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，人们进行了大量的实验和理论研究，以了解每个原子在纳开尔文温度下如何与其他原子合作，以及冷原子之间的迷人相关性如何在各种实验中表现出来。这一领域的里程碑实验包括观察光学晶格中铷原子的超流-莫特绝缘态跃迁，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。冷原子可以有效地模拟许多复杂的物理系统，如量子凝聚态系统，利用超冷物质研究多体物理中的各种突出问题是冷原子研究的前沿之一。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迷人而独特的机会，并将导致我们对相互作用超冷原子基本原理的理解取得各种突破。这些研究不仅将揭示冷原子在纳开尔文温度下的行为，而且还将揭示我们对高温超导性，量子计算等问题的理解;其影响可能远远超出原子，分子和光学物理学。该方案主要研究极端量子极限下超冷原子间的关联，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关联物质，或者更一般的光晶格中的量子磁性，c）分数拓扑激发的产生和探测以及冷原子自旋关联的探测，d）超冷原子自旋关联的产生和探测。d）超平均场相干动力学，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.