CAREER: Quantum Frustration, Topological Order in Solids and Topological

职业：量子挫败、固体拓扑序和拓扑

• 批准号: 0748925
• 负责人: Kirill Shtengel
• 金额: $ 50万
• 依托单位: University of California-Riverside
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0748925&HistoricalAwards=false
• 关键词: CAREER; Quantum; Frustration; Topological; Order

TECHNICAL SUMMARY:This CAREER award supports theoretical research on Quantum Frustration and Topological Order in Solids with a special focus on Topological Quantum Computation, combined with educational and outreach programs. The Division of Materials Research and the Physics Division contribute resources to this award.The two main research directions are: (i) Investigating the possibility of topological order in a variety of condensed matter systems such as frustrated magnets, bosonic and fermionic extended Hubbard models and related Josephson junction arrays, as well as ultra-cold atomic systems in optical traps. Special emphasis is placed on non-Abelian topological order, the conditions under which it may occur and possible methods of its experimental detection. (ii) Studying the feasibility of using topological phases for fault-tolerant quantum computation, specifically those expected to exist in Fractional Quantum Hall systems. Such an approach has an important potential advantage over other, more "conventional" proposed ways to realize quantum computing; error correction is automatically built into the correlated electron physics of an underlying solid state system. The related educational activities include developing a seminar series on quantum computation targeting college freshmen with the main goal of exposing them to the research, as well as exciting them about studying and doing active research in Physics. This series will be offered both at University of California, Riverside and California State University, Los Angeles and will be accompanied by an interactive website. More advanced topics of the research and related theoretical tools will be incorporated into a graduate level book of modern problems and solutions in condensed matter physics and a new graduate class "Field Theory Methods in Condensed Matter Physics.? NON-TECHNICAL SUMMARY:This CAREER award supports theoretical research in condensed matter physics and quantum information science combined with educational activities, some designed to stimulate interest in undergraduate students in physics. The Division of Materials Research and the Physics Division contribute resources to this award.The PI plans to study new states of matter that are theoretically predicted to exist in electrons confined to a plane and exposed to a high magnetic field perpendicular to the plane. These topological states of matter, as they are called, have intriguing quantum mechanical properties. For example, they are particularly resistent to ?noise? that disrupts inherent properties of quantum mechanical states that enable the highly parallel computation possible by manipulating quantum mechanical states. The research activities may lead to the discovery of new topological states of matter. Despite the great potential promise of topological quantum computation, many of the basic practical questions remain open. They must be resolved in order for this idea to become a reality, and they have connections to important fundamental physics. This research will engage these questions, among them are: Do these topological states actually exist in nature? How can they be manipulated in a practical way to enable computation? And, how can these states of matter be detected by experiments? Computing with quantum mechanical states holds the promise of formidable speed-up of important computational tasks with implications ranging from cryptography to quantum chemistry. The conceptual idea of using topological states for quantum computation has established deep connections between the fields of topology in mathematics and condensed matter physics. This research also invovles collaboration with industry through Microsoft Research, and will give participating graduate students first-hand experience in research conducted in industry. The concepts and insights developed here will contribute to American competitiveness. The related educational activities include developing a seminar series on quantum computation targeting college freshmen with the main goal of exposing them to the research, as well as exciting them about studying and doing active research in Physics. This series will be offered both at University of California, Riverside and California State University, Los Angeles and will be accompanied by an interactive website. More advanced topics of the research and related theoretical tools will be incorporated into a graduate level book of modern problems and solutions in condensed matter physics and a new graduate class "Field Theory Methods in Condensed Matter Physics.?

技术概述：该职业奖支持关于固体中量子受挫和拓扑秩序的理论研究，特别关注拓扑量子计算，并结合教育和推广计划。两个主要的研究方向是：(I)研究各种凝聚态系统，如受阻磁体、玻色子和费米子扩展的Hubbard模型和相关的约瑟夫森结阵列，以及光学陷阱中的超冷原子系统中拓扑有序的可能性。特别强调了非阿贝尔拓扑序，它可能发生的条件和可能的实验检测方法。(Ii)研究利用拓扑位相进行容错量子计算的可行性，特别是那些有望存在于分数量子霍尔系统中的拓扑位相。与其他更传统的实现量子计算的方法相比，这种方法具有重要的潜在优势；纠错会自动嵌入到底层固态系统的关联电子物理中。相关教育活动包括针对大学一年级学生开发量子计算系列研讨会，主要目的是让他们接触到这项研究，以及激发他们学习和从事积极的物理研究。这一系列课程将在加州大学河滨分校和加州州立大学洛杉矶分校提供，并将附带一个互动网站。更高级的研究主题和相关的理论工具将被纳入研究生水平的凝聚态物理现代问题和解决方案的书籍和一个新的研究生班级：凝聚态物理学中的场论方法。非技术总结：该职业奖支持凝聚态物理和量子信息科学的理论研究与教育活动相结合，其中一些旨在激发本科生对物理的兴趣。材料研究部和物理部为这一奖项贡献了资源。PI计划研究理论上预测存在于一个平面内的电子中并暴露在垂直于该平面的高磁场中的新的物质状态。物质的这些拓扑态，就像它们所说的那样，具有有趣的量子力学性质。例如，它们特别能抵抗噪音。这破坏了量子力学状态的固有属性，这些属性使得通过操纵量子力学状态实现高度并行计算成为可能。这些研究活动可能会导致发现物质的新拓扑态。尽管拓扑量子计算有着巨大的潜在前景，但许多基本的实际问题仍然悬而未决。为了使这一想法成为现实，这些问题必须得到解决，而且它们与重要的基础物理有联系。这项研究将涉及这些问题，其中包括：这些拓扑态是否真的存在于自然界？如何才能以实用的方式操纵它们以实现计算？那么，这些物质的状态是如何通过实验来检测的呢？使用量子力学状态的计算有望极大地加快重要计算任务的速度，涉及从密码学到量子化学的各种影响。利用拓扑态进行量子计算的概念在数学中的拓扑学和凝聚态物理学之间建立了深刻的联系。这项研究还通过微软研究院与工业界进行合作，并将为参与研究的研究生提供在工业界进行研究的第一手经验。这里提出的概念和见解将有助于提高美国的竞争力。相关教育活动包括针对大学一年级学生开发量子计算系列研讨会，主要目的是让他们接触到这项研究，以及激发他们学习和从事积极的物理研究。这一系列课程将在加州大学河滨分校和加州州立大学洛杉矶分校提供，并将附带一个互动网站。更高级的研究主题和相关的理论工具将被纳入研究生水平的凝聚态物理现代问题和解决方案的书籍和一个新的研究生班级：凝聚态物理学中的场论方法。