Strongly interacting cold atoms in optical lattices

自从观察到超冷原子的玻色-爱因斯坦凝聚以来，人们已经在实验和理论上做出了巨大的努力，以了解每个原子在纳开尔文温度下如何与其他原子合作，以及冷原子之间的有趣关联如何在各种实验中表现出来。这一领域的里程碑式的实验包括观察光学晶格中Rb原子的超流-Mott绝缘态转变，观察Tonk-Girardeau气体，观察锂或钾原子的Feshbach共振附近的分子和超流体。人们普遍认为，许多最复杂的物理系统，如量子凝聚态系统，都可以用冷原子有效地模拟，而冷原子研究的前沿之一就是利用超冷物质来研究多体物理中的各种悬而未决的问题。光学晶格为研究超流体、量子磁学和相干量子动力学提供了令人着迷和独特的机会，并将导致我们对相互作用的超冷原子的基本原理的各种突破。这些研究不仅将揭示冷原子在纳米开尔文温度下的行为，还将揭示我们对高温超导、量子计算等问题的理解；其影响可能远远超出原子、分子和光学物理。这个建议集中在极端量子极限中的超冷原子之间的关联；特别是，a)Feshbach共振和晶格Feshbach共振附近的超流体；b)超冷原子的超精细自旋相关物质，或者更广泛地说，光学晶格中的量子磁性；c)分数级拓扑激发的产生和检测，以及冷原子的自旋关联的检测；d)超越平均场的相干动力学，特别是相干自旋动力学。

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.