path can be divided into three regions: Gaussian state,transitional state,and Ring state.We have studied the steady-state Wigner distribution of the mechanical mode in the transitional region connecting the Gaussian state and the ring state,and found that the change of the mechanical steady-state Wigner distribution in it can directly reflect the corresponding bifurcation behaviors in classical dynamics,mainly including two types: the first is the supercritical Hopf bifurcation occurring at the instability boundary; the second is the saddle-node bifurcation occurring in the stable region and then the subcritical Hopf bifurcation occurring at the instability boundary.For the second bifurcation behavior,the transitional region will even deviate from the instability boundary and totally enter the stable region with the increase of the driving detuning.The study on the transitional region is more important compared with the instability boundary: On the one hand,the mechanical quantum second-order coherence function and the optomechanical entanglement,can be used to judge the corresponding bifurcation types in classical dynamics and estimate the parameter width and position of the transitional region.For example,the mechanical quantum second-order coherence function will have a spike in the transitional region as a signal for the saddle-node bifurcation,which is a feature that the first bifurcation behavior does not have.On the other hand,the entanglement of non-Gaussian states in transitional regions under different bifurcation behaviors is strongly robust to the thermal phonon noises,which is consistent with the conclusion that the entanglement is robust at the instability boundary under the weak coupling conditions.It is suggested that under the strong coupling conditions,the transitional region as a new boundary ribbon is expected to replace the instability boundary and become an important parameter region in future research applications.