Effect of dynamical spectral weight redistribution on effective interactions in time-resolved spectroscopy

The redistribution of electrons in an ultrafast pump-probe experiment causes significant changes to the effective interaction between electrons and bosonic modes. We study the influence of these changes on pump-probe photoemission spectroscopy for a model electron-phonon coupled system using the nonequilibrium Keldysh formalism. We show that spectral rearrangement due to the driving field preserves an overall sum rule for the electronic self-energy, but modifies the effective electron-phonon scattering as a function of energy. Experimentally, this pump-modified scattering can be tracked by analyzing the fluence or excitation energy dependence of population decay rates and transient changes in dispersion kinks.