外加规范场下旋量凝聚体量子现象的理论研究

The proposal aims at presenting a systematic study on the exotic quantum phenomena of spinor condensates in synthetic gauge fields or with the spin-orbit coupling. A recent progress in cold atom physics is that an artificial external abelian or non-abelian gauge potential, or the induced spin-orbit coupling can be generated by engineering the atom-light interactions. These latest achievements have stimulated many studies in condensates in the abelian or non-abelian gauge fields, forming a very new and fast growing area of research that promises to host an even richer variety of exotic phenomena unknown previously in the condensed matter physics. In comparison to scalar ones, spinor condensates exhibit richer static and dynamic properties due to the internal spin degrees of freedom. The interplay between spin-orbit coupling and the unique phases and spin dynamic properties will lead to many new physics which have not been investigated before..In this proposal, we intend to address the following topics: 1) the ground-state phase diagrams, the collective excitations, and the atom-atom interactions in spin-orbit coupled spinor condensate; 2) the vortex structure and other topological excitations (such as skyrmion), and the pump scheme of vortex; 3) the BKT transition in 2D spin-orbit coupled condensates; 4) quantum fluctuations in spin-mixing dynamics inside a spinor condensate in the synthetic gauge fields; 5) quantum dynamics and geometric phase interference effect in a double well potential; 6) the exotic phase diagrams and correlation effects in spin-orbit coupled quantum gas in the optical lattice. In contrast to the conventional condensates, the situation here is shown to be significantly more complicated, and the usual single-mode approximation is invalid due to the interplay of synthetic spin-orbit coupling and the unique hyperfine spin structure and the associated spin correlation effects in the spinor condensates. Spin-orbit interaction couples the internal (spin) and orbital (momentum or angular momentum) degrees of freedom of condensates, which significantly changes the single particle energy dispersion, or can lead to non-s-orbital band (such as p-orbital band) structure of the system in optical lattice. Based on these significant changes of single particle behaviors due to the strong spin-orbit coupling, we plan to construct new quantum many-body model and find theoretical approaches beyond the single-mode approximation and go beyond the mean-field description by including the effects of quantum fluctuations. The new results obtained in the exotic ground states, collective excitations, topological excitations, quantum dynamics in spin mixing, geometry phase, the BKT transition in 2D quantum gases, and the new phase diagram and correlation effects in optical lattice will have important implications not only in cold atom physics, but also in quantum many-body systems in condensed matter physics.

本项目着重于外加规范场下的旋量凝聚体的基态、低能激发，及其中的量子多粒子关联、自旋动力学和几何相位干涉现象的理论研究，揭示其中新的物理现象，为量子多体理论和基于冷原子体系的量子调控提供坚实的理论基础。.最近发展的基于光与原子相互作用的实验手段，可以在冷原子体系上附加外规范场，以造成人工合成的外电磁场或诱导出自旋-轨道耦合，为研究量子多体模型提供了可以精确调控的平台。本项目将针对旋量凝聚体丰富的自旋结构，考虑外加电磁场或自旋-轨道耦合引起的单粒子基态性质的显著改变，建立模型，有效地处理多粒子和自旋关联效应，并发展相关的数值计算方法，研究外规范场下旋量凝聚体中新奇的相，涡旋态的产生、调控和物理特性，自旋动力学行为、退相干机制和几何相位干涉现象，2维BKT转变，以及光晶格中自旋-轨道耦合引起的非s轨道能带所导致的基态和多粒子强关联性质等前沿问题。

本课题的主要目标是研究在外加人工合成规范场下冷原子体系的性质，在本课题的资助下，我们在冷原子系统人工合成规范场的机制，外加规范场下冷原子系统的性质和拓扑态，低维受限量子体系的输运、PT对称性及拓扑量子性质等方向上从事理论研究工作。主要创新成果包括：.1）规范场下冷原子体系中的量子性质和拓扑态。利用周期的磁场脉冲，提出了一种在冷原子体系中动力学地人工合成具有空间周期性的有效磁场的方案。当原子自旋绝热地随着有效磁场演化时，在原子质心运动中会产生一个规范场。等效势场形成honeycomb晶格，矢量势导致跳跃系数中出现复的Peierls相位因子，这有助于形成拓扑陈绝缘体。进一步调节外部参数，可以产生拓扑相变和拓扑平能带。.2）提出了冷原子体系人工合成空间周期变化的磁场或磁晶格的机制，磁晶格的晶格常数和晶格深度都可以通过实验调节。由此导出的哈密顿量在以往的凝聚态物理中未曾被系统研究过，而我们的研究结果表明其能带结构展现出新奇的效应，如可以支持拓扑非平庸相。人工合成的磁晶格将被应用于玻色子和费米子体系。.3）冷原子光晶格系统中s波超导体的自旋-轨道耦合。发现光晶格显著地改变了体系的单粒子能谱：格点模型可以在两个区域中产生majorana费米子。对于一个处在外谐振子约束势下的格点系统，发现存在一个上临界磁场，将拓扑超导相推移至约束势的两翼，此时majorana费米子可以存在于实空间的四个分立区域中。体系拓扑性质受到杂质的影响。.4）一维量子体系的Anderson局域化和拓扑性质。近年来在冷原子系统的实验已实现一维Aubry-André-Harper（AAH）模型。针对具有p波超导配对和余弦调制的最近邻跃迁项的AAH模型，发现当系统处于无公度情形时，由于跃迁项中的调制函数的存在，系统更容易被局域化。而对于有公度的情形，随着参数的改变，系统将会表现出平庸态，Su-Schrieffer-Heeger（SSH）型拓扑态以及Kitaev型拓扑态，并出现费米子分数化的现象。