Strong Correlations in Cold atoms and Dirac materials

涉及量子信息存储、传输和操作的量子技术是21世纪加拿大物理学研究的一个重要方向。目前正在为这些技术探索许多不同的平台。被认为是未来量子技术可能设置的两种物理系统是量子材料中的捕获冷原子和新型电子相。在这些系统中，在量子粒子之间的相互作用很强的体制中，发现了许多最基本的有趣和技术相关的新物理学。这激发了我的研究计划，其重点是发展理论技术来研究强相互作用量子系统，并将这些方法应用于当前感兴趣的特定物理系统。我提议研究的两个系统是I)无序和多体定域（MBL）冷原子系统和ii)石墨烯中的分数量子霍尔态和狄拉克费米子的推广。为了操纵量子信息，有必要存储它——MBL系统：不平衡的无序相互作用量子系统，已被建议作为可能的量子存储器。MBL的物理学仍在建立中，包括它是否可以在大于1的维度上发生，正如最近的冷原子实验所表明的那样。我已经开发了一种理论方法来描述由玻色哈伯德模型描述的冷原子的非平衡动力学，它提供了传统方法无法达到的物理学。我将扩展这种方法，并将其应用于实验实现的情况，以评估MBL的索赔。整数和分数量子霍尔（FQH）效应发生在二维系统，如石墨烯，被放置在强垂直磁场中。一些FQH状态被认为是容错量子计算的可能候选。由于石墨烯中准粒子的相对论色散和内部自由度（谷和自旋），石墨烯中的FQHE效应（FQHE）与传统半导体系统中的FQHE不同。这些特征，加上电子相互作用引起的对称性破缺态，导致石墨烯中可能存在丰富的FQHE态，这些态目前还没有通过实验来区分。我将发展理论来帮助区分不同的FQHE状态。我还将探讨在石墨烯中看到的狄拉克费米子的推广，这可能允许在高能物理中可以获得的相对论性粒子的材料实现的场景。本文的研究成果将对HQP当前存在的重要问题和高质量培训提供及时的理论贡献。这些贡献的见解可能会对量子技术的发展产生影响，例如使用冷原子进行量子模拟，使用MBL进行量子存储器或量子计算平台。

Quantum technologies that involve the storage, transmission and manipulation of quantum information are an important direction for Canadian Physics research in the 21st Century.  Many different platforms for these technologies are currently being explored.  Two physical systems that have been suggested as possible settings for future quantum technologies are trapped cold atoms and novel electronic phases in quantum materials.  In these systems much of the most fundamentally interesting and technologically relevant novel physics is found in regimes where interactions between quantum particles are strong.  This motivates my research program, which focuses on developing theoretical techniques to study strongly interacting quantum systems, and applying these methods to specific physical systems of current interest.  Two systems I propose to investigate are i) disordered and many body localized (MBL) cold atom systems and ii) fractional quantum Hall states in graphene and generalizations of Dirac fermions. In order to manipulate quantum information it is necessary to store it - MBL systems: disordered interacting quantum systems which do not equilibrate, have been suggested as possible quantum memories.  The physics of MBL is still being established, including whether it can occur in dimensions greater than one, as suggested by recent cold atom experiments.  I have developed a theoretical  approach to the out of equilibrium dynamics of cold atoms described by the Bose Hubbard model which gives access to physics inaccessible by conventional methods. I will extend this method and apply it to the experimentally realized situation to assess claims of MBL. The integer and fractional quantum Hall (FQH) effects take place when two dimensional systems, such as graphene, are placed in strong perpendicular magnetic fields. Some FQH states have been suggested as possible candidates for fault tolerant quantum computing.  The FQH effect (FQHE) in graphene differs from the FQHE in conventional semiconductor systems due to the relativistic dispersion and internal degrees of freedom (valley and spin) of quasiparticles in graphene.  These features, in conjunction with electron interaction induced broken symmetry states, lead to a rich array of possible FQHE states in graphene which are currently not distinguished by experiment.  I will develop theory to aid discrimination between different FQHE states.  I will also explore generalizations of the Dirac fermions seen in graphene, which may allow for scenarios for materials realizations of relativistic particles that go beyond those accessible in high energy physics. The results of this research will be timely theoretical contributions to important current problems and high quality training of HQP.  Insights from these contributions may have implications for developments in quantum technologies such as quantum simulation using cold atoms, the use of MBL for quantum memories, or platforms for quantum computation.