自旋轨道耦合超冷原子的少体物理及多体效应

Ultracold atomic gases provide an ideal platform and even more extensive environment for exploring the physics of spin-orbit coupling, as the system is clean from impurity or disorder and many experimental parameters are highly controllable. In this context, with the help of exact solutions of few-body problems, we plan to investigate brand new physics brought by spin-orbit coupling, in combination with different statistics, dimensions and scattering in different partial-wave channels. Specifically, our study will be carried out in the following three aspects. First is the effect of spin-orbit coupling to effective scattering in quasi low-dimensional(D) systems, as well as its many-body effect in the 1D hard-core system and 2D bosonic system. Second is the study of few-body bound states in fermion mixtures with spin-orbit coupling, and its influence to the property of polaron and the phase diagram of fermionic superfluidity. Third is to establish an interacting Hamiltonian with high partial-wave scattering (for example, p-wave) in the presence of spin-orbit coupling, and further based on which model to study the new features of possible topological superfluid transition. All these topics are in close contact with the very frontier of experimental and theoretical developments of cold atoms with spin-orbit coupling, and the questions raised therein are not only theoretically interesting but also timely and will have strong experimental impact. In a word, the purpose of this study is to search for new phases and new physics brought by spin-orbit coupling in ultracold atoms, and in turn to guide and push forward the exploration of new physical phenomena in experiments.

超冷原子气体作为一个高度可控可调且与杂质无序绝缘的实验系统，为研究自旋轨道耦合效应提供了理想而且更加广阔的物理环境。在此基础上，借助于少体问题的严格解，我们将充分挖掘自旋轨道耦合在不同统计，不同维数，及不同分波散射相互作用下所导致的新物理和新效应。本项目计划从以下三个方向来展开研究：一. 自旋轨道耦合对准低维量子气体的有效散射的影响，以及它在一维硬核和二维玻色子系统中产生的多体效应。二. 自旋轨道耦合下的费米混合体的少体束缚态，以及它们对极化子性质，及超流相图的影响。三. 自旋轨道耦合在高分波（p波）散射系统的理论模型建立，及在此基础上对拓扑超流相变的研究。这些课题均是立足于实验和理论的前沿，结合冷原子实验的最新进展提出的理论上亟待解决的问题，目的在于在冷原子这一理想平台上寻找自旋轨道耦合所诱导的新物态和新机制，从而指导和推动相应实验的进展。

在国家自然科学基金委面上项目“自旋轨道耦合超冷原子的少体物理及多体效应”的资助下，我们在自旋轨道耦合超冷原子系统的少体和多体特性上展开了一系列研究，取得了一批重要的研究成果。在少体问题方面，我们在国际上首次严格求解了自旋轨道耦合冷原子体系的三体问题，提示了多种新型的普适的三体束缚态的存在，受到国际同行的广泛关注和认可；在多体问题方面，我们重点研究了自旋轨道耦合所诱导的新奇费米超流，包括有限动量的FFLO超流以及拓扑超流，并发现了光晶格体系新型的超流-绝缘相变。此外，我们还针对极化子体系和一维强相互作用体系展开了一系列研究，揭示了自旋轨道耦合在这两种体系中所诱导的少体和多体效应，以及它们自身其它的一些可观测物理效应，包括Efimov三体关联效应、量子磁性、普适热力学性质等等。这些研究都是围绕项目计划书中的有关内容来展开的，同时又紧密结合冷原子实验的当前最新进展，不局限于项目研究内容，对多种类型冷原子系统的少体和多体性质展开了充分的理论研究，为多项实验提供了理论解释，同时多项预言也为今后的实验探测提供了理论支撑。受项目资助期间在Physical Review等主要物理学杂志上总共发表SCI论文26篇，包括PRX 1篇，PRL 3篇，PRA/B (rapid communication) 6篇。