低维纳米结构中微弱光电信号传输的基本物理问题
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摘要
人们对信息高效存储和准确处理的需要,促使作为信息技术和微电子工业基础的现代集成电路技术向更高集成度、更快运算速度、更低功耗方向发展。作为微电子技术基础的微米结构已经成为制约信息技术高速发展的瓶颈,人们急于寻找一条崭新的道路,使信息的处理发生质的改变。如今,以介观金属环、石墨烯、光子晶体波导、纳米金属等离子体波导、微波传输线、光学纳米光纤等为典型代表的低维纳米结构,由于他们的量子效应具有很强的可控性,使得他们在微电子、光电子器件、超高密度存储、量子计算机的物理实现等方面具有潜在的应用价值。因此,研究低维纳米结构中的量子相干输运,是目前物理学研究中最活跃和最具生命力的前沿领域之一。
在本论文中,我们采用量子波导理论,着重研究了介观金属环在周期性磁通驱动下的量子输运特性、低能激发电子在石墨烯的相干传输和一维光波导中的单光子相干输运等物理学前沿问题,研究发现周期性势垒驱动下的介观环系统中出现了光子辅助隧穿,并且在环上形成了明显的电流密度波；石墨烯闭环中的持续电流具有显著的尺寸效应；以及光子与二能级原子之间的耦合强度对共振光子的输运特性起着决定性作用等。研究成果有助于设计制作下一代量子开关、量子分束器等纳米元件。
具体研究了以下五个方面的内容：
第三章研究了周期性磁通驱动的介观金属环中的光子辅助隧穿。采用量子波导理论和Floquet散射理论,研究了介观环中的电子在含时磁通驱动下的动力学行为。数值结果显示,不同于静磁通驱动时的情况,电子的透射率在整数倍振荡能量时出现了涨落。这是由于电子在周期性磁通作用下,产生了一系列的边带,使得电子通过光子辅助隧穿的方式从介观环中透射出去。研究结果表明,光子辅助隧穿与动磁场的幅度和振荡频率有关。由于光子辅助隧穿明显地依赖于振荡磁通的频率,因此,双库开环系统可以用来实现对频率的精确测量,即可以通过测量电子透射率出现跳跃时的能量,从而计算出磁场的频率。
第四章研究了单库介观环在周期性磁场驱动下的电流密度波。我们采用量子波导理论和Floquet散射理论,系统地研究了电子在单环单库结构中的传输行为。研究发现当介观环在周期性磁通的驱动下,电极和环上将出现振荡的电流密度波,说明在只有一个库的电极上可以出现电流。因此,我们的数值结果指出通过调节动磁通的幅度,可以调控光子的辅助隧穿效应。当动磁通很弱时,具有不同能量的入射电子均被完全反射回来。然而强的动磁通使得反射率不再为100%。这是由于入射电子在光子辅助隧穿效应的作用下,通过吸收或发射光子,在不同的Floquet边带之间发生跃迁,导致在单库单环的电极中出现电流。
第五章研究了Dirac粒子在石墨烯结中的交流响应。采用无质量的Dirac方程和Tien-Gordon理论,系统地研究了准粒子在石墨烯结中的交流响应。当结的两边同时被外加时间周期性的外场驱动时,数值结果表明电子透射率的时间相关性与电子的入射角度有关。当电子垂直入射到石墨烯结上时,由于Klein隧穿的作用,使得其透射率始终为1,与外加势垒的高度、频率、相位等无关。当电子以一定的角度入射时,其透射率明显地依赖于势垒的高度、频率和相位。同时通过研究不同边带间的电子透射率,发现在本系统中同样存在光子辅助隧穿现象。
第六章研究石墨烯闭环的尺寸效应。采用无质量的Dirac方程,引入无穷大强制边界条件,讨论了石墨烯闭环中的Aharonov-Bohm效应。数值计算表明,外加磁通对时间反演对称性和电子的谷简并性均有影响。由于石墨烯特殊的空间反幺正对称性,使得其持续电流出现不同于金属环中的振荡特性。并且发现简并能级差和持续电流的涨落幅度等与石墨烯闭环的半径和宽度有关。这说明可以通过改变石墨烯的几何尺寸来调控它的时间反演对称性和谷简并性。
第七章研究了光子在一维光波导中的可控输运特性。光子在一维波导中被二能级原子散射时,光子透射率与耦合强度之间有直接的依赖关系。与对称耦合不同的是,我们的数值结果表明共振光子的透射率可以通过改变不同方向光子与二能级原子之间的耦合强度,从而使光子的透射率从0调节到100%。究其物理根源来自于光子被二能级原子散射之后能量和动量的再分配。因此,共振光子的透射率不仅与光子的频率有关,还与不同传输方向的光子与二能级原子之间的耦合强度有关。
The need of efficient storage and accurate processing of information urges the modern integrated circuit technology, which is the base of information technology and microelectronics industry, to develop toward higher integration level, faster computing speed, and lower power consumption. However, the micron-sized structures of microelectronic technology is said to have become the bottleneck that restricts the rapid development of information technology. Thus, scientists are anxious to find a revolutionary way to overcome this limitation, which makes the low-dimensional nano structure become the key subject investigated in such fields as modern condensed matter physics, and quantum information. Nowadays, mesoscopic metal rings, graphene, photonic crystal waveguides, nano-metal plasma waveguide, microwave transmission lines, and optical nano-fibers are considered to have potential application in next generation of devices. Because of their controllable quantum effects, the study of the quantum coherent transporting along these low-dimensional nanostructures is one of the active domains in microelectronics, optoelectronics, ultra-high density storage, and quantum computers.
In this thesis, we adopt the quantum waveguide theory to investigate the single electron transport along a mesocopic ring driven by time-period magnetic fluxes, Driac fermions transmission along Graphene junction driven by two ac signals, and the single photon transport along a nano quantum optical wavguide. We find that photon assisted tunneling reveals when the mesoscopic ring driven by time-period fluxes and current density waves appear along the mesoscopic ring and the lead connected the ring and the source; The time-depend transmission of the Dirac particles in Graphene nano junction has direct relation on the input angle of the electron; The transmission probabilities of the injected photon can by adjusted by the coupling strength between the photon and the two-level atom. We believe that the findings of our studies will have great effect on the potential experimental schemes of all-optical switches and quantum beam splitters.
In chapter3, the photon-assisted tunneling of the elctron transport along the mesoscopic ring driven by time-period fluxes is investigated. We used the quantum waveguide theory combined by the Floquet scattering theorem to investigate the electron transport along an open mesoscopic ring with two leads driven by a time-periodic magnetic flux. Numerical results showed the photon-assisted tunnelings are insensitive of the amplitude of the applied static magnetic flux. The dynamic component of the applied flux induces the photon-assisted tunnelings; i.e., the number of the appeared transmission peaks. The photon-assisted tunneling investigated could be utilized to measure the frequency of the applied oscillating external field.
In chapter4, current density wave along the mesoscopic ring is studied. We used the quantum waveguide theory combined with the Floquet scattering theorem to investigate electron transport along an open mesoscopic ring with only one lead driven by a time-periodic magnetic flux. We showed particularly that a current density wave could be excited along the open ring threaded by the time-periodic magnetic flux, and a net current could also be generated in the lead connected to only an electron reservoir. Numerical results showed that the amplitude of the dynamic fluxes can modulate the photon-assisted process between the lead and the ring. When the dynamic amplitude is relatively small, the electrons with different energies are reflected back to the lead and the current in the ring is not influenced. However, with the increase of the amplitude of the dynamic flux, the reflection coefficient could be less than unit.
In chapter5, Dirac particles response the ac driven signal in Graphene in considered. By utilizing the massless Dirac equation and Tien-Gordon theory, we have investigated the quasi-particles transporting through a graphene junction driven by two different time-periodic ac signals. Our numerical results show that the time-oscillating behaviors of transmissions depend on the particles' incident angles. Due to the Klein tunneling, the transmission probabilities for the normal incidence are insensitive to static potentials, phases, and driven frequencies. However, when the electrons are incident with a fixed angle, the probabilities begin to oscillate with time.
In chapter6, we investigate the size effect in closed graphene ring. We adopt the massless Dirac equation, combined by the infinite mass boundary condition, to investigate the Aharonov-Bohm effect in a closed graphene ring driven by magnetic flux. The numerical results clearly suggest that the applied magnetic flux breaks the time reversal symmetry and lifts the valley degeneracy in graphene ring. Particularly, the energy level, the energy difference between two valleys, and the absolute amplitude of the oscillating persistent current are all sensitive to the values of the radius and the width.
In chapter7, the single photon transport aong the one dimensional qautum optical waveguide is ivestigated. We study the single-photon transport along a one-dimensional optical waveguide containing an asymmetrically-coupled two-level aotm. Differing from the symmetric coupling cases discussed previously, we showed that the transmission probabilities of the incident single photons can vary from0to100%, depending on its asymmetrical couplings with the two-level aotm. This phenomenon is related to the redistribution of energy and momentum of photons after the scattering by the two-level aotm, as the present photon-atom interaction loses the usual spatial-symmetry. When the incident photon and the two-level aotm is on resonance, the amplitude of the excited spectra can still be adjusted by the coupling strength.
在本论文中,我们采用量子波导理论,着重研究了介观金属环在周期性磁通驱动下的量子输运特性、低能激发电子在石墨烯的相干传输和一维光波导中的单光子相干输运等物理学前沿问题,研究发现周期性势垒驱动下的介观环系统中出现了光子辅助隧穿,并且在环上形成了明显的电流密度波；石墨烯闭环中的持续电流具有显著的尺寸效应；以及光子与二能级原子之间的耦合强度对共振光子的输运特性起着决定性作用等。研究成果有助于设计制作下一代量子开关、量子分束器等纳米元件。
具体研究了以下五个方面的内容：
第三章研究了周期性磁通驱动的介观金属环中的光子辅助隧穿。采用量子波导理论和Floquet散射理论,研究了介观环中的电子在含时磁通驱动下的动力学行为。数值结果显示,不同于静磁通驱动时的情况,电子的透射率在整数倍振荡能量时出现了涨落。这是由于电子在周期性磁通作用下,产生了一系列的边带,使得电子通过光子辅助隧穿的方式从介观环中透射出去。研究结果表明,光子辅助隧穿与动磁场的幅度和振荡频率有关。由于光子辅助隧穿明显地依赖于振荡磁通的频率,因此,双库开环系统可以用来实现对频率的精确测量,即可以通过测量电子透射率出现跳跃时的能量,从而计算出磁场的频率。
第四章研究了单库介观环在周期性磁场驱动下的电流密度波。我们采用量子波导理论和Floquet散射理论,系统地研究了电子在单环单库结构中的传输行为。研究发现当介观环在周期性磁通的驱动下,电极和环上将出现振荡的电流密度波,说明在只有一个库的电极上可以出现电流。因此,我们的数值结果指出通过调节动磁通的幅度,可以调控光子的辅助隧穿效应。当动磁通很弱时,具有不同能量的入射电子均被完全反射回来。然而强的动磁通使得反射率不再为100%。这是由于入射电子在光子辅助隧穿效应的作用下,通过吸收或发射光子,在不同的Floquet边带之间发生跃迁,导致在单库单环的电极中出现电流。
第五章研究了Dirac粒子在石墨烯结中的交流响应。采用无质量的Dirac方程和Tien-Gordon理论,系统地研究了准粒子在石墨烯结中的交流响应。当结的两边同时被外加时间周期性的外场驱动时,数值结果表明电子透射率的时间相关性与电子的入射角度有关。当电子垂直入射到石墨烯结上时,由于Klein隧穿的作用,使得其透射率始终为1,与外加势垒的高度、频率、相位等无关。当电子以一定的角度入射时,其透射率明显地依赖于势垒的高度、频率和相位。同时通过研究不同边带间的电子透射率,发现在本系统中同样存在光子辅助隧穿现象。
第六章研究石墨烯闭环的尺寸效应。采用无质量的Dirac方程,引入无穷大强制边界条件,讨论了石墨烯闭环中的Aharonov-Bohm效应。数值计算表明,外加磁通对时间反演对称性和电子的谷简并性均有影响。由于石墨烯特殊的空间反幺正对称性,使得其持续电流出现不同于金属环中的振荡特性。并且发现简并能级差和持续电流的涨落幅度等与石墨烯闭环的半径和宽度有关。这说明可以通过改变石墨烯的几何尺寸来调控它的时间反演对称性和谷简并性。
第七章研究了光子在一维光波导中的可控输运特性。光子在一维波导中被二能级原子散射时,光子透射率与耦合强度之间有直接的依赖关系。与对称耦合不同的是,我们的数值结果表明共振光子的透射率可以通过改变不同方向光子与二能级原子之间的耦合强度,从而使光子的透射率从0调节到100%。究其物理根源来自于光子被二能级原子散射之后能量和动量的再分配。因此,共振光子的透射率不仅与光子的频率有关,还与不同传输方向的光子与二能级原子之间的耦合强度有关。
The need of efficient storage and accurate processing of information urges the modern integrated circuit technology, which is the base of information technology and microelectronics industry, to develop toward higher integration level, faster computing speed, and lower power consumption. However, the micron-sized structures of microelectronic technology is said to have become the bottleneck that restricts the rapid development of information technology. Thus, scientists are anxious to find a revolutionary way to overcome this limitation, which makes the low-dimensional nano structure become the key subject investigated in such fields as modern condensed matter physics, and quantum information. Nowadays, mesoscopic metal rings, graphene, photonic crystal waveguides, nano-metal plasma waveguide, microwave transmission lines, and optical nano-fibers are considered to have potential application in next generation of devices. Because of their controllable quantum effects, the study of the quantum coherent transporting along these low-dimensional nanostructures is one of the active domains in microelectronics, optoelectronics, ultra-high density storage, and quantum computers.
In this thesis, we adopt the quantum waveguide theory to investigate the single electron transport along a mesocopic ring driven by time-period magnetic fluxes, Driac fermions transmission along Graphene junction driven by two ac signals, and the single photon transport along a nano quantum optical wavguide. We find that photon assisted tunneling reveals when the mesoscopic ring driven by time-period fluxes and current density waves appear along the mesoscopic ring and the lead connected the ring and the source; The time-depend transmission of the Dirac particles in Graphene nano junction has direct relation on the input angle of the electron; The transmission probabilities of the injected photon can by adjusted by the coupling strength between the photon and the two-level atom. We believe that the findings of our studies will have great effect on the potential experimental schemes of all-optical switches and quantum beam splitters.
In chapter3, the photon-assisted tunneling of the elctron transport along the mesoscopic ring driven by time-period fluxes is investigated. We used the quantum waveguide theory combined by the Floquet scattering theorem to investigate the electron transport along an open mesoscopic ring with two leads driven by a time-periodic magnetic flux. Numerical results showed the photon-assisted tunnelings are insensitive of the amplitude of the applied static magnetic flux. The dynamic component of the applied flux induces the photon-assisted tunnelings; i.e., the number of the appeared transmission peaks. The photon-assisted tunneling investigated could be utilized to measure the frequency of the applied oscillating external field.
In chapter4, current density wave along the mesoscopic ring is studied. We used the quantum waveguide theory combined with the Floquet scattering theorem to investigate electron transport along an open mesoscopic ring with only one lead driven by a time-periodic magnetic flux. We showed particularly that a current density wave could be excited along the open ring threaded by the time-periodic magnetic flux, and a net current could also be generated in the lead connected to only an electron reservoir. Numerical results showed that the amplitude of the dynamic fluxes can modulate the photon-assisted process between the lead and the ring. When the dynamic amplitude is relatively small, the electrons with different energies are reflected back to the lead and the current in the ring is not influenced. However, with the increase of the amplitude of the dynamic flux, the reflection coefficient could be less than unit.
In chapter5, Dirac particles response the ac driven signal in Graphene in considered. By utilizing the massless Dirac equation and Tien-Gordon theory, we have investigated the quasi-particles transporting through a graphene junction driven by two different time-periodic ac signals. Our numerical results show that the time-oscillating behaviors of transmissions depend on the particles' incident angles. Due to the Klein tunneling, the transmission probabilities for the normal incidence are insensitive to static potentials, phases, and driven frequencies. However, when the electrons are incident with a fixed angle, the probabilities begin to oscillate with time.
In chapter6, we investigate the size effect in closed graphene ring. We adopt the massless Dirac equation, combined by the infinite mass boundary condition, to investigate the Aharonov-Bohm effect in a closed graphene ring driven by magnetic flux. The numerical results clearly suggest that the applied magnetic flux breaks the time reversal symmetry and lifts the valley degeneracy in graphene ring. Particularly, the energy level, the energy difference between two valleys, and the absolute amplitude of the oscillating persistent current are all sensitive to the values of the radius and the width.
In chapter7, the single photon transport aong the one dimensional qautum optical waveguide is ivestigated. We study the single-photon transport along a one-dimensional optical waveguide containing an asymmetrically-coupled two-level aotm. Differing from the symmetric coupling cases discussed previously, we showed that the transmission probabilities of the incident single photons can vary from0to100%, depending on its asymmetrical couplings with the two-level aotm. This phenomenon is related to the redistribution of energy and momentum of photons after the scattering by the two-level aotm, as the present photon-atom interaction loses the usual spatial-symmetry. When the incident photon and the two-level aotm is on resonance, the amplitude of the excited spectra can still be adjusted by the coupling strength.
引文
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