Propagation Properties Of Light In A Cavity Optomechanical System With A Bose-einstein Condensate

Optomechanical system has been proposed and attracted much at-tention in recent years. A generic optomechanical system is composed ofan optical nanocavity and a nanomechanical resonator. In such a sys-tem, the strong raidation pressure of the light drives the motion of theresonator near its resonance frequency, which will give feedback on thecavity field by modulating the optical path length of the cavity. As a re-sult, the nanomechanical resonator strongly couples to the cavity field bythe radiation pressure. Due to the fact that an optomechanical system isa hybrid structure consisting of an optical element (an optical nanocavity)and a mechanical element (a nanomechanical resonator), the motion stateof the mechanical element can be efectively modulated just by controllingthe optical field in such a coupled system. For example, a mechanical res-onator, coupling to an optical cavity, can be cooled to its quantum groundstate by the radiation pressure from the cavity field. For the other hand,the optical field in the optomechanical system can also be regulated bymodulating the mechanical element. For the reasons above, the optome-chanical system will have potential applications in sensitive measurement,classical or quantum information processing, optical switching or storage,and so on. In a coupled BEC(Bose-Einstein condensate)-cavity system, the col-lective oscillation of the BEC can be serve as a mechanical resonator, whichhas been demonstrated by the present experiments. Such a resonatorstrongly couples to the cavity field by the radiation pressure, which willmake the coupled BEC-cavity system present as a generic optomechani-cal system by analogy. In this thesis, the nonlinear optical efects as wellas the light propagation in the cavity optomechanical system with a BEChave been discussed detailedly. By solving Heisenberg equations of motionand then using an input-output relation for the cavity, the transmission ofthe probe laser and the relative output intensity of the four wave mixingcan be obtained. Taking the experiment data as realistic parameters, thenumerical results for the transmission of the probe laser as well as the out-put of the four wave mixing are presented. The slow light efect and thefour wave mixing efect in the cavity optomechanical system with a BEChave been discussed theoretically, and an all optical transistor as well asa single photon router based on this coupled system have been proposed.The whole thesis includes the following six chapters.In Chapter One, several typical optomechanical systems as well asthe related researches are introduced, the research progress of the slowlight efect, all optical switch, and all optical transistor is also reviewedin detail, and finally, the contents as well as the outline of this thesis areshown.In Chapter Two, the slow light efect in the cavity optomechanicalsystem with a BEC is studied. In this coupled system, the collectiveoscillation of the BEC serves as a mechanical resonator which stronglycouples to the cavity field by the radiation pressure, and as a result, theefective length thus the efective frequency of the cavity is modulated bythe collective oscillation of the BEC. While driving this system by a pump laser with a red cavity-pump detuning, the propagation of the probe laserthrough the cavity on resonance can be efectively modulated by the pumplaser. Increasing the amplitude of the pump laser, the transmission of theprobe laser on resonance will be enhanced and the phase of the probelaser will sufer a sharp increase, which will result in a large decrease ofthe group velocity of the probe laser, i.e., the probe laser through thecoupled BEC-cavity system will be delayed. The calculated results showthat the delayed time is as much as0.8ms.In Chapter Three, the propagation of the probe laser in the BEC-cavity optomechanical system with a blue cavity-pump detuning is stud-ied. Under blue detuned pumping, the efective interaction Hamiltonianbetween the collective oscillation of the BEC and the cavity field becomesone of parametric amplification. Therefore, when the power of the pumplaser is increased so large as to surpass the critical value, the interactionbetween the oscillator and the cavity field will play a main role for con-trolling the propagation of the probe laser in the cavity. As a result, theprobe laser will significantly be amplified. The transmission of the ampli-fied probe laser initially increases and finally approaches saturation withthe increase of the pump power. Based on the amplification efect onthe probe laser in the coupled BEC-cavity system, a practical scheme forrealizing an all optical transistor based on this coupled system is proposed.In Chapter Four, the four wave mixing efect in the cavity optome-chanical system with a BEC is discussed. In such a coupled system, thecollective oscillation of the BEC couples to the cavity field by the strongradiation pressure from the intracavity field, and as a result, a four wavemixing process will be induced by the collective oscillation of the BEC.The calculated results show that the pump laser can efectively switch theprocess of the four wave mixing, and the relative output intensity of the four wave mixing is sensitively dependent on the power of the pump laser.Initially, the relative output intensity increases quickly with the increasingpower of the pump laser, and finally, it approaches saturation.In Chapter Five, the propagation of the probe laser in the cavity op-tomechanical system, which is composed of a cavity with two transmissionsides and a trapped BEC, is studied in detail. For such a coupled system,the probe photon in the cavity can transmit from the left mirror or fromthe right one. In this chapter§the dependence of the route of the probephoton on the pump laser with a red cavity-pump detuning is discussed.The results show that the probe photon will transmit from the right mir-ror in the absence of the pump laser, but will leave the cavity from itsleft mirror while applying a pump laser with an appropriate power to thecavity. Due to the fact that the pump laser can efectively control theroute of the probe photon, this coupled BEC-cavity can sever as a singlephoton router.In Chapter Six, the main results obtained are summarized in detailand the future researches for the cavity optomechanical system with aBEC are discussed.This work was supported by the National Natural Science Founda-tion of China (Grants NO.10774101and No.10974133) and the NationalMinistry of Education Program for Training Ph.D.