Topological superconductivity and high order non-abelian excitations

摘要：统计性质是量子力学理解世界的核心。所有已知的粒子都有所谓的阿贝尔统计量，这意味着连续几个粒子交换的结果不依赖于交换的顺序。最近有人提出在一些奇异系统中可以实现具有非阿贝尔统计量的粒子，并报道了最简单的非阿贝尔粒子——马约拉纳费米子的特征。除了对科学的好奇之外，寻找这些难以捉摸的刺激的主要驱动力是实现容错量子计算机的可能性。基于马约拉纳费米子的量子比特在计算上不是通用的，这意味着一个人不能单独使用这些容错量子比特来执行所有的操作。本提案的主要目标是开发一种新的系统，在该系统中可以实现更完整的计算高阶非阿贝尔激励。计划向印第安纳州当地学校推广，并对学生进行量子材料合成和表征、量子计算和量子技术的融合技能培训。技术摘要：提出的研究目标是开发一个可以实现和操纵高阶非阿贝尔激励的系统。具体而言，将探索分数量子霍尔效应中的自旋跃迁，以实现具有分数电荷激励的可重构螺旋通道网络。这些通道中诱导超导性的证明将是一个重要的里程碑。超导与整数和强相互作用分数量子霍尔态之间的复杂相互作用将被研究。虽然在最近的实验中发现了具有非阿贝尔统计量的最简单的激发类型马约拉纳费米子的特征，但目前的实验无法证明非阿贝尔交换统计量。这一建议将解决一个系统的发展，其中高阶非阿贝尔激励（参数）可以实现和操纵。计划向印第安纳州当地学校推广，并对学生进行量子材料合成和表征、量子计算和量子技术的融合技能培训。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Non-technical Abstract:Statistical properties are central to the quantum mechanical understanding of the world. All known particles have so-called Abelian statistics, meaning that result of several consecutive particle exchanges does not depend on the order of the exchanges. Recently it has been proposed that particles with non-Abelian statistics can be realized in some exotic systems, and signatures of simplest non-Abelian particles – Majorana fermions – have been reported. The main driving force in the search for these elusive excitations, apart from scientific curiosity, is a possibility to realize a fault tolerant quantum computer. Qubits based on Majorana fermions are not computationally universal,, which means one cannot perform all the operations with these fault tolerant qubits alone. The main objective of this proposal is to develop a new system where more computationally complete higher order non-Abelian excitations can be realized. Outreach to local Indiana schools and training of students in convergent skills of quantum materials synthesis and characterization, quantum computing and quantum technologies is planned.Technical Abstract:The objective of the proposed research is to develop a system where high-order non-Abelian excitations can be realized and manipulated. Specifically, spin transitions in the fractional quantum Hall effect regime will be explored to realize a reconfigurable network of helical channels with fractionalized charged excitations. Demonstration of induced superconductivity in these channels will be a major milestone. An intricate interplay between superconductivity and integer and strongly interacting fractional quantum Hall states will be investigated. While signatures of Majorana fermions, the simplest type of excitations with non-Abelian statistics, have been seen in recent experiments, current experiments fall short of demonstrating non-Abelian exchange statistics. This proposal will address development of a system where high order non-Abelian excitations (parafermions) can be realized and manipulated. Outreach to local Indiana schools and training of students in convergent skills of quantum materials synthesis and characterization, quantum computing and quantum technologies is planned.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.