双层光晶格中超冷偶极原子系统的新颖量子相研究

The ultracold dipolar atomic system in optical lattices can be used to emulate the effect of dipole-dipole interactions present in the conventional crystal, and is also a promising candidate for quantum memory. Successful manipulations of quantum degenerate gases of Dy and Er in recent years provide a new opportunity to investigate the influence of dipole-dipole interactions on ground-state phase diagram of ultracold atoms in optical lattices. Most of the past investigations were concerned with monolayer optical lattices and obtained the ground-state phase diagram under the approximation that truncates the interaction range of dipole-dipole potential. However, this approximation not only makes some of the solid phases with commensurate fillings hidden but also impacts the configuration number and gap value of metastable states. Using analytic and numerical methods and calculating the whole-range dipole-dipole interactions, this project aims to investigate the ground-state phase diagram and the properties of low-lying metastable states of ultracold atoms in bilayered optical lattices. By introducing the effect of geometric frustrations and continuously tuning the polarization direction, the evolving behavior of different phase regions in the phase diagram will be investigated and novel quantum phases are hunted for. The quantitative relations between the number and gap value of metastable configurations and the lattice size and truncated ranges of interactions will be investigated, in order to analyze the influence of low-lying metastable configurations on the stability of ground-state phases. These investigations not only have important significance in fundamental researches but also have reference values to propose new schemes for the utilization of rare earth resources.

光晶格中的超冷偶极原子系统不仅能用来模拟传统晶体中的偶极相互作用效应，同时也是实现量子存储的候选方案之一。 近年实现的稀土Dy,Er等原子的简并气体，为研究偶极相互作用对光晶格中超冷原子基态相图的影响提供了新的机会。以往的研究大多关注单层光晶格情形，通过对偶极势做力程截断近似，得到系统的基态相图。力程截断不仅掩盖了基态相图中可能出现的公度填充固体相，而且也会影响低能亚稳态的组态数和激发能隙。本项目拟用解析和数值方法，在对偶极势不做力程截断近似的条件下，研究双层光晶格中超冷偶极原子系统的基态相图和低能亚稳态性质。通过引入几何失措效应和连续改变偶极极化方向， 研究相图中各相区的演化行为，寻找新的量子相。通过研究低能亚稳态的组态数和能隙与晶格尺寸和力程截断长度的定量关系，分析低能亚稳态是否会影响基态量子相的稳定性。 该研究不仅在基础研究领域有重要意义，对探索稀土资源的其它利用方式也有参考价值。

在项目执行期内，项目团队研究了光格子上冷原子气体中超固相概念的界定，厘清了晶格序的概念；研究了Dyson运动相互作用在低维量子磁性系统中影响，改进了处理格点约束的投影算符方法，发展了处理低维量子磁性系统的自旋波理论，我们称为双约束自旋波理论，解决了既有理论不自洽的问题；开发了处理双参量实验数据的程序，并用来处理实验室的磁化数据；系统总结了自旋的波色型，费米型，复合型以及自旋想干态表示，并揭示了不同表示之间的关系和适用条件；研究了斯格明子和螺旋磁结构的产生机理以及磁有序结构之上的元激发；研究了纳米盘中斯格明子磁结构与超导薄膜中涡旋磁场之间的相互作用能；研究了处理低维自旋格子系统的数值算法，编写了代码，积累了数值研究的经验。