In recent years significant experimental advances in nano-scale fabrication techniques and in available light sources have opened the possibility to study a vast set of novel light-matter interaction scenarios, including strong coupling cases. In many situations nowadays, classical electromagnetic modeling is insufficient as quantum effects, both in matter and light, start to play an important role. Instead, a fully self-consistent and microscopic coupling of light and matter becomes necessary. We provide here a critical review of current approaches for electromagnetic modeling, highlighting their limitations. We show how to overcome these limitations by introducing the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli–Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit, the formalism reduces to coupled Ehrenfest–Maxwell–Pauli–Kohn–Sham equations. We present an implementation of the approach in the real-space real-time code Octopus using the Riemann–Silberstein formulation of classical electrodynamics to rewrite Maxwell's equations in Schrödinger form. This allows us to use existing very efficient time-evolution algorithms developed for quantum-mechanical systems also for Maxwell's equations. We show how to couple the time-evolution of the electromagnetic fields self-consistently with the quantum time-evolution of the electrons and nuclei. This approach is ideally suited for applications in nano-optics, nano-plasmonics, (photo) electrocatalysis, light-matter coupling in 2D materials, cases where laser pulses carry orbital angular momentum, or light-tailored chemical reactions in optical cavities just to name but a few.

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Ehrenfest-Maxwell-Pauli-Kohn-Sham 框架内的光物质相互作用：基础、实现和纳米光学应用

近年来，纳米级制造技术和可用光源的重大实验进展为研究大量新型光-物质相互作用场景（包括强耦合情况）提供了可能性。在当今的许多情况下，经典电磁建模是不够的，因为物质和光中的量子效应开始发挥重要作用。相反，光和物质的完全自洽和微观耦合变得必要。我们在这里提供了对当前电磁建模方法的批判性评论，强调了它们的局限性。我们通过介绍耦合光子、电子、密度泛函方法的理论基础和实现细节来展示如何克服这些限制。和非相对论量子电动力学中的有效核。形式主义的出发点是 Pauli-Fierz 场论的推广，为此我们建立了外部场和内部变量之间的一一对应关系。基于这种对应关系，我们引入了 Kohn-Sham 结构，它为从头开始的光-物质相互作用提供了一种计算上可行的方法。在平均场极限中，形式化简化为耦合的 Ehrenfest-Maxwell-Pauli-Kohn-Sham 方程。我们使用经典电动力学的 Riemann-Silberstein 公式在实空间实时代码 Octopus 中展示了该方法的实现，以将麦克斯韦方程组重写为薛定谔形式。这使我们能够使用为量子力学系统开发的现有非常有效的时间演化算法也适用于麦克斯韦 s 方程。我们展示了如何将电磁场的时间演化与电子和原子核的量子时间演化自洽耦合。这种方法非常适用于纳米光学、纳米等离子体激元、（光）电催化、二维材料中的光物质耦合、激光脉冲携带轨道角动量的情况，或光腔中的光定制化学反应（仅举个例子）但有几个。