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.

近年来，纳米级制造技术和可用光源方面的重大实验进展为研究大量新颖的光-质相互作用场景（包括强耦合情况）提供了可能。如今在许多情况下，经典的电磁建模是不够的，因为物质和光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。在这里，我们对电磁建模的当前方法进行了严格的审查，突出了它们的局限性。我们介绍了如何通过引入耦合光子，电子的密度函数方法的理论基础和实现细节来克服这些局限性，非相对论量子电动力学中的有效核。形式主义的起点是Pauli-Fierz场论的概括，为此我们在外部场和内部变量之间建立了一对一的对应关系。基于此对应关系，我们介绍了Kohn-Sham构造，该构造为ab-initio光物质相互作用提供了计算上可行的方法。在均值范围内，形式主义简化为耦合的Ehrenfest-Maxwell-Pauli-Kohn-Sham方程。我们使用经典电动力学的Riemann-Silberstein公式，以Schrödinger形式重写Maxwell方程，在实时空间实时代码Octopus中介绍该方法的实现。这使我们可以将现有的非常高效的时间演化算法用于量子力学系统，也适用于Maxwell' 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地耦合。这种方法非常适合用于纳米光学，纳米等离子体激元，（光）电催化，2D材料中的光-质耦合，激光脉冲携带轨道角动量或光腔中的光定化学反应等应用。但是一些。