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

自旋 3/2 孔气体的非阿贝尔相和统计

• 批准号: 1307247
• 负责人: Leonid Rokhinson
• 金额: $ 40万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-06-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1307247&HistoricalAwards=false
• 关键词: Non; Abelian; phases; statistics; spin

****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.

* 技术摘要 * 本项目将讨论低维空穴气体中简并态的拓扑非平凡性质。非阿贝尔相位将在双环干涉装置中测量，其中阿贝尔相位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线邻近耦合到一个传统的超导体进行研究。我们将进行补充实验，探索束缚态的能谱和约瑟夫森结的相能关系。提出了几种制造方法，以减少本地化的影响，在介观器件的主要并发症。最后，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，他将接受半导体物理，制造和测量技术的培训，包括低温高磁场技术，真空技术，低噪声电气特性，扫描探针和电子束纳米光刻。这种广泛的经验将为学生在技术或学术界的成功职业生涯做好准备。一个推广计划包括为高中学生和物理教师开发纳米技术演示和配套材料。非技术摘要 * 量子统计，自旋和波函数的对称性是量子力学理解世界的核心。在大多数系统中，由粒子沿着轨迹累积的相位是可加的，并且两个粒子的交换相当于乘以相位因子。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，累积相位取决于系统的拓扑结构，并且粒子交换不必对易，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。 探测具有这些非常规特性的粒子的新技术也将被开发出来。如果成功，该研究将能够开发拓扑量子位，这是容错量子计算机革命性概念的关键要素，有望成倍增加某些资源密集型任务的计算能力，特别是对于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边缘工作的博士生，这是科学和工程领域最好的实践培训，有助于在技术或学术界取得成功。一个推广计划包括为高中学生和物理教师开发纳米技术演示和配套材料。