论文标题

在介观束上的两个相互作用电子的碰撞:经典极限中的精确解决方案

Collision of two interacting electrons on a mesoscopic beamsplitter: exact solution in the classical limit

论文作者

Pavlovska, Elina, Silvestrov, Peter G., Recher, Patrik, Barinovs, Girts, Kashcheyevs, Vyacheslavs

论文摘要

对沿量子大厅设置中边缘的隔离电子碰撞的碰撞的实验可以模仿光子与电子是充电费米子的重要区别。在所谓的电子hong-ou-mandel(hom)设置中,不相关的电子对被注入梁插曲仪。如果两个电子波数据包相同,则费米统计将迫使电子散射到不同的检测器上,但是这种量子抗挑战可能会被库仑的排斥力混淆。在这里,我们使用二次2D鞍点的电子HOM实验对梁的弹力板的电势进行建模,并在两个注射的电子之间进行强烈的磁场之间的库仑相互作用,并未经过强大的平面外磁场。我们表明,电子指导中心漂移动力学的经典运动方程采用了汉密尔顿方程的形式,用于符合鞍点电位和库仑电位的规范共轭变量的形式,其中质量中心坐标的动力学和相对坐标的动力学。我们使用这些方程来根据一些实验可调的参数来确定碰撞结果:不相关电子的初始能量,注射的相对时间延迟以及鞍点电位的形状。提出了确定性束和抗弹性散射结果的通用相图,其单个能级表征了由于一致电子的相互作用而导致的有效屏障高度的增加。我们建议采用清晰的实验策略来检测预测的影响,并在经典动态预期主导量子效应时对条件进行分析估计。

Experiments on collisions of isolated electrons guided along the edges in quantum Hall setups can mimic mixing of photons with the important distinction that electrons are charged fermions. In the so-called electronic Hong-Ou-Mandel (HOM) setup uncorrelated pairs of electrons are injected towards a beamsplitter. If the two electron wave packets were identical, Fermi statistics would force the electrons to scatter to different detectors, yet this quantum antibunching may be confounded by Coulomb repulsion. Here we model an electronic HOM experiment using a quadratic 2D saddle point potential for the beamsplitter and unscreened Coulomb interaction between the two injected electrons subjected to a strong out-of-plane magnetic field. We show that classical equations of motion for the drift dynamics of electrons' guiding centers take on the form of Hamilton equations for canonically conjugated variables subject to the saddle point potential and the Coulomb potential where the dynamics of the center-of-mass coordinate and the relative coordinate separate. We use these equations to determine collision outcomes in terms of a few experimentally tuneable parameters: the initial energies of the uncorrelated electrons, relative time delay of injection and the shape of the saddle point potential. A universal phase diagram of deterministic bunching and antibunching scattering outcomes is presented with a single energy scale characterizing the increase of the effective barrier height due to interaction of coincident electrons. We suggest clear-cut experimental strategies to detect the predicted effects and give analytical estimates of conditions when the classical dynamics is expected to dominate over quantum effects.

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