Strongly Interacting Ultra cold atoms in Optical Lattices

在这个提议中，我想提议研究光学晶格中强相互作用的超冷原子。我打算在未来几年研究的四个主要课题是：a）光学晶格中的费什巴赫共振，特别是强浅层二聚体散射和晶格势的独特影响。与Feshbach共振相关的其他问题是在幺正性极限下可能的新配对态和具有布居不平衡的超流体。我特别感兴趣的是由自旋单重态和三重态粒子-空穴激发介导的交换过程的影响。 B）高超精细自旋冷原子的自旋关联凝聚和绝缘态。本文主要研究F=2的Rb和Na原子的态，希望能为今后的高自旋冷原子实验提供一些参考。总的来说，我想探索光晶格中量子磁学和低维物理的新机会。c）各种自旋关联态和这些态中奇异激发的实验检测。我想建立自旋关联和条纹图案之间的牢固关系，理解当存在各种缺陷时TOF干涉中的条纹，以及分数循环量子对集体模式的影响。d）利用光学晶格中的冷原子设计量子哈密顿量;探索原子多体态作为量子计算资源的可能性，如普适团簇态、光学晶格中的Kitaev复曲面码等。

In this proposal, I would like to propose studying strongly interacting ultra cold atoms in optical lattices. The four major topics I intend to investigate in the next few years are:a) Feshbach resonances in optical lattices, especially the distinct effects of strong shallow dimer scattering and lattice potentials. The other issues related to Feshbach resonances are possible novel pairing states in the limit of unitarity and superfluids with population imbalance. I am particularly interested in the effect of exchange processes mediated by spin singlet and triplet particle-hole excitations.  b) Spin correlated condensates and insulating states of cold atoms with high hyperfine spins. Here I intend to make major efforts to investigate states of F=2 Rb and Na  and  and hopefully to offer some insight into furture experiments of high spin cold atoms. In general, I would like to explore the new opportunities in quantum magnetism and low dimensional physics in optical lattices.c) Experimental detection of various spin correlated states and exotic excitations inthese states. I would like to establish firm relations between spin correlations and the patterns of fringes, to understand the fringes in the TOF interference when various defects are present, and the influence of the fractionalized circulation quantum on collective modes.d) Designing quantum Hamiltonian using cold atoms in optical lattices; exploring possibility of having atomic many-body states as resources for quantum computation, such as universal cluster states, Kitaev toric codes in optical lattices.