纳米机械振子与超导电路耦合系统中的量子效应研究及其应用
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摘要
随着纳米技术的不断进步，机械振子的尺寸已经可以做到微米甚至纳米尺度.纳米机械振子通常具有极小的质量，较高的共振频率以及较低的耗散，因此在高精度位移测量、质量测量等方面有着重要的应用.此外，机械振子是观察宏观物体量子力学效应的一个很好的平台.通过将纳米机械振子耦合于不同的固体系统，比如光腔或者微波腔以及超导量子比特，研究人员最近在实验上成功地将机械振子冷却到量子基态，这为观察振子中叠加态、Fock态等非经典态以及能量量子化铺平了道路.纳米机械振子与超导微波腔之间通过辐射压力有效地耦合起来，形成了近年来一个新兴的研究领域—腔电机械系统，该系统中一些量子光学效应已经被观察到.本文中我们采用标准的泵浦-探测技术，研究了腔电机械系统中的电磁诱导透明现象和快慢光效应以及共振增强的四波混频现象，并且讨论了该系统在光子晶体管、单光子路由器以及质量传感器等方面的潜在应用.另一方面，超导量子比特是一种人造的两能级原子系统，可作为辅助系统用来读取纳米机械振子的运动，实现机械系统的量子调控.最近的技术进步使得利用这种人造两能级系统进行一些芯片上的量子光学实验变得可能.本文中我们理论上研究了纳米机械振子与库珀对盒子(电荷量子比特)耦合系统在质量测量上的应用.这两种耦合系统都易于集成在芯片上，从而在固态量子计算和量子信息中都有着重要的应用.论文共分为六章.
在第一章中，我们首先介绍了腔光机械系统的一些基本理论并举例说明了实验上实现的几种腔光机械系统，然后着重介绍了我们所研究的腔电机械系统的一些最新进展.此外，本章还介绍了三种基本的超导量子比特以及与纳米机械振子耦合系统的一些研究背景.最后，我们介绍了本论文研究的基础—电磁诱导透明现象及共振增强的三阶非线性效应.
在第二章中，我们研究了腔电机械系统中的电磁诱导透明现象和快慢光效应.当微波腔受到红失谐的泵浦场驱动时，辐射压力的作用使得探测场的透射谱中腔共振附近出现一个窄的透明窗口，且透明窗口的宽度随泵浦场功率增大而变宽，即出现了电磁诱导透明现象.此时系统中存在慢光效应，探测场的延迟时间最大可达到0.2ms.但当微波腔受到蓝失谐的泵浦场驱动时，系统中将出现快光效应，此时探测场的延迟时间为一负值.因此，通过改变泵浦场与腔场之间的失谐量可实现快慢光效应之间的转变，并且延迟时间的大小可由泵浦场的功率进行调节.
在第三章中，我们研究了腔电机械系统中可调的非线性效应.首先我们讨论了该系统中腔内光子数的双稳态现象，即泵浦场频率和功率选择恰当时，腔内光子数可能出现两个稳定的解.然后我们着重讨论了共振增强的四波混频现象.当满足电磁诱导透明的双光子共振条件时，四波混频作为一种重要的三阶非线性效应可被共振增强，并且随着泵浦场功率的增大四波混频的强度可被进一步提高.
在第四章中，我们讨论了腔电机械系统在光子晶体管和单光子路由器中的应用.当微波腔受到蓝失谐的泵浦场驱动时，探测场的透射率可出现大于1的情况，即微波信号可被放大，此时系统可用作光子晶体管.当微波腔受到红失谐的泵浦场驱动时，泵浦场功率达到一定强度后，腔共振处探测场将全部透射，但当泵浦场功率为零时，腔共振处探测场将被全部反射.因此可用一束可调的泵浦场来选择探测场从哪个输出口输出，反射出口和透射出口之间的路由可通过关闭和打开泵浦场实现.
在第五章中，我们研究了腔电机械系统以及纳米机械振子与库珀对盒子耦合系统在微小物质比如DNA分子质量测量方面的应用.由于纳米机械振子的质量和耗散极小，吸附微小物质后将导致其共振频率发生移动.这两种耦合系统的透射谱或者吸收谱中机械振子共振频率处会出现尖锐的边峰，因此可用于测量振子的共振频率以及吸附物质后的频率移动.根据移动的频率与增加的质量之间的关系，我们即可得到吸附物质的质量.
第六章是本文的主要结论和展望.
以上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.
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.
在第一章中，我们首先介绍了腔光机械系统的一些基本理论并举例说明了实验上实现的几种腔光机械系统，然后着重介绍了我们所研究的腔电机械系统的一些最新进展.此外，本章还介绍了三种基本的超导量子比特以及与纳米机械振子耦合系统的一些研究背景.最后，我们介绍了本论文研究的基础—电磁诱导透明现象及共振增强的三阶非线性效应.
在第二章中，我们研究了腔电机械系统中的电磁诱导透明现象和快慢光效应.当微波腔受到红失谐的泵浦场驱动时，辐射压力的作用使得探测场的透射谱中腔共振附近出现一个窄的透明窗口，且透明窗口的宽度随泵浦场功率增大而变宽，即出现了电磁诱导透明现象.此时系统中存在慢光效应，探测场的延迟时间最大可达到0.2ms.但当微波腔受到蓝失谐的泵浦场驱动时，系统中将出现快光效应，此时探测场的延迟时间为一负值.因此，通过改变泵浦场与腔场之间的失谐量可实现快慢光效应之间的转变，并且延迟时间的大小可由泵浦场的功率进行调节.
在第三章中，我们研究了腔电机械系统中可调的非线性效应.首先我们讨论了该系统中腔内光子数的双稳态现象，即泵浦场频率和功率选择恰当时，腔内光子数可能出现两个稳定的解.然后我们着重讨论了共振增强的四波混频现象.当满足电磁诱导透明的双光子共振条件时，四波混频作为一种重要的三阶非线性效应可被共振增强，并且随着泵浦场功率的增大四波混频的强度可被进一步提高.
在第四章中，我们讨论了腔电机械系统在光子晶体管和单光子路由器中的应用.当微波腔受到蓝失谐的泵浦场驱动时，探测场的透射率可出现大于1的情况，即微波信号可被放大，此时系统可用作光子晶体管.当微波腔受到红失谐的泵浦场驱动时，泵浦场功率达到一定强度后，腔共振处探测场将全部透射，但当泵浦场功率为零时，腔共振处探测场将被全部反射.因此可用一束可调的泵浦场来选择探测场从哪个输出口输出，反射出口和透射出口之间的路由可通过关闭和打开泵浦场实现.
在第五章中，我们研究了腔电机械系统以及纳米机械振子与库珀对盒子耦合系统在微小物质比如DNA分子质量测量方面的应用.由于纳米机械振子的质量和耗散极小，吸附微小物质后将导致其共振频率发生移动.这两种耦合系统的透射谱或者吸收谱中机械振子共振频率处会出现尖锐的边峰，因此可用于测量振子的共振频率以及吸附物质后的频率移动.根据移动的频率与增加的质量之间的关系，我们即可得到吸附物质的质量.
第六章是本文的主要结论和展望.
以上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.
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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