A Theory for Pump-Probe Resonant Inelastic X-ray scattering

Nonequilibrium approaches are widely used as powerful techniques in condensed matter physics to characterize the evolution of excitations. In recent years, resonant inelastic X-ray scattering (RIXS) has become an important tool to investigate specific collective excitations in correlated materials with momentum and energy resolution. Combined with the progress in ultrafast instrumentation, time-resolved RIXS (tr-RIXS) holds the promise to detect nonequilibrium dynamics of numerous collective modes, which play significant roles in emergent phenomena. Here we present a theoretical and numerical study of tr-RIXS. Through the evaluation of tr-RIXS for a few important physical models, we show that tr-RIXS has the capability to elucidate the dynamics of the particle-hole excitations. As a function of pump intensity, frequency, and time, tr-RIXS exhibits Floquet band replicas and renormalization even at this multi-particle level. The evolution of other collective excitations coupled to charge degrees of freedom can be revealed in the spectra, with distinct modulation and relaxation due to the core-hole potential in the intermediate state.