Strong correlations of atoms in optical lattices and electrons in quantum materials

许多当前科学和技术感兴趣的材料的新物理性质源于电子动能和势能之间的竞争所产生的强相关性。在操纵被困在光学晶格中的超冷原子的动能和相互作用的能力方面取得的进展，导致了使用冷原子来模拟其他系统（如相关量子材料）的想法。激发我研究计划的科学挑战是发展理论，以理解微观自由度的相互作用如何导致强相关量子系统中观察到的紧急宏观行为。我打算在未来五年的研究计划中采取的方法是：1)发展和完善具有广泛适用性的理论技术；2)从理论上研究特定的冷原子系统和强相关电子材料。我打算重点研究的具体项目有：a)最近发现的一类稀释磁性半导体（dms）中的铁磁性；b)有机电荷转移盐中的电荷波动效应；c)光学晶格中冷玻色子的非平衡动力学；d)冷原子的人工磁场和电场。**对强相关电子材料的兴趣可能来自潜在的应用或不寻常的物理性质。我提议的研究涵盖了这两种观点。1)今年发现了一类具有较高居里温度的新型dms。这提供了一个发展理论来解释铁磁性的机会，这可能有助于这类材料未来自旋电子应用的发展。II)有机电荷转移盐是一类有吸引力的材料，研究强相关性，因为它们表现出丰富的现象范围，如非常规超导性，自旋液体和弛豫铁电行为。我将研究这些系统中电荷波动效应对相关量子态的影响。**实时调整冷原子系统参数的能力使它们成为研究相互作用量子多体系统的非平衡动力学这一具有挑战性的问题的一个非常有吸引力的设置。我最近在玻色哈伯德模型中发展了一种描述这种物理的形式，它描述了光学晶格中的冷玻色子。对于不同的量子猝灭协议（量子临界点的动态遍历），最终状态可能是热化的，像玻璃一样冻结，或者有缺陷的扩散。我将计算在量子猝灭期间和之后秩序的空间和时间发展，给出一个微观图像，与最先进的实验相联系，这些实验是在单原子水平上成像的。冷原子是电中性的，因此不直接与电磁场耦合。人造磁场和电场已经产生，它们模拟物理场，但比实验室中可以实现的强得多。我将研究这些领域在平衡和非平衡状态下可能产生的新现象。**这项工作的结果将对自旋电子学、强相关电子和超冷原子领域的研究人员产生重大兴趣。更广泛地说，这项工作将有助于推动加拿大国内外这些领域的发展，通过结合新材料或量子模拟的未来技术，加拿大人将从中受益。该计划还将为年轻研究人员提供高质量的凝聚态理论培训。

The novel physical properties of many materials of current scientific and technological interest derive from the strong correlations that arise due to competition between electron kinetic and potential energy. Advances in the ability to manipulate kinetic energy and interactions in ultra-cold atoms trapped in optical lattices have led to the idea of using cold atoms to simulate other systems such as correlated quantum materials. The scientific challenge that motivates my research program is to develop theory to understand how the interplay of microscopic degrees of freedom leads to observed emergent macroscopic behaviour in strongly correlated quantum systems. The approaches I intend to take in my research program in the next five years are i) to develop and refine theoretical techniques with wide applicability and ii) to investigate specific cold atom systems and strongly correlated electron materials theoretically. Particular projects I intend to focus on are a) ferromagnetism in a very recently discovered class of diluted magnetic semiconductors (DMSs), b) charge fluctuation effects in organic charge transfer salts, c) out of equilibrium dynamics for cold bosons in optical lattices and d) artificial magnetic and electric fields for cold atoms.**Interest in particular strongly correlated electron materials may come from potential applications or unusual physical properties. My proposed research encompasses both points of view. I) This year a new class of DMSs with a relatively high Curie temperature has been discovered. This presents an opportunity to develop theory to explain the ferromagnetism which may assist the development of future spintronic applications of this class of materials. II) Organic charge transfer salts are an attractive class of materials in which to study strong correlations as they exhibit a rich range of phenomena such as unconventional superconductivity, spin liquid and relaxor ferroelectric behaviour. I will investigate the role of charge fluctuation effects in these systems in affecting correlated quantum states.**The ability to tune the parameters in cold atom systems in real time makes them a very attractive setting to study the challenging problem of the out of equilibrium dynamics of interacting quantum many-body systems. I recently developed a formalism to describe this physics in the Bose Hubbard model, which describes cold bosons in an optical lattice. For different quantum quench protocols (a dynamic traversal of a quantum critical point) the final state may be thermalized, frozen like a glass, or have a proliferation of defects. I will calculate spatial and temporal development of order during and after a quantum quench to give a microscopic picture to connect to state-of-the-art experiments which image at the single atom level. Cold atoms are electrically neutral and hence do not couple to electromagnetic fields directly. Artificial magnetic and electric fields have been generated which mimic physical fields but can be much stronger than those achievable in the laboratory. I will study novel phenomena that can arise from such fields both in and out of equilibrium. **The results of this work will be of significant interest to researchers working in the areas of spintronics, strongly correlated electrons and ultra cold atoms. More broadly, this work will contribute to efforts to advance these fields both in and outside Canada, the benefits of which will reach Canadians through future technologies incorporating novel materials or quantum simulation. This proposal will also provide high quality training in condensed matter theory for young researchers.