近日，兰州大学物理科学与技术学院的应祖建及其研究团队取得一项新进展。经过不懈努力，他们揭示具有斯塔克非线性耦合Jaynes-Cummings模型中自旋缠绕和跃迁的拓扑性质。相关研究成果已于2024年5月3日在国际知名学术期刊《物理评论A》上发表。

本文对具有斯塔克非线性耦合的Jaynes-Cummings模型中的TPTs进行了严格的研究。根据厄米多项式的性质，研究人员证明本征函数的拓扑结构与节点的自旋缠绕具有精确的对应关系，从而产生了一个没有反缠绕节点的全自旋缠绕。研究人员发现相邻的福克态之间的叠加导致一个非平凡的自旋缠绕。他们发现，在无穷远处，对绕角圈数的伪分数贡献实际上是一个整数。因此，该模型中的相变展现出TPTs（拓扑相变）的特性，其中激发数被赋予了拓扑量子数。

模型中的主跃迁开创了一种新的范式，这一跃迁既属于破坏对称性的朗道跃迁类型，又具备保护对称性的拓扑跃迁特征，而传统上这两类跃迁由于对称要求相反而不相容。这种跃迁类调和是通过保留更高的对称性(这里是宇称)来实现的，它保护了TPTs，而对称破缺涉及到子对称性。他们还解释了在反向旋转条件下非常规TPTs的起源。这项研究结果可能为光-物质相互作用中的少体相变提供更深入的见解。

据悉，除了探索新的跃迁模式外，全面了解跃迁性质是相变研究的终极追求。光-物质相互作用的基本模型表现为单量子比特拓扑相变(TPTs)，除了数值研究外，还需要解析论证。

附：英文原文

Title: Spin winding and topological nature of transitions in the Jaynes-Cummings model with Stark nonlinear coupling

Author: Zu-Jian Ying

Issue&Volume: 2024/05/03

Abstract: Besides exploring novel transition patterns, acquiring a full understanding of the transition nature is an ultimate pursuit in studies of phase transitions. The fundamental models of light-matter interactions manifest single-qubit topological phase transitions (TPTs), which call for an analytical demonstration apart from numerical studies. We present a rigorous study of TPTs in the Jaynes-Cummings model generally with Stark nonlinear coupling. In terms of the properties of Hermite polynomials, we show that the topological structure of the eigenfunction has an exact correspondence to the spin winding by nodes, which yields a full spin winding without antiwinding nodes. We find it is the superposition between neighboring Fock states that leads to such a nontrivial spin winding. The spurious fractional contribution to the winding number of the winding angle at infinity is found to be actually an integer. Thus, the phase transitions in the model have the nature of TPTs and the excitation number is endowed as a topological quantum number. The principal transition establishes a paradigmatic case in which a transition is of both the symmetry-breaking Landau class of transition and the symmetry-protected topological class of transition, while conventionally these two classes of transitions are incompatible due to the contrary symmetry requirements. Such a transition-class reconciliation is realized by a preserved higher symmetry (here the parity) which protects the TPTs, while the symmetry breaking involves the subsymmetries. We also explain the origin of unconventional TPTs in the presence of counterrotating terms. Our results may provide deeper insight into the few-body phase transitions in light-matter interactions.

DOI: 10.1103/PhysRevA.109.053705

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.053705