Topological superconductivity and high order non-abelian excitations

非技术摘要：统计特性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，这意味着几个连续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的粒子，并且已经报道了最简单的非阿贝尔粒子-马约拉纳费米子的签名。除了科学好奇心之外，寻找这些难以捉摸的激发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，这意味着不能单独使用这些容错量子比特执行所有操作。这个建议的主要目标是开发一个新的系统，在计算上更完整的高阶非阿贝尔激发可以实现。外展到当地的印第安纳州学校和培训学生的收敛技能的量子材料的合成和表征，量子计算和量子technology.Technical摘要：拟议的研究的目标是开发一个系统，高阶非阿贝尔激发可以实现和操纵。具体而言，自旋跃迁的分数量子霍尔效应制度将探讨实现可重构网络的螺旋通道与分数带电激发。在这些通道中诱导超导性的证明将是一个重要的里程碑。超导性和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。虽然马约拉纳费米子的签名，最简单的类型的激发与非阿贝尔统计，已在最近的实验中看到，目前的实验没有证明非阿贝尔交换统计。这项建议将解决一个系统的发展，高阶非阿贝尔激发（parafermions）可以实现和操纵。该奖项反映了NSF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.