Topics in Ultracold Fermi Gases and Topological Quantum Computing

该奖项支持理论研究和教育，将探索凝聚态理论的两个独立领域。第一个领域涉及非常简并的费米或玻色系统的理论中的各种问题，特别是关于超冷碱性气体系统，在那里它们可能会收到实验输入。具体地说，将研究（a）含磁性杂质的s波超导体中是否发生一级相变;（B）？伪库埃特流中存在的偶极力;（c）角动量的一个？p+ip？费米超流体（d）玻色凝聚系统中持续电流的衰变。第二个领域将评估在强层状超导体Sr_2O_3中实现拓扑量子计算的前景。所要研究的问题是：（a）在这个系统中，可能的Domain-type在齐次性中所引起的复杂性;（B）系统稳定性存在的一般条件？半量子漩涡在p+ip费米超流体，以及可能的原因未能观察到他们在A相的超流氦;（三）的性质的多体基态波函数的系统，可以维持？马约拉纳费米子？简并费米子系统中库珀对的形成问题早在50多年前就已提出。虽然在过去的半个世纪里，在平均场水平上取得了进展，但许多问题，即使是简单的s波配对，仍然没有答案。例如，在什么情况下（如果有的话），磁性杂质会在低温下引起一级相变？在各向异性配对的情况下，一些更基本的问题，如被认为对应于超流氦A相的状态的固有角动量，仍然没有得到明确的答案。现在有真实的希望在超冷碱性气体中通过实验来回答这些问题，这个项目将为这样的实验提供一个理论框架。在过去几年中，量子信息领域出现了一个最有趣的想法，即拓扑量子计算，这个项目也将在这个项目中得到解决。一个明确的分析，不仅是基本激发的拓扑非平凡类的系统的问题，但也多体基态的性质将进行，以及更多？螺母和螺栓？由于选择的具体系统的物理性质的限制的评估。该研究计划将提供良好的机会，教育和培训研究生在凝聚态理论研究的前沿分析和数学方法。非技术总结该奖项支持两个广泛领域的理论研究和教育。其中一个利用原子在非常低的温度下被光波捕获的潜力来解决材料研究中提出的概念问题，例如超导体，其在足够低的温度下发展出合作的电子状态，通常以其携带电流而不耗散的能力而闻名。这些基本问题很难在材料中解决，但可能会屈服于对被困冷原子系统的实验。第二个领域涉及对一种不寻常的超导体中的涡旋的研究，在那里，理论上已经表明，人们可以通过相互移动涡旋来进行基本的计算操作。PI将研究这种形式的量子计算，即操纵量子力学状态进行计算，在理论上是可能的，通过仔细研究超导电子状态和其他缺陷的影响，除了漩涡。该研究计划将为凝聚态理论研究前沿的分析和数学方法研究生的教育和培训提供绝佳的机会。

TECHNICAL SUMMARYThis award supports theoretical research and education that will explore two separate realms of condensed matter theory. The first area concerns various questions in the theory of very degenerate Fermi or Bose systems, with particular reference to the ultracold alkali gas systems where they may receive experimental input. Specifically, studies will be made of (a) the occurrence or not of a first- order phase transition in an s-wave superconductor containing magnetic impurities; (b) ?pseudo-Couette? flow in the presence of dipolar forces; (c) the angular momentum of a ?p+ip? Fermi superfluid; and (d) the decay of persistent currrents in a Bose-condensed system.The second area will be evaluating the prospects for the implementation of topological quantum computation in the strongly layered superconductor strontium ruthenate. The questions to be investigated are (a) the complications caused by the probable domain-type in homogeneities in this system; (b) the general conditions for the existence of thermodynamically stable ?halfquantum vortices? in a p+ip Fermi superfluid, and possible reasons for the failure to observe them in the A phase of superfluid helium; and (c) the nature of the many-body groundstate wave function of a system that can sustain ?Majorana fermions? and the general conditions for the latter to exist.The problem of the formation of Cooper pairs in a system of degenerate fermions was posed more than 50 years ago. Although progress has been made at the mean-field level in the past half-century, many questions, even in the case of simple s-wave pairing, remain unanswered. For example, under what circumstances, if any, do magnetic impurities induce a first-order phase transition at low temperatures? In the case of anisotropic pairing, some even more basic questions, such as the intrinsic angular momentum of the state believed to correspond to the A phase of superfluid helium, have still not received a definitive answer. There is now a real hope of answering some of these questions experimentally in the ultracold alkali gases, and this project will provide a theoretical framework for such experiments.A specific implementation of one of the most intriguing ideas to have emerged in the field of quantum information over the last few years, namely topological quantum computation, will also be addressed in this project. An explicit analysis not only of the elementary excitations of the topologically nontrivial class of systems in question but also of the nature of the many-body groundstate will be undertaken, as well as a more ?nuts and bolts? assessment of the constraints due to the physical properties of the specific system of choice.This research program will provide excellent opportunities for the education and training of graduate students in analytical and mathematical methods at the cutting edge of condensed matter theory research. NON-TECHNICAL SUMMARYThis award supports theoretical research and education in two broad areas. One exploits the potential of atoms at very low temperature trapped by light waves to address conceptual issues raised by the study of materials, such as superconductors which develop a cooperative electronic state at sufficiently low temperatures often noted for its ability to carry electric current without dissipation. These fundamental questions are difficult to resolve in materials, but might succumb to experiments on systems of trapped cold atoms. The second area involves the study of vortices in an unusual kind of superconductor, where it has been theoretically shown that one can carry out the fundamental operations of computing by moving vortices around each other. The PI will study the extent to which this form of quantum computing, the manipulation of a quantum mechanical state to perform computation, is theoretically possible through a careful study of the superconducting electronic state and the effects of other defects, besides vortices. This research program will provide excellent opportunities for the education and training of graduate students in analytical and mathematical methods at the cutting edge of condensed matter theory research.