Theory for time-resolved resonant inelastic x-ray scattering

Time-resolved measurements of materials provide a wealth of information on quasiparticle dynamics, and have been the focus of optical studies for decades. In this paper, we develop a theory for explicitly evaluating time-resolved resonant inelastic X-ray scattering (tr-RIXS). We apply the theory to a non-interacting electronic system and reveal the particle-hole spectrum and its evolution during the pump pulse. With a high-frequency pump, the frequency and amplitude dependence analysis of the spectra agrees well with the steady state assumptions and Floquet excitations. When the pump frequency is low, the spectrum extracts real-time dynamics of the particle-hole continuum in momentum space. These results verify the correctness of our theory and demonstrate the breadth of physical problems that tr-RIXS could shed light on.