AI 中文总结
研究针对光子晶体中发射器与光相互作用建模难题，结合对称约束紧束缚结构、光子能带结构和场分布，构建量子光学晶格描述，克服传统方法权衡，能重现光子色散，实现非微扰模拟，应用于二维光子晶体取得成果，搭建电磁与量子光学建模桥梁。
AI 中文摘要
近期进展使量子发射器能与光子晶体相互作用，其电磁模式具有复杂色散关系、空间模式结构和极化纹理。在这些系统中对光与物质行为建模面临权衡：基于麦克斯韦方程求解器的电磁方法能提供现实矢量描述，但难与量子多体和非微扰方法整合；简化量子光学晶格模型易处理，但依赖标量且空间独立的光与物质耦合，忽略了这些结构化光子环境的关键特征。本文引入一个建设性框架来推导克服此权衡的量子光学晶格描述。结合对称约束紧束缚结构与数值计算的光子能带结构和场分布，我们的方法产生最小化、对称强制的晶格哈密顿量，能重现目标光子色散，同时保留光与物质耦合的模式分辨（位置和极化相关）结构。我们表明这些模型在微扰区域恢复基于格林函数的发射器动力学，同时提供超越仅发射器描述的非微扰量子动力学模拟。作为原理证明，我们将该框架应用于二维光子晶体，表明它能捕捉标量模型无法实现的极化相关定向发射，同时能分析非马尔可夫光与物质动力学和纠缠。我们的结果在经典电磁模拟工具与光子晶体环境中的量子光学多体和非马尔可夫建模之间提供了实用桥梁。
英文摘要
Recent advances are enabling quantum emitters to interact with photonic crystals, whose electromagnetic modes exhibit complex dispersion relations, spatial mode structure, and polarization textures. However, modeling light-matter behavior in these systems faces a persistent trade-off: electromagnetic approaches based on Maxwell-equation solvers provide realistic vectorial descriptions but are difficult to integrate with quantum many-body and non-perturbative methods, whereas simplified quantum-optical lattice models are tractable but typically rely on scalar and spatially independent light-matter couplings that miss essential features of these structured photonic environments. Here, we introduce a constructive framework to derive quantum-optical lattice descriptions that overcome this trade-off. Combining symmetry-constrained tight-binding constructions with numerically computed photonic band structures and field profiles, our method yields minimal, symmetry-enforced lattice Hamiltonians that reproduce the target photonic dispersion while retaining the mode-resolved (position- and polarization-dependent) structure of the light-matter coupling. We show that these models recover Green's-function-based emitter dynamics in the perturbative regime, while providing access to non-perturbative quantum dynamical simulations beyond emitter-only descriptions. As a proof of principle, we apply the framework to a two-dimensional photonic crystal and show that it captures polarization-dependent directional emission inaccessible to scalar models, while enabling the analysis of non-Markovian light-matter dynamics and entanglement. Our results provide a practical bridge between classical electromagnetic simulation tools and quantum-optical many-body and non-Markovian modeling in photonic crystal settings.
Comments21 pages, 4 figures, including appendices. v2: corrected conflation of frequency and angular frequency throughout; figures, parameters, and time scales updated accordingly
