Study of ultra-cold orbital, large spin, and dipolar systems in optical lattices

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TECHNICAL SUMMARYThis award supports the theoretical study of novel states of matter with cold atoms and dipolar molecules, which are not easily accessible in typical materials. It also provides theoretical guidance for current experimental efforts. The PI will use both analytical and numerical methods including self-consistent mean-field theory, classical and quantum field theoretical methods, and quantum Monte-Carlo simulations. The research has three foci: 1.) The study of exotic states of ultra-cold bosons and fermions in the high orbital bands of optical lattices. For orbital bosons, based on his previous study on unconventional Bose-Einstein condensations beyond the 'no-node' theorem, the PI will further investigate their collective excitations and quantum phase transitions. The research on fermions will focus on the quantum anomalous Hall insulators with interesting band topology and exotic Mott insulators with frustrated orbital exchanges. 2.) The study of the competing phases of ultra-cold large-spin alkali and alkaline earth atoms with a particular focus on the exotic quantum magnetism characterized by strong quantum fluctuations. 3.) The study of unconventional Cooper pairing that arises from ultra-cold electric and magnetic dipolar interactions leading to new mechanisms for p-wave triplet Cooper pairing. This project seeks to predict new states of matter that have not yet been found in materials but are currently the subject of cold atom experiments. This research lies at the interface between condensed matter and cold atom physics and will benefit both fields. Students will receive train-ing in analytical and numerical methods for strongly correlated systems, and will develop broad research interests. Research results will be incorporated into advanced graduate courses. NONTECHNICAL SUMMARYThis award supports theoretical research and education that seek to study new states of matter that arise in a kind of 'crystal of light,' which is made from atoms that are very close to the absolute zero of temperature and are trapped in laser beams forming a regular array of atoms. These ultra-cold atoms can behave in ways that are analogous to electrons moving in materials and provide another way to discover and study electronic states of matter that arise as a consequence of strong interactions among electrons. These novel electronic states may live in a class of mate-rials known as strongly correlated materials. An advantage of studying ultra-cold atom analogs is that the interactions between atoms trapped in laser light can be more easily tuned than the elec-trons in a material.Ultra-cold atoms trapped by lasers are interesting in their right as they can form novel quantum mechanical states that cannot occur or are not easily observed in the electrons of a material. The interactions among atoms can be more complex than those among electrons leading to interesting novel states of matter. The PI aims to develop theories to explain the novel quantum mechanical properties of these cold atoms in crystals of light. The theories provide guidance for new experiments, deepening our understanding of quantum physics and states of matter of ultra-cold atoms and electrons alike, and leading to new discoveries.This is fundamental research that lies at the interface of atomic and condensed matter physics. Systems of cold atoms are intriguing and may hold possibilities for future technologies. Conspicuous among these is the potential to realize powerful new methods of computation based on the principles of quantum mechanics. Students will receive training in advanced theoretical condensed matter physics which will stimulate students to develop broad interests and skills in the scientific frontiers. Aspects of the research, particularly the underlying theoretical techniques, form part of the subject matter of the advanced physics courses that the PI will develop.