Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light–matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

We present 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 for the effective nuclei 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. For the implementation we use the Riemann-Silberstein formulation of classical electrodynamics and rewrite Maxwell's equations in Schrödinger form. This allows us to use existing time-evolution algorithms developed for quantum-mechanical systems also for Maxwell's equations. We introduce a predictorcorrector scheme and show how to couple the Riemann-Silberstein time-evolution of the electromagnetic fields self-consistently to the time-evolution of the electrons and nuclei. Furthermore, the Riemann-Silberstein approach allows to seamlessly combine macroscopic dielectric media with a microscopic coupling to matter currents. For an efficient absorption of outgoing electromagnetic waves, we present a perfectly matched layer for the Riemann-Silberstein vector. We introduce the concept of electromagnetic detectors, which allow to measure outgoing radiation in the far field and provide a direct way to record various spectroscopies. We present a multi-scale approach in space and time which allows to deal with the different length-scales of light and matter for a multitude of applications. We apply the approach to laser-induced plasmon excitation in a nanoplasmonic dimer system. We find that the self-consistent coupling of light and matter leads to significant local field effects which can not be captured with the conventional light-matter forward coupling. For our nanoplasmonic example we show that the self-consistent foward-backward coupling leads to changes in observables which are larger than the difference between local density and gradient corrected approximations for the exchange correlation functional. In addition, in our example we observe harmonic generation which appears only beyond the dipole approximation and can be directly observed in the outgoing electromagnetic waves on the simulation grid. The self-consistent coupling of the electromagnetic fields to the ion motion reveals significant energy transfer from the electromagnetic fields to matter on the scale of a few tens of femtoseconds. Overall, our 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 to name but ...

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