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

技术综述：该奖项是根据瑞安的一项提议颁发的，并对网络基础设施产生了影响。它支持关于限制在两个维度的新物质状态的理论和计算研究和教育。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超冷原子的关联态。对量子霍尔效应特别感兴趣的是新发现的朗道能级占据v=4/11、4/13和5/13的平台。对4/11态的研究一直存在争议，并与实验不完全一致。PI将基于层次图追求一种不同的攻击方法，用Laughlin态的相互作用(玻色子)准粒子来表示低能电子激发。在两个非平凡的测试用例中，该方法被证明能够准确地再现低能谱。该方法可用于计算和改进电子基态和低能激发的能量和波函数。PI还计划使用这种方法来研究4/13状态。3/8和3/10两种状态还没有被发现。PI还致力于设计数值方法，通过计算当一个准粒子围绕另一个准粒子运动时积累的Berry位相，来“测量”准粒子统计。这些将扩展到展示非阿贝尔统计的情况，这些统计似乎在拓扑量子计算中具有实际应用。最后，冷原子系统的项目包括研究Feshbach共振和获得玻色子原子最低朗道能级区密度分布的多体自洽方法。研究v=2填充下快速旋转的自旋1/2原子的相变，特别是当系统扫过共振时不同的拓扑序的演化，可能会加深我们对这些系统中量子相变的理解。国际和平研究所还将研究费什巴赫共振附近的玻色子原子。这个项目主要是计算性的，在瑞研究所进行。学生在多处理器分布式内存计算机和超级计算机上学习并行计算技能。他们还接受量子物理和基本量子信息理论的一对一指导，因为它们与理解拓扑相和量子计算有关。鉴于该机构位于洛杉矶市区，并被联邦政府指定为“少数族裔机构”，该项目为拉美裔和非裔美国学生提供了参与前沿研究的宝贵机会。该提案还将有助于升级本国机构的计算基础设施。虽然现在下结论可能还为时过早，但拓扑量子计算机仍有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的方法。非-技术总结：该奖项是根据一个少数民族机构的芮提案颁发的，并对网络基础设施产生了影响。它支持关于限制在两个维度的新物质状态的理论和计算研究和教育。PI将研究纯电子物质的状态，这些状态被限制在二维范围内，并受到强磁场的影响。这样的电子系统可以在半导体器件中的特殊制造的异质结构或量子阱配置中实验实现。众所周知，许多材料中的原子和电子以有序的状态自我组织，例如，它们可能以规则的阵列组织，显示出晶体的有序。PI将研究的新物质状态中的电子显示出一种新的、明显不同的有序，一种有趣的自组织状态，称为拓扑有序。拓扑序不在描述从一个阶段到另一个阶段的转换的标准理论之外。理解呈现出拓扑有序的物质的性质在智力上是令人兴奋的，并可能影响包括高温超导体在内的各种有趣的材料。它也可能是实现新的革命性计算方法的关键。PI的目的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，从而在制造拓扑量子计算机方面有实际应用。PI还将研究另一种新颖的物质--旋转的冷原子，在那里他将探索不同拓扑序的状态之间的转变。这个项目主要是计算性的，在瑞安的一个机构进行。学生在多处理器分布式内存计算机和超级计算机上学习并行计算技能。他们还接受量子物理和基本量子信息理论的一对一指导，因为它们与理解拓扑相和量子计算有关。鉴于该机构位于洛杉矶市区，并被联邦政府指定为“少数族裔机构”，该项目为拉美裔和非裔美国学生提供了参与前沿研究的宝贵机会。该提案还将有助于升级本国机构的计算基础设施。虽然现在下结论可能还为时过早，但拓扑量子计算机仍有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的方法。

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.