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的物理性质源于由于电子动能和势能之间的竞争而产生的强烈的相关性。在光学晶格中囚禁的超冷原子中操纵动能和相互作用的能力的进步，导致了使用冷原子来模拟其他系统的想法，如关联量子材料。激励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在强关联量子系统中观察到的新的宏观行为。我打算在未来五年的研究计划中采取的方法是：i)发展和完善具有广泛适用性的理论技术；ii)从理论上研究特定的冷原子系统和强关联电子材料。我打算关注的具体项目是a)最近发现的一类稀磁半导体(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。特别是强关联的电子材料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个观点。I)今年发现了一类居里温度相对较高的DMS。这为发展解释铁磁性的理论提供了机会，这可能有助于这类材料未来自旋电子应用的发展。Ii)有机电荷转移盐是研究强关联的一类很有吸引力的材料，因为它们表现出一系列丰富的现象，如非传统超导、自旋液体和弛豫铁电行为。我将研究这些系统中的电荷涨落效应在影响关联量子态中的作用。实时调整冷原子系统中的参数的能力使它们成为研究相互作用的量子多体系统的非平衡动力学这一挑战性问题的一个非常有吸引力的环境。我最近开发了一种形式主义，在玻色-哈伯德模型中描述这种物理，该模型描述了光学晶格中的冷玻色子。对于不同的量子猝灭协议(动态遍历量子临界点)，终态可能被加热、像玻璃一样冻结，或者具有大量的缺陷。我将计算在量子猝灭过程中和之后秩序的空间和时间发展，以给出一张微观图像，以连接到在单个原子水平上成像的最先进的实验。冷原子是电中性的，因此不会直接与电磁场耦合。已经产生了模拟物理场的人造磁场和电场，但其强度可能比实验室中所能达到的要强得多。我将研究这些领域中可能出现的新现象，无论是在平衡状态下还是在平衡状态之外。这项工作的结果将对自旋电子学、强关联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，这项工作将有助于在加拿大国内外推进这些领域的努力，加拿大人将通过未来采用新材料或量子模拟的技术获得这些领域的好处。这一建议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.