The Study On Mechanical Resonator Squeezing Based On Optomechanical System Under Unresolved Sideband Limit

In recent years,the optomechanical system is a rapidly growing field of the quantum information processing tasks,in which the main research is the interac-tion between light and mechanical resonator via radiation pressure,optical gradient,or photothermal forces.Originally,the goal of studying the optomechanical inter-action is to detect gravitational wave.As research continues,the optomechanical system has been developed to investigate quantum-to-classical transition studying and quantum coherence of macroscopical object.Many research projects of cavi-ty optomechanical systems have been conceived and demonstrated experimentally,such as red-sideband laser cooling,coherent-state transiting,normal-mode split-ting,macroscopical entanglement,optomechanically induced transparency,and the squeezing of mechanical resonator.The squeezing phenomenon of macroscopical mechanical resonator is very important for studying the macroscopical quantum ef-fects and the precision metrology of weak forces.As we all know,the high quality factor Q of optical cavity is contradictory with the large eigenfrequency of mechan-ical resonator and strong optomechanical coupling strength.Thus,how to achieve the quantum information processing tasks is great significance in the cavity op-tomechanical system with the low quality factor Q.We will study the squeezing phenomenon of macroscopical mechanical resonator in cavity optomechanical sys-tems with unresolved sideband limit(?>>?m).We have proposed a scheme to achieve the steady-state mechanical squeezing base on a hybrid atom-optomechanical system.In the scheme,the leakage rate of op-tical cavity is far larger than the eigenfrequency of mechanical resonator(?>>?m).The quantum interfering of atomic ensemble restrains effectively the effect of large cavity leakage rate for the mechanical resonator steady-state squeezing results.We can achieve the steady-state squeezing of mechanical resonator by using the in-trinsic nonlinearity of mechanical resonator and ground state cooling in squeezing transformed frame.The calculation effectiveness and feasibility of the scheme have been proved by numerical simulation,which indicates that the mechanical resonator steady-state squeezing can be achieved when the system parameters are chose ap-propriately.Furthermore,there is a problem of the needed large number atoms in the hybrid atom-optomechanical system.For overcoming the problem,we also propose another scheme with double-cavity optomechanical system.We theoretically analyze the reason of steady-state mechanical squeezing by a more concise computing process.We further study the relationship between the mechanical resonator squeezing and the system parameter by utilizing the nonlinearity and ground state cooling process of the mechanical resonator.And we have demonstrated the steady-state mechanical squeezing can be achieved in parametric resonance situation.At last,the correctness of calculation and the feasibility of scheme are proved by numerical simulation.