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

点击翻译按钮获取中文摘要

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.