Electron Self-Organisation and Applications

在大多数情况下，半导体中的电子可以被认为是自由的，它们的能量由它们的总数和它们的有效质量决定，相互排斥只略微改变了这一自由电子图景。然而，在较低的载流子浓度下，电子在固体中扩散的方式可能会受到排斥力的支配，大量的理论表明，在足够低的温度下，电子可以将自己排列成晶态整体。这被称为维格纳晶体，或维格纳晶格，以维格纳第一个预测这种现象的人的名字命名。事实证明，观察这种现象相当困难，因为对规则结构的观察并不简单，而且由于无序的存在，往往找不到理论的预测。在一个维度中，电子形成一条线，而维格纳晶体是电子寻求规则周期的微不足道的例子。然而，随着限制的减弱，或电子斥力的增加，当电子试图最大化它们的分离时，电子线可能会扭曲。在限制中，该行分为两个单独的行。研究的实验系统为分子束外延生长的Ga As-Al As异质结中的电子气，样品是用高分辨电子束光刻制备的。在这些样品中，当样品足够短时，可以通过施加电压的图案化栅极来控制限制势，电子在没有被随机杂质或缺陷散射的情况下以弹道方式漂移。在这种情况下，一维导线的电导值为2e2/h，其中2的因子源于自旋简并，e是电子电荷，h是普朗克常数。因此，当一行电子分裂成两行时，观察到基态的电导为4e2/h。当限制条件改变时，通过跟随电导的值，可以得到作为限制势函数的能级的运动。已经观察到了这一点，我们将由于电子-电子排斥而形成的两个行称为初始维格纳晶格，IWL。对能级移动的结果的分析表明，在形成两个单独的行之前，形成了杂化态，其中在两个行之间共享两个电子，使得它们形成扭曲的单行。量子力学规定，以这种方式共享的两个电子必须具有相反的自旋，因此它们可能会被纠缠，因此它们各自“知道”对方所处的量子态。纠缠是一种引人注目的现象，在这种现象中，如果电子被分离，但仍然纠缠在一起，那么一个电子的状态改变将导致另一个电子的状态改变。这一显著的性质是量子信息处理和量子逻辑的许多提议的核心，并可能引起尚未预料到的实际后果。在这个研究项目中，我们建议研究IWL，并优化电子纠缠混合态的创建。一旦完全了解这种状态，就可以通过将纠缠电子从IWL注入到其他量子结构中来研究纠缠电子的性质，这些结构基本上形成了早期的量子集成电路。纠缠电子的特征之一是，如果其中两个电子处于这种状态，那么它们的波长变化实际上是单个电子的两倍。因此，如果我们进行干涉实验，纠缠电子和正常电子的行为之间会有直接的差异，这就是我们将探索的影响。这项工作的最终目标是开发一种传输纠缠电子流的方法，然后在一系列集成量子器件中演示纠缠，以期实现它们的实际应用

In most situations electrons in semiconductors can be regarded as free with their energy determined by their total number and their effective mass with the mutual repulsion only slightly modifying this free electron picture. However at low values of carrier concentration the repulsion can dominate the manner in which the electrons diffuse in the solid, a voluminous amount of theory has shown that at sufficiently low temperatures the electrons can arrange themselves into a crystalline ensemble. This is termed a Wigner Crystal, or Wigner Lattice, after Wigner who first predicted such a phenomenon, it has proved rather difficult to observe as the observation of a regular structure is not simple and often the predictions of theory are not found due to the presence of disorder. In one dimension the electrons form a single line and the Wigner Crystal is the trivial case of the electrons seeking a regular periodicity. However, as the confinement weakens, or the electron repulsion increases, so it is possible for the line of electrons to distort as electrons attempt to maximise their separation. In the limit the row splits into two separate rows. The experimental system for such investigations is the electron gas in the GaAs-AlGaAs heterostructure grown by Molecular Beam Epitaxy and the samples are fabricated using high resolution electron beam lithography. In these samples it is possible to control the confinement potential by patterned gates to which voltages are applied, when the samples are sufficiently short electrons drift through ballistically which is without being scattered by random impurities or defects. In this regime the conductance of a one-dimensional wire takes a value 2e2/h where the factor of 2 arises from the spin degeneracy, e is the electron charge and h is Planck's constant. Consequently when a row of electrons splits into 2 rows a conductance of 4e2/h is observed as the ground state. By following the values of conductance as the confinement is changed so the movement of energy levels can be obtained as a function of confinement potential. This has been observed and we call the two rows formed as a result of the electron-electron repulsion the Incipient Wigner Lattice, IWL.Analysis of the results on the movement of energy levels has shown that prior to the formation of the two separate rows a hybridised state is formed in which two electrons are shared between the two rows such that they form a distorted single row. Quantum Mechanics dictates that two electrons shared in this way must have opposite spins and they can be entangled as a consequence of which they each "know" the quantum state the other is in. Entanglement is a remarkable phenomenon in which if the electrons are separated but still entangled then a change of state of one will produce a change in the state of the other. This remarkable property lies at the heart of many proposals for quantum information processing and quantum logic and may give rise to practical consequences not yet envisaged.In this research project we propose to study the IWL and optimise the creation of the hybrid state in which the electrons are entangled. Once this state is completely understood the properties of entangled electrons will be studied by injecting them from the IWL into other quantum structures which essentially form an early quantum integrated circuit. One of the characteristics of entangled electrons is that if two of them are in this state then a variation of the wavelength of them is effectively doubled compared to a single electron. Consequently if we perform an interference experiment there is an immediate difference between the behaviour of entangled and normal electrons, this is the effect which we will explore. The ultimate objective of the work is to develop a method of delivering a stream of entangled electrons and then demonstrate the entanglement in a series of integrated quantum devices with a view to their practical application