This award supports the theoretical research and education on novel states of matter with ultra-cold atoms and molecules cooled down to ultra-cold temperatures at one millionth of a degree above absolute zero. Atoms and molecules are often trapped in the artificial crystalline structures generated by laser beams. In spite of very different energy scales, atoms and molecules develop quantum coherence and behave very similarly to electrons in solids. Compared to solid state systems, a major advantage of the ultra-cold atom and molecular systems is that interaction effects can be controlled at an unprecedented level. This opens up a whole new opportunity for the study correlated electron motion in materials through the study of ultra-cold atoms in crystals of light. The physics of ultra-cold atoms and molecules opens new directions and new states of matter than cannot exist or at least would be very difficult to make using electrons in materials. The Coulomb interaction between electrons depends only on their separation. In contrast, the interaction between two dipolar molecules depends on the orientation of the displacement vector joining the two molecules. These new features lead to novel and complex many-body physics which are not easily accessible in materials. The PI aims to develop new directions in the study of ultra-cold atoms and molecules and to provide theoretical guidance for the experimental effort to find new states of matter. This research lies at the interface between cold atom and condensed matter physics, and will bring new understanding on quantum states of matter including magnetism, superconductivity, and topological states. Students will be involved in the research and will receive solid training to develop broad interests and skills in the frontiers of condensed matter physics through course study, seminars, and communications with experimentalists. The application and appreciation of the principles of symmetry and topology will be emphasized. Advances in cold atom physics will be incorporated into course studies with an up-to-date perspective from many-body physics that is not traditionally provided.
This award supports the theoretical research and education to study important direction in ultra-cold atoms and dipolar molecules with multiple internal degrees of freedom. The PI will use both analytical and numerical methods to explain experimental results and predict novel properties for future experimental tests. Knowledge gained from this research will greatly enrich the physics of superfluidity, quantum magnetism, and topological states. The research has the following foci: 1) The non-perturbative study of quantum magnetism. An itinerant ferromagnetic ground state has been proved to exist for a class of systems with two and three dimensional p-orbital bands filled with cold fermions. Systematic quantum Monte-Carlo simulations free of the sign problem are planned to illuminate open issues of ground-state and thermodynamic properties of itinerant ferromagnetism. The exotic quantum antiferromagnetism of alkaline-earth fermions exhibit SU(2N) symmetries. The PI will study the challenging problem of the strong charge and magnetic fluctuations using quantum Mote-Carlo simulations. 2) The PI plans to study ultra-cold atoms in the p-orbital bands in the diamond lattice, including strong-correlation effects in the three dimensional flat bands, and the frustrated superfluid state described by a novel statistical 4-coloring model. 3) The PI will explore the application of quaternions in the study of 3D topological states for ultra-cold atoms with synthetic spin-orbit coupling. In particular, the study will focus on the three dimensional Landau levels with quaternionic analytic properties. 4) The study of interaction effects in Majorana flat bands in unconventional pairing states with dipolar fermions. This projects aims at exploring new states of matter in multi-component cold atom and molecular systems. This research lies at the interface between condensed matter and cold atom physics and will greatly benefit both fields. Students will be involved in the research and will receive solid training to develop broad interests and skills in the frontiers of condensed matter physics through course study, seminars, and communications with experimentalists. The application and appreciation of the principles of symmetry and topology will be emphasized. Advances in cold atom physics will be incorporated into course studies with an up-to-date perspective from many-body physics that is not traditionally provided.