Simulating strong-field electron-hole dynamics in solids probed by attosecond transient absorption spectroscopy

We investigate the ultrafast electron dynamics of a model of a wide-band-gap material with inner, valence, and conduction bands excited by an intense few-femtosecond pump and monitored by a delayed attosecond extreme-ultraviolet probe pulse. Complementary computational methods are utilized and compared, based on the semiconductor Bloch equations (SBEs) and time-dependent density functional theory (TDDFT). TDDFT is employed to study a finite-size system, while the SBEs are utilized to investigate the corresponding solid with periodic boundary conditions imposed, with the crystal-momentum-dependent energy bands and interband couplings calculated in the parallel-transport structure gauge. The resulting strong-field electron dynamics are used to predict experimentally accessible attosecond transient absorption spectroscopy (ATAS) signals as a function of the probe-pulse frequency and pump-probe interpulse delay. Both simulation protocols similarly capture the time-delay-dependent spectral features in the ATAS signals. The very good agreement between our ab initio TDDFT simulations and SBE-based results allows us to validate our SBE-based model and identify the key contributing interband couplings. An interpretation model building on these validated SBE-based results allows us to quantify the amplitude of the ATAS spectral features in terms of the intraband dynamics of the electron-hole pairs generated by the attosecond probe pulse.