Technical review: Time-dependent density functional theory for attosecond physics ranging from gas-phase to solids

First-principles electron dynamics calculations can be applied in the investigation of a wide range of ultrafast phenomena in attosecond physics. They offer unique microscopic insight into light-induced ultrafast phenomena in both gas and condensed phases of matter, and thus, they are a powerful tool to develop our understanding of the physics of attosecond phenomena. We specifically review techniques employing time-dependent density functional theory (TDDFT) for investigating attosecond and strong-field phenomena. First, we describe this theoretical framework that enables the modeling of perturbative and non-perturbative electron dynamics in materials, including atoms, molecules, and solids. We then discuss its application to attosecond experiments, focusing on the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) measurements. We also briefly review first-principles calculations of optical properties of solids with TDDFT in the linear response regime and their extension to calculations of transient optical properties of solids in non-equilibrium phases, by simulating experimental pump-probe setups. We further demonstrate the application of TDDFT simulation to high-order harmonic generation in solids. First-principles calculations have predictive power, and hence they can be utilized to design future experiments to explore non-equilibrium and nonlinear ultrafast phenomena in matter and characterize and control metastable light-induced quantum states.