Engineering Future Quantum Technologies in Low-Dimensional Systems

传统上，三维固体中的电子可以在所有可能的方向上改变它们的动量。然而，半导体中的电子可以被操纵，使它们被限制在较低的维度中移动。这种系统的一个完美的例子是GaAs/AlGaAs的半导体异质结构，在其结处形成仅几纳米厚的电子平面，其中电子具有量子化能量和在平面中改变动量的自由。这种非相互作用电子的显着集合被称为二维电子气（2DEG）。2DEG系统中的电子是高度移动的，并且在低温下，由于与晶格振动（声子）的相互作用的减少，它们的运动主要是无散射的，并且几乎没有杂质散射。当2D电子被静电压缩以形成窄的1D通道时，其有效尺寸小于用于散射的电子平均自由程，然后与电子相关联的量子现象被解决。在这种情况下，1D电子的能量变得量子化并形成离散能级。在电子的低载流子浓度下，如果限制1D电子的电势被放松，那么电子可以将自己排列成周期性的之字形方式，形成维格纳晶体，以维格纳命名，他在1936年首次预测了金属中的这种现象。最近，人们观察到一条电子线扭曲成锯齿形，然后变成两行独立的电子，并观察到丰富的自旋和电荷相。限制的一个非常微妙的变化可以导致两行从锯齿形状态出现，这表明存在一个狭窄的范围，其中波函数分离并形成纠缠态。纠缠是一种显著的现象，其中一个电子的状态变化将引起另一个电子的状态变化。这种惊人的性质构成了量子信息处理的基础，并具有与量子技术相关的实际后果，这将在本提案中进行研究。我的奖学金提案的另一个最重要的方面是研究锯齿状制度或放松的1D系统，在没有磁场的情况下寻找分数量子态。在大磁场的存在下，2DEG的能量被量子化，形成朗道能级，这导致了1980年和1982年分别发现的量子霍尔效应和分数量子霍尔效应。这些意想不到的发现提出了一个问题，即在任何晶格或拓扑绝缘体中，在没有任何磁场的情况下，是否可以观察到分数量子态？然而，在没有磁场的情况下，没有任何分数态的观测报告，直到最近在锗基一维系统中发现了由弛豫之字形态产生的e/2和e/4的分数电荷。该提议的灵感来自于此，以及最近在传统GaAs基1D量子线中发现的非磁性自组织分数量子态的实验结果，这是完全出乎意料的。该研究的目的是引入新的见解，量子物理学的新方面，通过利用低维半导体中的相互作用效应，以可控的方式操纵电子波函数，以允许基本量子物理学的技术开发。要研究的主要挑战：自旋和电荷操纵，证明电子纠缠和检测，映射自组织分数态及其自旋态，控制操纵和检测混合分数态，并确定它们是否纠缠。这项研究计划开辟了一个新的领域，在凝聚态物质的量子物理与生成的非阿贝尔分数，可用于拓扑量子计算方案。

Classically electrons in a three-dimensional solid can change their momentum in all possible directions. However, electrons in semiconductors can be manipulated so that they are constrained to move in lower dimensions. One of the perfect examples of such a system is a semiconductor heterostructure of GaAs/AlGaAs forming a plane of electrons, only a few nanometer thick, at its junction where electrons possessing quantised energy and freedom to change momentum in the plane. Such remarkable ensemble of non-interacting electrons is known as the two-dimensional electron gas (2DEG). The electrons in a 2DEG system are highly mobile and at low temperatures their motion is mainly scattering free due to the reduction in the interaction with lattice vibrations (phonons) and there is little impurity scattering. When the 2D electrons are electrostatically squeezed to form a narrow, 1D channel whose effective size is less than the electron mean free path for scattering then quantum phenomena associated with the electrons becomes resolved. In this situation, the energy of 1D electrons becomes quantised and discrete levels are formed. At a low carrier concentration of electrons, if the potential which is confining the 1D electrons is relaxed then electrons can arrange themselves into a periodic zig- zag manner forming a Wigner Crystal, named after Wigner who first predicted such a phenomenon in metal in 1936. Recently the distortion of a line of electrons into a zig-zag and then into two separate rows of electrons was observed and associated rich spin and charge phases. A very subtle change in confinement can result in two rows emerging from a zig-zag state which indicates that there is a narrow range where wavefunctions separate and form entangled states. Entanglement is a remarkable phenomenon in which a change in state of one electron will introduce a change in state of another. This amazing property forms the basis for quantum information processing with practical consequences related to quantum technologies, which will be investigated in this proposal. Another most important aspect of my Fellowship proposal is investigating the zig-zag regime or relaxed 1D system in search of fractional quantum states in the absence of a magnetic field. In the presence of a large magnetic field the energy of a 2DEG is quantized to form Landau levels which gave rise to two celebrated discoveries of the Integer and fractional quantum Hall effects in 1980 and 1982 respectively. Such unexpected revelations then pose a question whether fractional quantised states in the absence of any magnetic field in any lattice or topological insulators could ever be observed? However, there were no reports of observations of any fractional states without a magnetic field until the recent discovery of fractional charges of e/2 and e/4 arising from the relaxed zig-zag state in a Germanium-based 1D system. The proposal is inspired by this and the recent experimental finding of non-magnetic self-organised fractional quantum states in tradition GaAs based 1D quantum wires, which was completely unanticipated. The research aim is to introduce new insights, and new aspects of quantum physics, by exploiting the interaction effects in low-dimensional semiconductors by manipulating electron wavefunctions in a controllable manner to allow technological exploitation of basic quantum physics. The major challenges to be investigated: spin and charge manipulation, demonstrating electron entanglement and detection, mapping self-organised fractional states and their spin states, controlled manipulation and detection of hybrid fractional states and establishing if they are entangled. This research proposal opens up a new area in the quantum physics of condensed matter with the generation of Non-Abelian fractions which can be used in a Topological Quantum Computation scheme.