Non-Abelian phases and statistics in spin-3/2 hole gases

*技术摘要*这个项目将解决低维空穴气体中简并态的拓扑非平凡性质。非阿贝尔相将在双环干涉装置中测量，其中阿贝尔相的贡献可以被最小化。非阿贝尔统计的激发将在一维半导体导线中被研究，这些导线与常规超导体接近耦合。将进行补充实验，探索约瑟夫森结的束缚态能谱和相-能关系。提出了几种制造方法来减少局域化的影响，局域化是介观器件中的主要复杂因素。最后，我们将研究波函数的非阿贝尔性质和激发的非阿贝尔统计之间的相互作用。该项目将支持一名博士生，他们将接受半导体物理、制造和测量技术方面的培训，包括低温强磁场技术、真空技术、低噪音电特性、扫描探针和电子束纳米光刻。这一广泛的经验将为学生在技术或学术界取得成功的职业生涯做好准备。推广计划包括为高中生和物理教师开发纳米技术演示和辅助材料。*非技术性摘要*量子统计、波函数的自旋和对称性是理解世界的量子力学的核心。在大多数系统中，粒子沿轨迹积累的相是相加的，两个粒子的交换相当于相因子的乘积。然而，在过去的几十年里，人们已经意识到，在非常特殊的设置中，累积的相位取决于系统的拓扑结构，并且粒子交换不必交换，这意味着排列的结果取决于粒子交换的顺序。这项工作的主要目标是设计一种新的物质状态，在这种状态下，具有非对易性质的奇异粒子可以存在。还将开发检测具有这些非常规性质的粒子的新技术。如果成功，这项研究将使拓扑量子比特的开发成为可能，这是容错量子计算机这一革命性概念的关键元素，它有望成倍增加一些资源密集型任务的计算能力，特别是对国家安全至关重要的加密算法。该项目将培养一名在纳米技术前沿工作的博士生，这是为在技术或学术界取得成功而进行的最好的科学和工程实践培训。一项外展计划包括为高中生和物理教师开发纳米技术演示和配套材料。

****TECHNICAL ABSTRACT****This project will address topologically non-trivial properties of degenerate states in low dimensional hole gases. Non-Abelian phases will be measured in double-ring interferometric devices, where the contribution of Abelian phases can be minimized. Excitations with non-Abelian statistics will be studied in 1D semiconducting wires proximity-coupled to a conventional superconductor. Complementary experiments exploring the energy spectrum of bound states and phase-energy relation of Josephson junctions will be performed. Several fabrication approaches are proposed to reduce effects of localization, the major complication in mesoscopic devices. Finally, an interplay between non-Abelian nature of the wavefunction and non-Abelian statistics of excitation will be investigated. This project will support a PhD student who will be trained in semiconductor physics, fabrication and measurement techniques, including low temperature high magnetic field techniques, vacuum technology, low noise electrical characterization, scanning probe and electron-beam nanolithography. This broad experience will prepare the student for a successful career in technology or academia. An outreach program includes development of nanotechnology demonstrations and accompanying materials for high school students and physics teachers.****NON-TECHNICAL ABSTRACT****Quantum statistics, spin and symmetry of the wavefunction are central to the quantum mechanical understanding of the world. In most systems phases accumulated by a particle along a trajectory are additive and exchange of two particles amounts to a multiplication by a phase factor. However, over the last few decades it has been realized that in very special settings the accumulated phase depends on the topology of the system and particle exchanges do not have to commute, meaning the outcome of permutations depends on the order of the particle exchanges. The main objective of this work is to engineer a new state of matter where exotic particles with non-commuting properties can exist. New techniques to detect particles with these unconventional properties will be also developed. If successful, the research will enable development of a topological quantum bit, a key element of a revolutionary concept of a fault-tolerant quantum computer, which promises to increase computational power for some resource-intensive tasks exponentially, especially for encryption algorithms paramount for national security. The project will train a PhD student working at the edge of nanotechnology, which is the best hands-on training in science and engineering for a successful career in technology or academia. An outreach program includes development of nanotechnology demonstrations and accompanying materials for high school students and physics teachers.