Quantum Cooling And Manipulation Of Multiple Mechanical Resonators In Cavity Optomechanical Systems

Quantum manipulation of the system involved multiple mechanical resonators has become an important research topic in cavity optomechanics.This is because this system not only provides a promising platform for investigating macroscopic mechanical coherence,quantum many-body effects,and topological energy transfer,but also can be used as high-performance sensors,transducers,and mechanical computers.To suppress the thermal noise in those applications,the simultaneous ground state cooling of these mechanical resonators becomes an obligatory and important task.Though great advances have been made in the ground-state cooling of a single mechanical resonator,the simultaneous groundstate cooling of multiple mechanical resonators remains a long-standing challenge in cavity optomechanics.Meanwhile,optical transmission and delay directly determine the information transfer efficiency and storage time,respectively.It remains a long-standing challenge to significantly broaden the linewidth of the transmission window.To solve the two problems in cavity optomechanics,we propose the two schemes to cool multiple mechanical resonators and investigate how to control the optical transmission in cavity optomechanical systems involving multiple mechanical resonators.This thesis consists of four parts.The first part is chapter one and chapter two,where we systematically introduce the concepts and structures and mechanisms of cavity optomechanical system,optomechanical cooling and optomechanical induced transparency.This is the basics of the discussions in subsequent chapters.The second part includes chapter three where we propose a cascade-cooling scheme to cool an array of mechanical resonators connected in series.The final mean phonon numbers in the two mechanical resonators are calculated exactly and the results show that the ground-state cooling is achievable in the resolvedsideband regime and under the optimal driving.By adiabatically eliminating the cavity field in the large-decay regime,we obtain analytical results of the cooling limits,which show the smallest achievable phonon numbers and the parameter conditions under which the optimal cooling is achieved.Finally,the scheme is extended to the cooling of a chain of coupled mechanical resonators.The third part is chapter four where we propose a dark-mode-breaking mechanism to realize the simultaneous ground-state cooling of multiple mechanical resonators connected to a cavity mode in parallel.In a loop-coupled configuration formed by the phonon-exchange coupling and the linearized optomechanical interactions,a nonreciprocal energy transfer induced by the quantum interference between the two paths provides an effective way to break the dark mode,and allows both the simultaneous ground-state cooling and directional flow of phonons between the two mechanical resonators.We also extend this method to the simultaneous cooling of multiple mechanical resonators.This physical mechanism can be generalized to break other dark-mode and dark-state effects in physics.The last part is chapter five where we propose a dark-mode-controlling mechanism to realize the tunable optical transmission and switching.We find that the dark-mode effect in this two-mechanicalmode optomechanical system can lead to a twice-amplified optomechanically induced transparency(OMIT)window and a higher efficiency of the second-order sideband in comparison with the case of the standard optomechanical system.This is because the effective mechanical decay rate relating to the linewidth of the OMIT window becomes a twofold increase in the weak-coupling limit.When the dark-mode effect is broken,the controllable double transparency windows appear and the second-order sideband as well as the light delay or advance is significantly enhanced.For an N-mechanical-mode optomechanical system,we find that in the presence of the dark-mode effect,the amplification multiple of the linewidth of the OMIT window is nearly proportional to the number of the mechanical modes,and that the OMIT with a single window becomes the one with N tunable windows by breaking the dark-mode effect.The study will be useful in optical information storage within a large frequency bandwidth and multi-channel optical communication based on optomechanical systems.The cascade-cooling and dark-mode-breaking mechanisms proposed in this thesis are useful for quantum manipulation of the system involved multiple mechanical resonators.In particular,this dark-mode-breaking mechanism is universal and can be generalized to break the dark-state or dark-mode effects in other physical systems.