Low Dimensional Quantum Gases: Resonance, Quantum magnetism and Non-Abelian vortices

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Quantum many-body systems in 2D can exhibit surprising features and unique correlations that otherwise do not exist in 3D. The best known example is perhaps fractional quantum hall states where excitations carry a fraction of electron charge. 2D Quantum gases are another example.This proposal focuses on 2D quantum gases with strong emphases on near-resonance physics, interplay between quantum magnetism in optical lattices and Feshbach resonances, and the hydrodynamics of non-Abelian vortices and non-Abelian gauge fields in 2D superfluids. Experimentally, near-resonance 2D quantum gases can be realized by combining optical confinement and Feshbach resonance. Theoretically, we plan to explore the interplay between few- and many-body physics in 2D, especially three-body correlations and the many-body effects on few-body clusters which can be studied in the loss spectroscopy. The other direction we are going to pursue is on quantum magnetism via Feshbach resonance; we suggest a proposal of studying quantum magnetism by combining Feshbach resonances and optical lattices to dramatically increase the range of temperatures within which magnetic ordering and phase transitions can be studied. The last direction is about low dimension spin correlated quantum gases; we plan to study the hydrodynamics of non-Abelian vortices in 2D gases, artificial non-Abelian gauge fields and dynamic generation of vortices in rotating quasi 2D traps.