| Due to the rapid development of microfabrication and nanotechnology,cavity optomechanical system has become an ideal platform for studying macroscopic quantum phenomena and quantum information processing.so far,many significant progresses relying on cavity optomechanical platform in both experiment and theory have been made.In the aspect of quantum manipulation of mechanical modes,many quantum schemes has been proposed,such as the ground-state cooling of single or multiple mechanical oscillators,non-classical states preparation,quantum teleportation,and so on.In the aspect of quantum manipulation of cavity field,a series of quantum optical phenomena have been discovered,such as optical-mechanical induced transparency,optical-mechanical induced absorption and fast and slow light phenomena.Among these achievements,the preparation of mechanical squeezing has been a significantly important goal in both fundamental studies and numerous potential applications related to quantum computation,quantum communication,and high-precision metrology,etc.After years of development,various schemes have been proposed to realize the mechanical squeezing,even strong mechanical squeezing.One of the main methods is to use the amplitude modulation method of the driving field.On the other hand,non-Hermitian systems with PT-symmetry,whose eigenspectrum can be real,have attracted considerable attention since the pioneering work of Bender and Boettcher in 1998.Moreover,a phase transition between the unbroken-PT-symmetry and broken-PT-symmetry will occur at the exceptional point(EP),where the eigenvalues and the corresponding eigenvectors coalesce and some novel physical phenomena may appear.Therefore,PT-symmetry physics has become an active research area.Based on a double-cavity optomechanical system with PT-symmetry,combined with the drive-field amplitude modulation technique,this paper studies the mechanical squeezing in the resolved-sideband regime and the unresolved-sideband regime,respectively.The main research contents of the paper are as follows:.Firstly,this paper describes model,derives the dynamics of covariance matrix of the system,analyzed the PT symmetry in the system and calculated the expression for the EP point.Secondly,the stability of the system are analyzed.It found that the strong coupling and low gain-loss ratio are beneficial to the stability of the system,and the system is more likely to be stable in the unbroken-PT-symmetry regime than in the broken-PT-symmetry regime.Thirdly,this paper studies mechanical squeezing and robustness in both the unresolved-sideband and resolved-sideband regime.Amplitude-modulated of the external driving field makes the variation of the spring constant of the mechanical motion in time with just twice the frequency of the mechanical motion,leading to the squeezing of the mechanical mode,and the 3 d B limit of the mechanical squeezing can be broken in the resolved-sideband regime.At the same time,because the gain of the active cavity can balance a part of the dissipation of the passive cavity,the active-passive-coupled system has stronger robustness against the thermal noise than that in the passive-passive-coupled system.Finally,by analyzing the relation of mechanical mode squeezing parameter with the cavity-cavity coupling strength,it shows that the mechanical squeezing in the unbroken-PT-symmetry regime is stronger than that in the broken-PT-symmetry regime.In summary,this work can not only provide an effective quantum resource for quantum information and quantum precision measurement based on cavity optomechanics,but also may be meaningful for the study of PT-symmetric physics in the quantum regime. |
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