Novel Quantum Phases in Orbital and Large Spin Systems with Cold Atoms

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TECHNICAL SUMMARY:This award supports theoretical research and education on novel quantum phases in orbital and large spin systems with cold atoms. The research explores novel quantum phases and emergent symmetries with cold atoms which are not accessible in usual solid state systems and provides guidance for new experiments. The application of symmetry principles is essential for this project which not only deepens our understanding but also provides the guidance to new discoveries. A variety of methods in condensed matter physics and field theory are employed, including bosonization, the renormalization group, the large-N method, the self-consistent mean-field theory, and band structure calculations.The first research topic is the study of novel quantum phases in high orbital bands in optical lattices. The p-orbital bosons exhibit complex-valued many-body wave functions characterized by the formation of on-site orbital angular momentum moments. The research encompasses orbital superfluidity in various lattices which exhibit collinear ordering (e.g., staggered and stripe-like), non-collinear ordering, and ''frustrated'' distributions of orbital angular momentum moments. For fermionic orbital systems, the research will focus on the honeycomb lattice, which is a p_xy-orbital counterpart of graphene. The second research topic is the study of large spin physics with cold fermions. Particular attention is paid to spin-3/2 systems which possess a generic SO(5) symmetry without fine tuning. The symmetry gives rise to important consequences such as the protected degeneracy in collective excitations, new properties of the quantum Monte-Carlo sign problem, the quintet pairing superfluidity, and the four-fermion quartetting superfluidity. Planned investigations include quantum magnetism in the spin-3/2 systems and other large spin systems as well, such as the pseudospin-1 systems and the spin-5/2 systems. The research will provide new ideas on exotic orbital superfluidity, orbital exchange physics, and emergent quantum magnetic states. It also suggests new directions for future experiments. Knowledge gained from this research deepens our understanding on strong correlation physics in both cold atom and condensed matter systems.This research lies at the interface between condensed matter and cold atom physics and will benefit both fields. Students will receive training in the application of the symmetry principles and the research will stimulate students to develop broad interests and skills in the frontiers of strongly correlated systems. Aspects of the research, particularly the underlying theoretical techniques, form part of the subject matter of the advanced physics courses being developed by the PI at his university.NONTECHNICAL SUMMARY:This award supports theoretical research and education that seeks to predict new states of matter composed of ultracold atoms in artificial crystals of light. Researchers have found that atoms can be trapped in modulated laser beams much like electrons are trapped in the force fields of atomic nuclei in a crystalline solid. Electrons have two internal configurations; these are related to their magnetic properties. Atoms can have many more internal configurations, leading to possible new states of matter that have no counterparts in conventional materials, but have intriguing properties and may display interesting phenomena. The research develops 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 and leading to new discoveries. This is fundamental research that lies at the interface of atomic and condensed matter physics. However, 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. This research lies at the interface between condensed matter and cold atom physics and will benefit both fields. Students will receive training in the application of the symmetry principles and the research will stimulate students to develop broad interests and skills in the frontiers of strongly correlated systems. Aspects of the research, particularly the underlying theoretical techniques, form part of the subject matter of the advanced physics courses being developed by the PI at his university.