标题： 流形形成和超冷晶格自旋原子在中间相互作用区域的交叉 显示英文标题

标题： Manifold formation and crossings of ultracold lattice spinor atoms in the intermediate interaction regime

摘要： 超冷自旋原子在弱相互作用和强相互作用区域已经得到了广泛的研究，而在中间区域的行为则了解较少。 我们数值研究了有限尺寸的超冷自旋原子系综在中间相互作用区域的行为，并揭示了从强相互作用区域到中间区域的本征态演化。 在强相互作用区域，已知低能本征能谱呈现出良好的分隔多层结构，能量间隙保护了本征态的分类。 在中间相互作用区域，发现本征态的分类得以保持，而本征能谱变为准连续谱，不同层之间开始重叠。 重叠导致了相邻层之间的直接交叉和避免交叉，这由交叉中涉及的本征态的组合对称性决定。 推导出一个改进的t-J模型来描述中间区域的低能本征态，该模型可以捕捉到层的形成和交叉。 还研究了通过避免交叉进行的状态制备。 显示英文摘要

摘要： Ultracold spinor atoms in the weak and strong interaction regime have received extensive investigations, while the behavior in the intermediate regime is less understood. We numerically investigate ultracold spinor atomic ensembles of finite size in the intermediate interaction regime, and reveal the evolution of the eigenstates from the strong to the intermediate regime. In the strong interaction regime, it has been well known that the low-lying eigenenergy spectrum presents the well-gaped multi-manifold structure, and the energy gaps protect the categorization of the eigenstates. In the intermediate interaction regime, it is found that the categorization of the eigenstates is preserved, and the eigenenergy spectrum become quasi-continuum, with different manifolds becoming overlapped. The overlapping induces both direct and avoided crossings between close-lying manifolds, which is determined by the combined symmetries of the eigenstates involved in the crossing. A modified t-J model is derived to describe the low-lying eigenstates in the intermediate regime, which can capture the formation and crossings of the manifolds. State preparation through the avoided crossings is also investigated.