Strong Mechanical Squeezing And Optomechanical Steering Via Continuous Monitoring In Optomechanical Systems

Cavity optomechanics is a physical branch based on the interaction between light and mechanical resonators due to radiation pressure on a macroscopic scale.At present,with the rapid development of practical technologies for cavity optomechan-ics,exploring quantum effects such as superposition states,quantum entanglement and steering,light or mechanical squeezing in macroscopic optomechanical system-s has become a hot research area.Up to now,many theoretical schemes have been proposed for preparing the squeezed state of mechanical vibrators,but the maximal degree of squeezing in the steady-state regime is almost limited by 3dB(about 50%of vacuum fluctuations),and studies have shown that optomechanical system only ex-hibits very weak optomechanical steering under continuous driving.For this reason,in this paper we consider to utilize time-continuous measurement to achieve steady and strong mechanical squeezing and optomechanical steering in a cavity optomechanical system.First,we consider the generation of mechanical squeezing in a dispersively or dis-sipatively coupled optomechanical system by continuously homodyning the output field of the optomechanical cavity.The Langevin equations of motion for the cavity mode and the mechanical mode are derived according to the Hamiltonian of op-tomechanical system.Then,we invoke the semi-classical method to linearize the Hamiltonian and the Langevin equations.Next,we consider the stochastic master e-quation and the effective Hamiltonian after continuous-measurement and derive the covariance correlation matrix between the optical cavity and the mechanical oscilla-tor?The mechanical squeezing generated in different types of systems are compared by numerical calculations.It is found that strong steady-state mechanical squeezing beyond the 3 dB limit can be achieved in both of the optomechanical systems,but the properties of the squeezing are quite different for the two types of systems,and the reasons for the differences are analyzed.We also see that the combination of the two types of coupling leads the mechanical squeezing to be considerably enhanced in the regime of red detuning ?c>0,compared to the case of purely dispersive or purely dissipative coupling.In this paper,we also propose a scheme to achieve strong optomechanical steerable correlations in the dispersive or dissipative optomechanical system via continuously monitoring the position of the mechanical oscillator.The position monitoring can be realized by dispersively coupling the mechanical oscillator weakly to another bad cavity whose output field is subject to continuous homodyne detection.Similar to the process of studying mechanical squeezing,numerical analysis is performed based on the correlation matrix between the optical cavity and the mechanical oscillator.It is revealed that the monitoring can lead the steady-state optomechanical entanglement to be enhanced considerably such that strong steerable correlations can be achieved between the mechanical oscillator and the cavity field.In addition,it is found that,similar to mechanical squeezing,in the region of cavity detuning ?c>0,the optome-chanical entanglement and two-way quantum steering are also significantly improved in the combination of two kinds of coupling.Furthermore,we discuss the effects of thermal phonons and it is shown that the generated squeezing and steering are quite robust against the thermal fluctuations.