Strong Correlations in Cold atoms and Dirac materials

涉及量子信息的存储、传输和处理的量子技术是21世纪加拿大物理学研究的一个重要方向。目前正在探索这些技术的许多不同平台。被建议为未来量子技术的可能环境的两个物理系统是量子材料中的囚禁冷原子和新的电子相。在这些系统中，许多最基本的有趣和技术相关的新物理都是在量子粒子之间相互作用强烈的区域发现的。这激发了我的研究计划，该计划专注于开发理论技术来研究强相互作用的量子系统，并将这些方法应用于当前感兴趣的特定物理系统。我建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Dirac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被认为是可能的量子存储器。MBL的物理学仍在建立中，包括它是否可以像最近的冷原子实验所建议的那样出现在超过一维的维度上。我已经开发了一种理论上的方法来研究玻色-哈伯德模型所描述的冷原子的非平衡动力学，该模型提供了用传统方法无法获得的物理学。我将扩展这一方法，并将其应用于实验实现的情况，以评估MBL的索赔。当二维体系(如石墨烯)置于强垂直磁场中时，会产生整数和分数量子霍尔(FQH)效应。一些FQH态被认为是容错量子计算的可能候选态。由于石墨烯中准粒子的相对论弥散和内部自由度(谷和自旋)，石墨烯中的FQH效应(FQHE)不同于传统半导体系统中的FQHE。这些特征，加上电子相互作用引起的对称态破裂，导致石墨烯中丰富的可能的FQHE态，目前还没有通过实验加以区分。我将开发理论来帮助区分不同的FQHE态。我还将探索石墨烯中狄拉克费米子的概括，这可能会为相对论粒子的材料实现提供超出高能物理可及范围的场景。这项研究的结果将为当前的重要问题和HQP的高质量培训提供及时的理论贡献。这些贡献的见解可能对量子技术的发展有所启示，例如使用冷原子进行量子模拟，将MBL用于量子存储器，或用于量子计算的平台。

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.