自旋-轨道耦合超冷原子体系中人工规范场及相应量子相变研究

The spin-orbit coupled ultra-cold atomic system provides an ideal platform for quantum simulations for investigating the gauge field theories because of its manifested macroscopic quantum effects and its high degree of controllability and experimental observability. Most of the existing studies on constructing artificial gauge fields in ultra-cold atomic systems are concentrated in the domain of electrostatics. It is not enough to meet the needs for simulating the spatio-temporal dynamics of the truly existing gauge fields in nature. This project is devoted to exploring the theory of artificial gauge fields with sound spatiotemporal dynamics in the ultra-cold atomic systems based on the spin-orbit coupling mechanism by using cavity optomechanics and local field effect, and to studying the artificial gauge field system with higher intrinsic degrees of freedom. For the artificial gauge field with sound spatiotemporal features constructed in the spin-orbit coupled ultra-cold atomic system, this project will study the novel quantum states and quantum phase transitions in the system, and determine the relation between the critical point of the quantum phase transition and the spin-orbit coupling, and give the phase diagram of the system. The results of this project can broaden the potential of the spin-orbit coupled ultra-cold atomic system functioning as the quantum simulator for investigating the general gauge theories, and promote the discovery of new quantum states and exotic quantum phenomena. They will support for the investigations of the gauge theories in the fields of high energy physics, condensed matter physics and atomic physics.

自旋-轨道耦合超冷原子体系因其所表现出的宏观量子效应及其高度可调控性与实验可观测性，为人们提供了一个用以构造并研究规范理论的理想量子模拟实验平台。现有的在超冷原子体系中构造人工规范场的研究大都集中在静电学的范畴内，尚无法满足人们模拟研究自然界中真实存在的规范场的时空动力学特性的需要。本项目致力于探索基于自旋-轨道耦合机制，采用腔光力学和局域场效应等方法在超冷原子体系中构造具有良好时空动力学特性人工规范场的理论，并且研究具有更高内禀自由度的人工规范场系统。针对自旋-轨道耦合超冷原子体系中构建的具有良好时空特性的人工规范场，本项目将研究系统中的新奇量子态和量子相变，确定量子相变临界点与自旋-轨道耦合的关系，并描绘体系的相图。研究成果可以拓宽自旋-轨道耦合超冷原子系统作为规范理论模拟器的潜能，推动新物态和奇异量子现象的发现，为高能物理、凝聚态物理和原子分子物理等领域中规范理论的研究提供支持。

腔量子电动力学 (CQED) 系统是一个可以用于研究物质与电磁场之间相互作用所产生的量子现象的重要多功能平台。腔光力学系统是最重要的例子之一，它涉及量子谐振子和腔场之间的相互作用，具有非常高的可控性。通过将腔量子电动力学与冷原子物理研究的最新进展相结合，本项目研究了 CQED 系统中玻色-爱因斯坦凝聚体 (BEC) 的腔光动力学和磁量子序。 我们提出可以将BEC 囚禁在环形腔中，与行波腔场相互作用， 这会在冷原子中诱导非常规的半量子化自旋-轨道耦合。这种自旋-轨道耦合在本质上是一种人造的规范场，可以改变系统基本元激发的动力学行为。更重要的是，这种人造的规范场会诱导出一种长程的原子间相互作用。这种长程相互作用将使得冷原子系统的能谱具有新颖的量子简并形式，从而产生一种全新的过渡量子相。这些结果为基于超冷原子系统的量子动力学以及量子相变研究提供了新视角和新思路。