Strongly interacting cold atoms in optical lattices

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Since the observation of Bose-Einstein condensation of ultra cold atoms, there have been tremendous experimental and theoretical efforts to understand how each individual atom cooperates with others at nanokelvin temperatures and how fascinating correlations between cold atoms manifest themselves in various experiments. Milestone experiments in this field include the observation of superfluid-Mott insulating state transitions of rubidium atoms in optical lattices, the observation of Tonk-Girardeau gases, the observation of molecules and superfluids near Feshbach resonances of lithium or potassium atoms. It is widely accepted that many most sophisticated physical systems such as quantum condensed matter systems can be effectively simulated using cold atoms and one of the forefronts of cold atom research is to use ultra cold matter to investigate various outstanding issues of many-body physics. Optical lattices provide fascinating and unique opportunities to study superfluids, quantum magnetism and coherent quantum dynamics, and will lead to various breakthroughs in our understanding of fundamentals of interacting ultra cold atoms. These studies will shed light not only on how cold atoms behave at nanokelvin temperatures, but also on our understanding of issues such as high temperature superconductivity, quantum computation; the impact can go far beyond atomic, molecular and optics physics. This proposal focuses on correlations between ultra cold atoms in extreme quantum limits; especially, a) superfluids near Feshbach resonances and lattice Feshbach resonances; b) hyperfine spin correlated matter of ultra cold atoms, or more generally quantum magnetism in optical lattices; c) creation and detection of fractionalized topological excitations and detection of spin correlations of cold atoms; d) beyond-mean-field coherent dynamics especially coherent spin dynamics.