Studies On Cold Damping Feedback Cooling Of Multi-mode Mechanical Oscillator In Optomechanical Systems

Optomechanical systems describe the interactions between the optical field in the cavity and the mechanical vibration by radiation pressure.It can be used to explore the mechanical properties by using optical means,and manipulate the statistics of the cavity field by mechanically changing the boundary of the cavity.It plays an important role in quantum information processing and high-precision measurement.However,all of these potential applications are based on the fact that mechanical resonators must be cooled close to the quantum ground state of the system.Therefore,the realization of ground-state cooling for mechanical resonators has become a very important topic at the moment.At present,great progress has been made in realizing ground-state cooling of a single mechanical resonator.Simultaneous ground-state cooling of multiple mechanical resonators remains a challenge in cavity opto-mechanics.This is because the dark mode effect exists in multiple degenerate(or near-degenerate)mechanical resonators,thus hindering the simultaneous ground-state cooling of multiple mechanical resonators.In this paper,by using the cold damping feedback technology,the ground state cooling of multiple mechanical oscillators in the cavity optomechanical system at degenerate and near-degenerate locations is realized by adding auxiliary mechanical coupling(AMC).Its main contents are as follows:This article is divided into three parts.In the first part,the basic concepts and theories of cavity optomechanical system and optomechanical cooling are introduced.These contents will be the basis for the discussion in the following chapters.In the second part,we mainly introduce the ground state cooling of a single mechanical resonator in a cavity optical system.We have carried out the detailed derivation in this chapter.Starting from the motion equation of a single mechanical resonator,we deduce the quantum Langevin motion equation and the detailed calculation process of the average number of phonons.By simplifying the position spectrum of the mechanical resonator,we obtained the effective susceptibility and noise spectrum of the mechanical resonator,and made a simple explanation of the cooling mechanism by analyzing the effective damping rate and noise spectrum.Finally,we briefly analyzed and discussed the dependence of the final average phonon number on the parameters.In the third part,we propose a feedback cooling scheme for two mechanical modes.In our model,two mechanical resonators can achieve ground-state cooling simultaneously in degenerate and near-degenerate conditions by applying auxiliary mechanical coupling(AMC)to remove the dark mode effect.We obtain precise analytical solutions for effective magnetic susceptibility,net cooling rate,and mechanical frequency shift.We find that the cooling rate is significantly enhanced when AMC-off is switched to AMC-on(?_m?10~6?_m,where?_m is the decay rate of the mechanical resonator).These significantly amplified net cooling rates result in significantly enhanced cooling performance of the mechanical resonator.Physically,the AMC mechanism provides a useful strategy to remove the dark mode effect in the near-degenerate window,thereby re-establishing the cooling channel to extract the thermal phonons stored in the dark mode.Our model is general and can provide a way to cool multiple mechanical resonators in the unresolved-sideband regime by removing dark modes.