计算机模拟量子围栏中电子的行为

本文应用MATLAB数学软件、用计算机模拟处于圆形“量子围栏”内金属表面态电子的波函数及概率密度分布 .     

原子围栏中金属表面电子波函数的计算及图像模拟

首先用薛定谔方程求解被束缚在原子围栏中金属表面电子的波函数,包括圆形,矩形,跑道形的围栏.然后应用M atlab数学软件,利用有限元方法,借助于计算机分别模拟出三种形式围栏内金属表面电子的分布图,描述了原子围栏中金属表面电子的分布情况.最后,将计算机模拟图与用实验所绘图像进行比较.     

对量子围栏扫描隧道谱的诠释

文章先列出量子围栏谱线中的现象，然后利用薛定谔方程解出电子在无限高圆环势阱中的波函数及其能量.利用波函数对谱中出现的现象加以解释及对量子图象简要的理论推导.     

抛物势量子点电荷量子比特的消相干

通过求解能量的本征方程得出了抛物线性限制势下柱形量子点中电子的基态、激发态本征波函数及其本征能量,将基态、激发态二能级系统作为一个量子比特,利用费米黄金规则讨论了量子点受限长度对量子点消相干速率的影响,同时讨论了电子在空间概率密度分布的时间演化和振荡周期.数值计算结果表明,量子比特的消相干速率随受限长度的增加而减小,振荡周期随受限长度的增加而增加.电子的概率密度在空间呈周期性的变化.     

二维量子阱中单电子量子比特的性质

通过求解能量本征方程,得到弱磁场作用下的二维势阱中电子的本征能量及其波函数,进而以基态和第一激发态波函数构造了一个量子比特.数值计算结果表明,量子比特内电子的空间概率密度随空间坐标和时间的变化而变化,在阱的边缘处出现的概率值为零,在其他位置相对较大;各个空间点的概率密度均随时间做周期振荡,振荡周期与阱宽有关,与外磁场无关,它随阱宽的增加而增大.     

量子盘中量子比特的性质

在考虑电子与体纵光学声子强耦合的条件下,通过求解能量本征方程,得出了量子盘中电子的基态能量和第一激发态能量及其相应的本征波函数;采用幺正变换和元激发理论方法研究了声子效应;并以极化子的基态和第一激发态为基础构造一个量子比特.对KBr量子盘的数值计算表明:量子盘的尺寸效应显著,其能量随半径的减小迅速增大;量子比特内电子的概率密度与空间坐标和时间有关,当角坐标和时间给定时,概率密度随半径的变化而变化,在盘中心位置处电子的概率密度最大,在盘界面处概率密度为零;当半径和时间给定时,概率密度随角坐标的变化而变化;并且各个空间点的概率密度均随时间作周期性振荡.     

准一维量子线中电子的传导性

一条理想的量子线同一条无序量子线耦合在一起,理想链中能量为E的电子波函数,能被无序链中某些格点能量Vn,2在电子能量E附近的格点强烈散射.在Vn,2=E格点,能量为E的电子波函数能发生全反射,也就是"反共振效应".在无序度W较大时,随着W的增大,无序链中能够强烈影响周期链的格点数减少,这使得周期链中电子的局域长度增大,与数值计算结果一致.     

有限深对称量子阱中电子量子比特的性质

通过求解有限深对称量子阱中电子的能量本征方程,得到电子的能量状态;并以此为基础利用基态和第二激发态叠加构造一个量子比特,研究电子量子比特的性质.数值计算结果表明:概率密度的振荡周期与量子阱宽度和深度均有关,当势阱深度给定时,振荡周期随量子阱宽度的增大而增大,当阱宽给定时,振荡周期随势阱深度的增大而减小.各坐标点的概率密度幅值不同,量子阱中心位置概率密度幅值最大,其它位置较小.电子的概率密度以周期T在z方向振荡,不同时间点的概率密度幅值不同,在一个周期内,当t=0T,1T时电子概率密度在阱内中心达到最大,当t=0.5T时电子概率密度在阱内中心达到最小;在阱外电子的概率密度都是向两边逐渐衰减的.     

波函数对有限深方形量子线中电子及杂质能量的影响

以一维线性谐振子的波函数为基展开而成的波函数作为单电子的波函数,分别讨论了单电子及类氢杂质的能量,并将所得结果与波函数取作一维有限深量子阱中波函数的乘积的情况进行了比较.结果表明：已有文献选取的波函数,在计算单电子的能量及杂质的束缚能时只在阱宽较大时适用;在计算单电子的振子强度时,带来较大误差.     

抛物线性限制势量子点量子比特的振荡周期

在抛物量子点中电子与体纵光学声子强耦合的条件下，应用Pekar变分方法得出了电子的基态和第一激发态的本征能量及基态和第一激发态本征波函数．量子点中这样二能级体系可作为一个量子比特．当电子处于基态和第一激发态的叠加态时，计算出电子在空间的几率分布作周期性振荡．并且得出了振荡周期随受限长度及耦合强度的变化关系．     

Quantum mirages formed by coherent projection of electronic structure

Image projection relies on classical wave mechanics and the use of natural or engineered structures such as lenses or resonant cavities. Well-known examples include the bending of light to create mirages in the atmosphere, and the focusing of sound by whispering galleries. However, the observation of analogous phenomena in condensed matter systems is a more recent development, facilitated by advances in nanofabrication. Here we report the projection of the electronic structure surrounding a magnetic Co atom to a remote location on the surface of a Cu crystal; electron partial waves scattered from the real Co atom are coherently refocused to form a spectral image or 'quantum mirage'. The focusing device is an elliptical quantum corral, assembled on the Cu surface. The corral acts as a quantum mechanical resonator, while the two-dimensional Cu surface-state electrons form the projection medium. When placed on the surface, Co atoms display a distinctive spectroscopic signature, known as the many-particle Kondo resonance, which arises from their magnetic moment. By positioning a Co atom at one focus of the ellipse, we detect a strong Kondo signature not only at the atom, but also at the empty focus. This behaviour contrasts with the usual spatially-decreasing response of an electron gas to a localized perturbation.     

氢原子电子云分布的可视化分析

针对量子力学中氢原子波函数的抽象概念,分别给出了氢原子电子云的径向分布、角度分布以及空间分布函数,并利用Matlab软件绘制了对应的分布图。分析结果表明,氢原子电子云的分布形状由径向和角度概率分布共同决定,电子云分布密度不均匀,可以看出轨道的痕迹。此方法直观地揭示了氢原子电子云径向、角度和空间的几率分布规律,为量子力学抽象波函数的可视化分析提供了思路。     

PdFe(110)电子结构及电催化性能的理论研究

利用密度泛函理论(DFT)的平面波赝势方法计算了不同注入电荷和掺杂Fe原子比例的PdxFey(110)表面原子结构和电子结构特性。结果表明,Fe原子比例对表面褶皱s影响较小,注入电荷数量对表面褶皱s影响很大;Fe原子掺杂使Pd的4d10轨道电子向低能级轨道移动,增加了d空穴。布居分析表明电极的表层电荷分布比金属态表面增多;Fe掺杂的表层电荷分布比不掺杂电极表面增多。电子结构分析表明,电极表面的s、p、d轨道电子和总电子均比金属态表面减少;Fe掺杂后,Pd和Fe的表面原子趋向于杂化构型,Pd表层原子向Fe表层原子发生电子转移,增加表面反应活性,有利于电催化反应。     

Electrons surfing on a sound wave as a platform for quantum optics with flying electrons

Electrons in a metal are indistinguishable particles that interact strongly with other electrons and their environment. Isolating and detecting a single flying electron after propagation, in a similar manner to quantum optics experiments with single photons, is therefore a challenging task. So far only a few experiments have been performed in a high-mobility two-dimensional electron gas in which the electron propagates almost ballistically. In these previous works, flying electrons were detected by means of the current generated by an ensemble of electrons, and electron correlations were encrypted in the current noise. Here we demonstrate the experimental realization of high-efficiency single-electron source and detector for a single electron propagating isolated from the other electrons through a one-dimensional channel. The moving potential is excited by a surface acoustic wave, which carries the single electron along the one-dimensional channel at a speed of 3 μm ns(-1). When this quantum channel is placed between two quantum dots several micrometres apart, a single electron can be transported from one quantum dot to the other with quantum efficiencies of emission and detection of 96% and 92%, respectively. Furthermore, the transfer of the electron can be triggered on a timescale shorter than the coherence time T(2)* of GaAs spin qubits. Our work opens new avenues with which to study the teleportation of a single electron spin and the distant interaction between spatially separated qubits in a condensed-matter system.     

概率波新释

分析了固体材料中影响价电子状态的因素及价电子状态的量子力学描述方法,给几率波意义的阐释提供了一种物理图像;讨论了凝聚态物理学理论的发展困境及难点,认为量子力学方法描述凝聚态系统是合适的,但是可能由于计算工具、方法、模型等方面的问题阻碍了凝聚态物理学理论的发展。     

Wave-particle duality of C(60) molecules

Quantum superposition lies at the heart of quantum mechanics and gives rise to many of its paradoxes. Superposition of de Broglie matter waves' has been observed for massive particles such as electrons, atoms and dimers, small van der Waals clusters, and neutrons. But matter wave interferometry with larger objects has remained experimentally challenging, despite the development of powerful atom interferometric techniques for experiments in fundamental quantum mechanics, metrology and lithography. Here we report the observation of de Broglie wave interference of C(60) molecules by diffraction at a material absorption grating. This molecule is the most massive and complex object in which wave behaviour has been observed. Of particular interest is the fact that C(60) is almost a classical body, because of its many excited internal degrees of freedom and their possible couplings to the environment. Such couplings are essential for the appearance of decoherence, suggesting that interference experiments with large molecules should facilitate detailed studies of this process.     

氢原子三重微分散射截面与能量分配的关联

氢原子单离化是原子物理中最简单的三体相互作用问题，但是由于长程的库仑作用的影响，带电粒子与原子碰撞的单离化过程仍有许多难以克服和未能解决的困难．利用跃迁矩阵元的后滞形式，同时，取末态波函数为库仑波函数和平面波函数的乘积，在初态里，波函数被分成两部分，一部分是库仑波和氢原子基态的乘积，另一部分是两电子的相对运动的库仑波和质心运动的平面波．对于快电子仍然取为平面波，如果在忽略了质心运动和两电子相对库仑波的指数因子的情况下，所得出的理论计算结果与一些实验在数值上符合得较好。     

Observation of the Kapitza-Dirac effect

In their famous 1927 experiment, Davisson and Germer observed the diffraction of electrons by a periodic material structure, so showing that electrons can behave like waves. Shortly afterwards, Kapitza and Dirac predicted that electrons should also be diffracted by a standing light wave. This Kapitza-Dirac effect is analogous to the diffraction of light by a grating, but with the roles of the wave and matter reversed. The electron and the light grating interact extremely weakly, via the 'ponderomotive potential', so attempts to measure the Kapitza-Dirac effect had to wait for the development of the laser. The idea that the underlying interaction with light is resonantly enhanced for electrons in an atom led to the observation that atoms could be diffracted by a standing wave of light. Deflection of electrons by high-intensity laser light, which is also a consequence of the Kapitza-Dirac effect, has also been demonstrated. But the coherent interference that characterizes wave diffraction has not hitherto been observed. Here we report the diffraction of free electrons from a standing light wave-a realization of the Kapitza-Dirac effect as originally proposed.