| Due to the great advance in nanotechnology, it is now possible tofabricate mechanical resonators with dimensions on the micro and evennanometer scale. Because of their very small masses, high frequencies andlow intrinsic dissipations, nanomechanical resonators have important ap-plications in high-precision displacement detection and mass sensing. Me-chanical resonators are also promising candidates for observing quantummechanical efects in macroscopic objects. Recently, by coupling nanome-chanical resonators to other solid-states systems such as optical cavity, mi-crowave cavity and superconducting qubits, researchers have successfullycooled the mechanical resonators to their quantum ground states, whichpaves the way towards observing nonclassical states in resonators suchas superposition states and Fock states, as well as energy quantization.Nanomechanical resonator can couple with superconducting microwavecavity via radiation pressure force, which yields an emerging research feldnamed cavity electromechanical system, where some quantum optical ef-fects have been observed. In this thesis, using the standard pump-probetechnique, we have studied the phenomenon of electromagnetically induced transparency(EIT), slow and fast light efect, and resonantly enhancedfour-wave mixing(FWM) efect in the cavity electromechanical system.Some potential applications in photonic transistor, single-photon routerand mass sensor based on this coupled system have also been discussed.On the other hand, superconducting qubits behave like artifcial atoms,which can be used to readout the nanomechanical motion and realize thequantum control of a mechanical system. Recent technological advancesmake it possible to implement quantum-optics experiments on a chip usingthese artifcial atoms. Here, we have mainly investigate theoretically themass sensing scheme based on the coupled nanomechanical resonator andCooper-pair box(charge qubit) system. Both the above two coupled sys-tems are compatible with integration on a chip, which enables them someimportant applications in solid-state quantum computation and quantuminformation. The whole thesis is consisted of six chapters.In Chapter One, we frst introduce some basic theories about cavityoptomechanical systems and provide some experimentally realized exam-ples. Then we give some special emphasis on the introduction of recentdevelopments in the fled of cavity electromechanical systems, which is thesystem we'll study. Introduction to the research backgrounds of supercon-ducting qubits and their couplings to nanomechanical resonators is alsogiven. Finally, we introduce the phenomenon of electromagnetically in-duced transparency(EIT) and resonantly enhanced three-order nonlinearprocess based on EIT.In Chapter Two, we investigate the phenomenon of electromagnet-ically induced transparency(EIT) as well as slow and fast light efect incavity electromechanical system. When the cavity is driven by a properred-detuned pump feld, a narrow transparency window will appear inprobe transmission spectrum, which can be further broadened by increas- ing the power of the pump feld. Slow light efect appears at this time,and the maximum time delay can reach about0.2ms. However, whenthe cavity is driven by a blue-detuned pump feld, fast light efect willappear, and the time delay is a negative value. Therefore, the transitionbetween slow light and fast light efect can be achieved by modulating thefrequency of the pump feld, and the magnitude of the time delay can becontrolled by the power of the pump feld.In Chapter Three, the controllable nonlinear response of the cavityelectromechanical system is investigated. We frst study the bistable be-havior of intracavity photon number in this system, that is, two stablevalues of the intracavity photon number may exist if the frequency andpower of the pump feld are properly chosen. Then we study the resonantlyenhanced four-wave mixing(FWM) under conditions of EIT. When thetwo-photon resonance condition is satisfed, the magnitude of FWM, animportant three-order nonlinear process, can be enhanced greatly. More-over, the magnitude can be further increased by enlarging the power ofthe pump feld.In Chapter Four, we demonstrate two potential applications of cavityelectromechanical system in photonic transistor and single-photon router.When the cavity is driven by a blue-detuned pump feld, the magnitudeof the transmitted probe feld on resonance can exceed unity, thus themicrowave signal can be amplifed in this case, which can be employed asa photonic transistor. However, when the cavity is driven by a red-detunedpump feld, the probe feld on resonance can be totally transmitted if thepump power increases above a critical value, while the probe feld wouldbe totally refected in the absence of the pump feld. Therefore, we canuse a controllable pump feld to choose what output port of the probe feldis delivered. Routing between the refection output port and transmission output port can be achieved by turning of and on the pump feld.In Chapter Five, we present a scheme for mass sensing in tiny objectssuch as DNA molecule based on cavity electromechanical system as wellas the coupled nanomechanical resonator and Cooper-pair box system.Because the mass and intrinsic dissipation of the nanomechanical resonatorare very small, a frequency shift of the resonator will be induced by landinga tiny object on it. Two sharp sideband peaks appear exactly at theresonance frequency of the resonator in the transmission or absorptionspectrum of the above two systems, which provides us an efcient way tomeasure the frequency of the resonator and the corresponding frequencyshift after adsorption. According to the relation between the frequencyshift and the added mass, we can obtain the mass.In Chapter Six, it is the main conclusions and the prospect.This work was supported by the National Natural Science Foundationof China under contract NO.10774101and No.10974133, as well as theNational Ministry of Education Program for Training Ph.D.
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