玻色—爱因斯坦凝聚体腔光机械系统中的光传播特性研究
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摘要
光机械系统是近年来被提出并引起广泛关注的一个研究课题。一个典型的光机械系统一般由一个纳米光腔和一个纳米机械振子耦合形成。在该系统中,内腔场强辐射压驱动机械振子在其固有频率附近作机械振动,而该振动反过来将会调制光场的分布,因而在场辐射压作用下,机械振子和光场由于相互调制而耦合在一起。因为光机械系统把光场与力学元件耦合在了一起,因此我们可以通过改变光场来调节力学元件的运动状态,如通过控制光场可以实现将力学振动冷却至其振动基态。相反,我们也可以通过改变力学元件的特征而实现对光场的有效调节。基于此原因,光机械系统在精密测量、经典及量子信息处理、光开关及光存储等领域有着潜在的应用价值。
在玻色-爱因斯坦凝聚体与光腔耦合的系统中,实验证明玻色-爱因斯坦凝聚体在光腔中的集体振动可近似看做一个机械振子的简谐振动,在内腔场辐射压的作用下,该振动与内腔场耦合在一起,形成一个典型的光机械系统。在本论文中,我们研究了玻色-爱因斯坦凝聚体腔光机械系统中的非线性光学效应及光传播特征。通过求解体系满足的海森堡运动方程并利用腔满足的输入-输出关系,我们得到了探测光的透射率及四波混频的相对输出强度。以实验数据为实际参数,我们进行了具体的数值计算,分别讨论了在有效腔-泵浦失谐量满足“红”失谐和“蓝”失谐条件下泵浦光场对探测光场透射谱的调控作用。我们研究了该耦合系统中的慢光效应及四波混频效应,并基于该光机械系统提出了实现全光晶体管和单光子路由器的设计方案。全文共分为如下六章。
在第一章中,介绍了几种典型的光机械系统并对其研究进展做了较为详细的综述,介绍了慢光效应及全光开关和全光晶体管的研究进展,最后介绍了本论文的研究内容及全文的结构安排。
在第二章中,研究了玻色-爱因斯坦凝聚体腔光机械系统中的慢光效应。在该系统中,由于内腔场辐射压驱动玻色-爱因斯坦凝聚体的集体振动与内腔场相耦合,因此,玻色-爱因斯坦凝聚体的集体振动将改变腔的有效长度因而调节腔的有效频率。当有效腔-泵浦失谐量满足“红”失谐条件时,在泵浦光场的驱动下,共振探测光束通过该耦合系统时将受到泵浦场的有效调制。随着泵浦场振幅的增大,共振探测光的透射率增大,其相位也急剧增加。因而共振探测光的群速度将大大减小,即探测光会发生延迟。研究结果表明,在该系统中探测光的延迟时间最长可达0.8ms.
在第三章中,研究了在有效腔-泵浦“蓝”失谐条件下玻色-爱因斯坦凝聚体与光腔耦合形成的光机械系统中的光传播特征。在“蓝”失谐条件下,由于玻色-爱因斯坦凝聚体的集体振动和内腔场的相互作用哈密顿量呈现放大的特征,因此当泵浦光功率达到某一临界值时,系统相互作用项的放大特征将起主要作用,共振探测光的透射将被有效地放大。共振探测光的放大率起初随着泵浦光功率的增大而增大,最后随之趋于饱和。根据“蓝”失谐条件下泵浦光对共振探测光的放大作用,我们提出了利用玻色-爱因斯坦凝聚体腔光机械系统实现全光晶体管的方案。
在第四章中,研究了玻色-爱因斯坦凝聚体腔光机械系统中的四波混频效应。在该耦合系统中,由于在内腔场辐射压的驱动下玻色-爱因斯坦凝聚体的集体振动与内腔场耦合,因而在玻色-爱因斯坦凝聚体集体振动的激发下,腔内将发生由两个泵浦光子和一个探测光子参与的四波混频过程。研究表明,泵浦光场对四波混频的产生起开关的作用,四波混频的输出强度随泵浦场功率的增大而增大并最后趋于饱和。
在第五章中,研究了玻色-爱因斯坦凝聚体与双边透射腔耦合形成的光机械系统中的光传播特征。在该耦合系统中,由于光腔是双边透射腔,因而探测光子既可以从右腔镜透出也可以从左腔镜透出。我们研究了该系统中泵浦光在满足有效腔-泵浦“红”失谐条件下对探测光透射的调控作用。研究表明,当仅用一束共振探测光驱动该耦合系统时,共振探测光将完全从右腔镜透出；而当用理想功率的泵浦光以及共振探测光共同驱动该系统时,共振探测光却完全从左腔镜透出。因而,在该系统中,可以通过调节泵浦光来有效地控制探测光的路径。根据这一原理,我们提出了基于该耦合系统实现单光子路由器的设计方案。
第六章对本论文的研究成果做了详细的总结并对后续的研究工作做了进一步的展望.
本论文的研究得到了国家自然科学基金(10774101和10974133)和教育部高校博士点基金的资助。
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.
在玻色-爱因斯坦凝聚体与光腔耦合的系统中,实验证明玻色-爱因斯坦凝聚体在光腔中的集体振动可近似看做一个机械振子的简谐振动,在内腔场辐射压的作用下,该振动与内腔场耦合在一起,形成一个典型的光机械系统。在本论文中,我们研究了玻色-爱因斯坦凝聚体腔光机械系统中的非线性光学效应及光传播特征。通过求解体系满足的海森堡运动方程并利用腔满足的输入-输出关系,我们得到了探测光的透射率及四波混频的相对输出强度。以实验数据为实际参数,我们进行了具体的数值计算,分别讨论了在有效腔-泵浦失谐量满足“红”失谐和“蓝”失谐条件下泵浦光场对探测光场透射谱的调控作用。我们研究了该耦合系统中的慢光效应及四波混频效应,并基于该光机械系统提出了实现全光晶体管和单光子路由器的设计方案。全文共分为如下六章。
在第一章中,介绍了几种典型的光机械系统并对其研究进展做了较为详细的综述,介绍了慢光效应及全光开关和全光晶体管的研究进展,最后介绍了本论文的研究内容及全文的结构安排。
在第二章中,研究了玻色-爱因斯坦凝聚体腔光机械系统中的慢光效应。在该系统中,由于内腔场辐射压驱动玻色-爱因斯坦凝聚体的集体振动与内腔场相耦合,因此,玻色-爱因斯坦凝聚体的集体振动将改变腔的有效长度因而调节腔的有效频率。当有效腔-泵浦失谐量满足“红”失谐条件时,在泵浦光场的驱动下,共振探测光束通过该耦合系统时将受到泵浦场的有效调制。随着泵浦场振幅的增大,共振探测光的透射率增大,其相位也急剧增加。因而共振探测光的群速度将大大减小,即探测光会发生延迟。研究结果表明,在该系统中探测光的延迟时间最长可达0.8ms.
在第三章中,研究了在有效腔-泵浦“蓝”失谐条件下玻色-爱因斯坦凝聚体与光腔耦合形成的光机械系统中的光传播特征。在“蓝”失谐条件下,由于玻色-爱因斯坦凝聚体的集体振动和内腔场的相互作用哈密顿量呈现放大的特征,因此当泵浦光功率达到某一临界值时,系统相互作用项的放大特征将起主要作用,共振探测光的透射将被有效地放大。共振探测光的放大率起初随着泵浦光功率的增大而增大,最后随之趋于饱和。根据“蓝”失谐条件下泵浦光对共振探测光的放大作用,我们提出了利用玻色-爱因斯坦凝聚体腔光机械系统实现全光晶体管的方案。
在第四章中,研究了玻色-爱因斯坦凝聚体腔光机械系统中的四波混频效应。在该耦合系统中,由于在内腔场辐射压的驱动下玻色-爱因斯坦凝聚体的集体振动与内腔场耦合,因而在玻色-爱因斯坦凝聚体集体振动的激发下,腔内将发生由两个泵浦光子和一个探测光子参与的四波混频过程。研究表明,泵浦光场对四波混频的产生起开关的作用,四波混频的输出强度随泵浦场功率的增大而增大并最后趋于饱和。
在第五章中,研究了玻色-爱因斯坦凝聚体与双边透射腔耦合形成的光机械系统中的光传播特征。在该耦合系统中,由于光腔是双边透射腔,因而探测光子既可以从右腔镜透出也可以从左腔镜透出。我们研究了该系统中泵浦光在满足有效腔-泵浦“红”失谐条件下对探测光透射的调控作用。研究表明,当仅用一束共振探测光驱动该耦合系统时,共振探测光将完全从右腔镜透出；而当用理想功率的泵浦光以及共振探测光共同驱动该系统时,共振探测光却完全从左腔镜透出。因而,在该系统中,可以通过调节泵浦光来有效地控制探测光的路径。根据这一原理,我们提出了基于该耦合系统实现单光子路由器的设计方案。
第六章对本论文的研究成果做了详细的总结并对后续的研究工作做了进一步的展望.
本论文的研究得到了国家自然科学基金(10774101和10974133)和教育部高校博士点基金的资助。
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.
引文
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