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

2D中的量子多体系统可以显示出在3D中不存在的令人惊讶的特征和独特的关联。最著名的例子可能是分数量子霍尔态，其中激发携带一小部分电子电荷。2D量子气体是另一个例子。这个提议主要关注2D量子气体的近共振物理，光学晶格中的量子磁性和Feshbach共振之间的相互作用，以及2D超流体中非阿贝尔涡旋和非阿贝尔规范场的流体动力学。在实验上，将光学限制和Feshbach共振相结合，可以实现近共振的2D量子气体。理论上，我们计划在2D中探索少体物理和多体物理之间的相互作用，特别是三体关联和多体效应对少体团簇的影响，这可以在损失谱中进行研究。我们要追求的另一个方向是通过Feshbach共振研究量子磁学；我们建议通过将Feshbach共振和光学晶格相结合来研究量子磁学，以显著增加研究磁有序和相变的温度范围。第四个方向是关于低维自旋相关量子气体；我们计划研究2D气体中非阿贝尔涡旋的流体力学、人工非阿贝尔规范场以及旋转准2D囚禁中涡旋的动态产生。

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.