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

二维量子多体系统可以表现出令人惊讶的特征和独特的相关性，否则在三维中就不存在。最著名的例子可能是分数量子霍尔态，其中激发带一小部分电子电荷。量子气体是另一个例子。本文主要研究二维量子气体的近共振物理，光学晶格中量子磁性与费什巴赫共振之间的相互作用，以及二维超流体中非阿贝尔涡旋和非阿贝尔规范场的流体动力学。实验上，将光约束与费什巴赫共振相结合可以实现二维量子气体的近共振。理论上，我们计划探索二维中少体和多体物理之间的相互作用，特别是三体相关和多体对少体团簇的影响，这些可以在损失光谱中研究。我们要研究的另一个方向是通过费什巴赫共振研究量子磁性；我们建议通过结合费什巴赫共振和光晶格来研究量子磁性，从而大大增加可以研究磁有序和相变的温度范围。最后一个方向是关于低维自旋相关量子气体；我们计划研究二维气体中非阿贝尔涡的流体动力学、人工非阿贝尔规范场和旋转准二维圈闭中涡的动态生成。

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.