RUI: Highly Correlated Systems of Reduced Dimensionality: Quantum Hall Effect and Ultracold Atoms

RUI：高度相关的降维系统：量子霍尔效应和超冷原子

• 批准号: 0606566
• 负责人: Edward Rezayi
• 金额: $ 15.6万
• 依托单位: California State L A University Auxiliary Services Inc.
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0606566&HistoricalAwards=false
• 关键词: RUI; Highly; Correlated; Systems; Reduced

TECHNICAL SUMMARY:This award is made on an RUI proposal and has an impact on cyberinfrastructure. It supports theoretical and computational research and education on novel states of matter restricted to two dimensions. Numerical calculations will be performed to address outstanding questions about the quantum Hall effect and to study correlated states of ultracold atoms in rapidly-rotating traps. Of particular interest regarding the quantum Hall effect are newly discovered plateaus at Landau level occupation v = 4/11, 4/13, and 5/13. Studies of the 4/11 state have been controversial and are not entirely consistent with experiment. The PI will pursue a different method of attack based on the hierarchy picture, representing the low energy electronic excitations in terms of interacting (boson) quasi-particles of the Laughlin state. In two non-trivial test cases this method is shown to reproduce the low-lying spectrum accurately. The method can be used to calculate, and improve upon, the energies and wavefunctions of the electronic ground state and low energy excitations. The PI also plans to use this approach to study the 4/13 state. Other states of interest for which plateaus have not yet been seen are the 3/8 and 3/10. The PI also aims to devise numerical methods for "measuring" quasi-particle statistics by calculating the Berry phase accumulated when one quasiparticle is moved around another. These will be extended to cases exhibiting non-Abelian statistics which appear to have practical applications for topological quantum computing. Finally, projects in the cold atom system include studies of Feshbach resonance and a many-body self-consistent method of obtaining the density profile in the lowest Landau level regime for boson atoms. The studies of the phase transition in rapidly-rotating spin-1/2 atoms at v = 2 filling, particularly the evolution of a different topological order as the system is swept through the resonance, is likely to deepen our understanding of quantum phase transitions in these systems. The PI will also study boson atoms near the Feshbach resonance.This project is primarily computational in nature and carried out at an RUI institution. Students learn parallel computation skills on multi-processor distributed memory computers and supercomputers. They also receive one-on-one instruction in quantum physics and elementary quantum information theory as they relate to understanding topological phases and quantum computing. Given that the home institution is in the urban Los Angeles area and has been designated as a "Minority Institution" by the federal government, this project provides valuable opportunities for Hispanic and African American students to participate in cutting-edge research. The proposal will also help upgrade the computing infrastructure of the home institution. While it may be too early to tell, topological quantum computers may yet prove feasible and possibly provide the most practical way of making quantum computers.NON-TECHNICAL SUMMARY:This award is made on an RUI proposal from a Minority Institution and has an impact on cyberinfrastructure. It supports theoretical and computational research and education on novel states of matter restricted to two dimensions. The PI will study states of pure electron matter restricted to two-dimensions and subject to intense magnetic fields. Such an electron system can be realized experimentally in specially fabricated heterostructure or quantum well configurations in semi-conductor devices. It is commonly known that atoms and electrons in many materials organize themselves in ordered states, for example they may organize in regular arrays that exhibit crystalline order. The electrons in the novel states of matter that the PI will study exhibit a newly appreciated and distinctly different kind of order, an intriguing state of self-organization known as topological order. Topological order lies outside the standard theory that describes transformations from one phase to another. Understanding the properties of matter that exhibit topological order is intellectually exciting and may impact classes of interesting materials including high temperature superconductors. It may also hold the key to realizing new revolutionary methods of computation. The PI aims to understand newly discovered quantum Hall states to see whether or not they possess sufficiently "dense" quantum information to have practical applications for making topological quantum computers. The PI will also study another kind of novel matter, rotating cold atoms, where he will explore transitions between states of different topological order. This project is primarily computational in nature and carried out at an RUI institution. Students learn parallel computation skills on multi-processor distributed memory computers and supercomputers. They also receive one-on-one instruction in quantum physics and elementary quantum information theory as they relate to understanding topological phases and quantum computing. Given that the home institution is in the urban Los Angeles area and has been designated as a "Minority Institution" by the federal government, this project provides valuable opportunities for Hispanic and African American students to participate in cutting-edge research. The proposal will also help upgrade the computing infrastructure of the home institution. While it may be too early to tell, topological quantum computers may yet prove feasible and possibly provide the most practical way of making quantum computers.

技术摘要：该奖项是根据RUI的提案颁发的，对网络基础设施产生了影响。它支持理论和计算研究以及限制在两个维度上的新物质状态的教育。将进行数值计算，以解决有关量子霍尔效应的悬而未决的问题，并研究快速旋转陷阱中的超冷原子的相关态。关于量子霍尔效应特别感兴趣的是在朗道能级占据v = 4/11、4/13和5/13处新发现的平台。对4/11状态的研究一直存在争议，并不完全符合实验。PI将根据层次图寻求不同的攻击方法，代表劳克林态的相互作用（玻色子）准粒子的低能电子激发。在两个非平凡的测试情况下，这种方法被证明是准确地再现低的频谱。该方法可用于计算和改进电子基态和低能激发态的能量和波函数。PI还计划使用这种方法来研究4/13状态。尚未看到平台的其他感兴趣的状态是3/8和3/10。PI还旨在通过计算当一个准粒子围绕另一个移动时积累的Berry相位来设计用于“测量”准粒子统计的数值方法。这些将被扩展到展示非阿贝尔统计的情况下，似乎有拓扑量子计算的实际应用。最后，在冷原子系统中的项目包括Feshbach共振的研究和多体自洽方法获得的最低朗道能级制度的玻色子原子的密度分布。对快速旋转自旋为1/2的原子在v = 2填充时的相变的研究，特别是当系统被扫过共振时不同拓扑序的演化，可能会加深我们对这些系统中量子相变的理解。PI还将研究Feshbach共振附近的玻色子原子。该项目主要是计算性质的，并在RUI机构进行。学生学习在多处理器分布式内存计算机和超级计算机上的并行计算技能。他们还接受量子物理学和基本量子信息理论的一对一指导，因为它们涉及到理解拓扑相和量子计算。鉴于家庭机构是在城市洛杉矶地区，并已被指定为“少数民族机构”的联邦政府，该项目提供了宝贵的机会，为西班牙裔和非洲裔美国学生参与前沿研究。这项建议亦有助提升原校的电脑基础设施。虽然现在下结论可能还为时过早，但拓扑量子计算机可能被证明是可行的，并可能提供制造量子计算机的最实用方法。非技术摘要：该奖项是根据少数机构的RUI提案颁发的，对网络基础设施产生了影响。它支持理论和计算研究以及限制在两个维度上的新物质状态的教育。 PI将研究纯电子物质的状态限制在二维和强磁场。这样的电子系统可以在实验上在半导体器件中的特别制造的异质结构或量子阱配置中实现。众所周知，许多材料中的原子和电子以有序状态组织自己，例如它们可以组织成呈现晶体有序的规则阵列。PI将研究的新型物质状态中的电子表现出一种新认识到的且明显不同的秩序，一种有趣的自组织状态，称为拓扑秩序。 拓扑序不属于描述从一个相到另一个相的变换的标准理论。理解表现出拓扑秩序的物质的性质是智力上令人兴奋的，可能会影响包括高温超导体在内的有趣材料的类别。它也可能是实现新的革命性计算方法的关键。PI的目标是了解新发现的量子霍尔态，看看它们是否具有足够的“密集”量子信息，以实际应用于制造拓扑量子计算机。PI还将研究另一种新物质，旋转冷原子，在那里他将探索不同拓扑顺序的状态之间的转换。该项目主要是计算性的，并在RUI机构进行。学生学习在多处理器分布式内存计算机和超级计算机上的并行计算技能。他们还接受量子物理学和基本量子信息理论的一对一指导，因为它们涉及到理解拓扑相和量子计算。鉴于家庭机构是在城市洛杉矶地区，并已被指定为“少数民族机构”的联邦政府，该项目提供了宝贵的机会，为西班牙裔和非洲裔美国学生参与前沿研究。这项建议亦有助提升原校的电脑基础设施。虽然现在下结论还为时过早，但拓扑量子计算机可能证明是可行的，并可能提供制造量子计算机的最实用方法。