We develop a quantum theory of plasmon polaritons in chains of metallic nanoparticles, describing both near- and far-field interparticle distances, by including plasmon–photon umklapp processes. Taking into account the retardation effects of the long-range dipole–dipole interaction between the nanoparticles, which are induced by the coupling of the plasmonic degrees of freedom to the photonic continuum, we reveal the polaritonic nature of the normal modes of the system. We compute the dispersion relation and radiative linewidth, as well as the group velocities of the eigenmodes, and compare our numerical results to classical electrodynamic calculations within the point-dipole approximation. Interestingly, the group velocities of the polaritonic excitations present an almost periodic sign change and are found to be highly tunable by modifying the spacing between the nanoparticles. We show that, away from the intersection of the plasmonic eigenfrequencies with the free photon dispersion, an analytical perturbative treatment of the light-matter interaction is in excellent agreement with our fully retarded numerical calculations. We further study quantitatively the hybridization of light and matter excitations through an analysis of Hopfield's coefficients. Finally, we consider the limit of infinitely spaced nanoparticles and discuss some recent results on single nanoparticles that can be found in the literature.

中文翻译：

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金属纳米粒子链中等离子体激元的量子理论：从近场到远场耦合机制

我们开发了金属纳米粒子链中等离子体极化子的量子理论，通过包括等离子体 - 光子 umklapp 过程来描述近场和远场粒子间距离。考虑到纳米粒子之间长程偶极-偶极相互作用的延迟效应，这是由等离子体自由度与光子连续体的耦合引起的，我们揭示了系统正常模式的极化性质。我们计算色散关系和辐射线宽，以及本征模式的群速度，并将我们的数值结果与点偶极子近似内的经典电动力学计算进行比较。有趣的是，极化激发的群速度呈现出几乎周期性的符号变化，并且通过改变纳米粒子之间的间距发现其高度可调。我们表明，远离等离子体本征频率与自由光子色散的交叉点，光-物质相互作用的分析微扰处理与我们的完全延迟数值计算非常一致。我们通过分析霍普菲尔德系数进一步定量研究光和物质激发的混合。最后，我们考虑了无限间隔纳米粒子的极限，并讨论了一些可以在文献中找到的关于单个纳米粒子的最新结果。远离等离子体本征频率与自由光子色散的交叉点，光-物质相互作用的分析微扰处理与我们的完全延迟数值计算非常一致。我们通过分析霍普菲尔德系数进一步定量研究光和物质激发的混合。最后，我们考虑了无限间隔纳米粒子的极限，并讨论了一些可以在文献中找到的关于单个纳米粒子的最新结果。远离等离子体本征频率与自由光子色散的交叉点，光-物质相互作用的分析微扰处理与我们的完全延迟数值计算非常一致。我们通过分析霍普菲尔德系数进一步定量研究光和物质激发的混合。最后，我们考虑了无限间隔纳米粒子的极限，并讨论了一些可以在文献中找到的关于单个纳米粒子的最新结果。