填充里德堡原子周期光学结构中的光子态及其几何特性研究

The in-depth study of the continuous invariant properties of the photonic states in periodic optical structures leads to the emergency of topological photonics. The current topological photonics research mainly focuses on the linear systems. The aim of this project is to investigate the properties of photonic wave functions in the periodic photonic structures filled with Rydberg atoms and reveal the photonic states and their geometrical properties (such as topological phase). There are two kinds of periodic photonic structures considered in our project: photonic band gap crystals with periodic defects; atomic gases confined by lattice potentials with consist of optical standing waves. The dipole-dipole interaction between the Rydberg atoms leads to nonlocal nonlinear optical polarization, which makes that there are nonlinear couplings between the localized optical fields in different locations. The project is to establish and develop effective models to describe the nonlocal interaction between the localized optical fields in different optical structures by using the tight-binding models and the optical Schrödinger equations with paraxial approximation; study all the possible modes and singularity of optical patterns, such as zero-energy boundary states, and so on; explore the influence of different interaction forms between Rydberg atoms on the photon states; reveal the mechanism and law of the photon modes in these kind of systems; explore the nature of photonic systems in the low momentum region and reveal potential applications in the simulations of high-energy physics (analogue of nonlinear Dirac equations, and so on). Such a kind of research will promote the study of the topological properties of nonlinear system, and extend the research category of topological photonics, which is of great scientific significance and potential valuable applications to photonics research.

周期光学结构中光子态连续变换不变性的深入研究催生了新学科——拓扑光子学。当前拓扑光子学研究主要针对线性系统。本项目拟开展填充里德堡原子的周期光学结构(如周期缺陷的光子能隙晶体或光晶格)中光子态及其几何特性(如拓扑性质)的研究。里德堡原子间偶极偶极相互作用导致非局域非线性光学极化效应，这使得局域在不同位置的光场间存在非线性耦合。项目旨在利用紧束缚模型和傍轴近似光学薛定谔方程建立能描述不同周期光学结构局域光场间非线性相互作用的有效模型；研究不同周期结构中可能的光子态和其奇异性，如边界态等；揭示不同系统中光子态出现的机制与规律以及几何特性；探索里德堡原子间不同形式相互作用对光子态的影响；探寻低动量区域的光子态性质并揭示其在高能物理模拟中的潜在应用(如类非线性狄拉克方程等)。这将一定程度推进非线性系统光子态和几何性质的研究，扩展拓扑光子学的研究范畴，对光子学研究具有重要的科学意义和潜在应用价值。

周期光学结构中光子态连续变换不变性的深入研究催生了新学科——拓扑光子学。本项目拟开展填充里德堡原子的周期光学结构(如周期缺陷的光子能隙晶体或光晶格)中光子态及其几何特性(如拓扑性质)的研究。为厘清上述复杂问题，我们对模型进行了简化，并取得一定的成果：1、给出了不同驱动条件的广义PT对称Rabi模型的解析解，结果表明双态量子系统即使在考虑耗散条件下，周期性驱动系统其动力学性质也表现出许多奇异特性，相关结论对了解具有吸收或者增益特性的里德堡原子介质光学特性及其控制具有一定的促进左右；2、研究了基于分子磁体相干介质的微波诱导周期性相位光栅的形成机制，提出了在分子磁体晶体中利用电磁感应诱导产生光学周期结构——相位光栅的方案，可通过控制场的耦合强度、失谐量和相互作用长度有效调节相位光栅的性能，对光场建构周期光学结构提供了可供选择的方案。.拓扑性质强烈依赖于格点间的邻近相互作用。里德堡原子间存在长程的偶极偶极相互作用，如将其填充到相邻区域可用来建构可调谐的非局域化的线性和非线性光学效应。我们项目组建立了理论模型对里德堡原子间的非线性相互作用、紧束缚模型下里德堡原子填充光子晶体产生的色散关系、非线性非局域条件下的哈密顿量以及拓扑关系.目前，项目组编译了基于周期光学结构中填充相干介质的光场模式分布的计算程序用于求解非线性光子石墨烯系统的局域场分布模式。虽然经过不断的调试改进，程序一直存在以下问题：收敛速度较慢；模式迭代存在不收敛的现象；程序的有效性正确性得不到保证。虽然非常努力的进行问题梳理，但是依旧不能解决相关问题。数值模拟结果的不可靠性，导致项目一直无法进一步推进，撰写的关键性文章也没法正常发表。总的来说，本项目未能取得预期成果。