玻色氣體中配對超流體及配對超固體的數值研究在光晶格實驗中，操控冷原子技術上的成功，已能模擬凝聚態物理中許多基礎的量子系統。這些系統中，不同的相互作用的強度及密度，都能高度調控並實現在不同維度的晶格上。尋找各樣的非傳統量子基態，並了解其量子態在強相關系統中的物理性質，已成為冷原子實驗的其中一個重要目標。在本計劃中，我們將集中對配對超流體(pair superfluid)和配對超固體(pair supersolid)在相關系統中的形成與性質，進行量子蒙地卡羅數字計算的研究。我們將針對有三體限制的玻色哈伯(Bose-Hubbard)模型、兩類玻色子共存的玻色哈伯模型及長距離偶極作用下的玻色哈伯模型，研究當中不同的配對超流體和配對超固體基態的特性，詳細分析並加以比較，並對真實實驗中的定量觀察作出可靠的指引。 The numerical study of pair superfluid and pair supersolid in Bose gases. Ultracold bosonic atoms have been successfully trapped in optical lattices with controllable parameters that mimic Hamiltonian of fundamental interest in condensed matter physics. These highly tunable systems can be demonstrated in one, two and three dimensional lattices with variable interaction strength and particle density as well. Considerable attentions have been focused on the search of unconventional quantum phases that may enhance our understanding of strongly correlated quantum systems. In this project, we plan to numerically study the nature of the novel pair superfluid and pair supersolid phases that may arise in various models. In particular, we focus on the three-body constraint extended Bose-Hubbard model, the two-species hard-core Bose-Hubbard model, and the two-components Bose-Hubbard model with long-range dipole interaction. The study of the appearances of the pair super-states on these models will provide us more insight on the realization of these exotic phases in the optical experiments.
