Ground-state Cooling And Squeezing In A Two-mechanical-mode Optomechanical System

Recently,cavity optomechanics,as a subject of studying the interaction between a radiation field and mechanical oscillation,has become an exciting research area for exploring quantum behavior in macroscopic systems as well as applications in quan-tum information processing.It is widely used for studying quantum phenomena on the macroscopic scale,such as ground-state cooling of the mechanical resonator,macroscopic entanglement,blockade effect,mechanical squeezing,ultrahigh precision metrology,and quantum-classical-mechanics boundary etc.However,the realization of these quantum effects may be destroyed due to the inevitable environmental thermal noise.It is a prerequi-site to cool the mechanical resonators to their ground-state for these potential applications.On the other hand,the study of squeezed-state in an optomechanical system have provided new methods and approaches for applications in high-sensitivity displacement detection,biological measurements,and gravitational wave detection.As we all know,the request of high quality factor Q for optical cavity is contradictory with the large eigenfrequency of mechanical resonator and strong optomechanical coupling strength.Thus,how to achieve the quantum information processing tasks in the cavity optomechanical system with the low quality factor Q is an urgent problem to be solved.We will study the cooling and squeezing effect of macroscopical mechanical resonator in cavity optomechanical system with unresolved sideband limit(k>>?m).The main contents are arranged as follows:Firstly,we propose a theoretical scheme for improving the cooling of two coupled mechanical resonators by imposing periodic frequency modulation upon the system to suppress the Stokes heating processes.By the methods of covariance analysis and nu-merical simulations,it is demonstrated that the cooling of double mechanical resonators can be realized in both stable and unstable regions with high efficiency compared to the cooling without frequency modulation,even if in unresolved sideband regime.By adjusting the system parameters appropriately,the cooling efficiencies of two mechanical resonators can be manipulated.Secondly,we propose a scheme to generate quadrature-squeezed states of double mechanical resonators using periodic amplitude modulation in an optical cavity embed-ded with an atomic ensemble.By the methods of covariance analysis and numerical simulations,the results show that compared with the optomechanical system without atomic ensemble,the introduction of atomic ensemble greatly reduces the fluctuation of mechanical resonators in one quadrature,and the two mechanical resonators can be in a quadrature-squeezed-state simultaneously under the periodic amplitude driving.This scheme can be extended to the squeezing for the multiple mechanical resonators.