Non-equilibrium Electron Dynamics In Pump-Probe Spectroscopy: Role Of Excited Phonon Populations

The time- and angle-resolved photoemission spectroscopy(tr-ARPES) has emerged as a powerful tool to study the single-particle as well as collective dynamics of elementary excitations. The dynamics allow for the measurement of energy transfer between degrees of freedom such as electrons and phonons. When significant energy is deposited by the pump, or when the phonons are resonantly excited, the effect of excited phonons on the electrons plays an important role. We examine the relaxation dynamics of electrons coupled to a bath of optical phonons when subjected to an ultrafast optical excitation be solving the equation of motion for the coupled system within a non-equilibrium Keldysh formalism. By comparing the decay rates of electron populations when interacting with the phonons of fixed properties to those of dynamically modified properties, we gain insight into the role of the excited phonon populations; they are found to significantly suppress the decay rates at different excitation energies and to induce strong time dependence. We will also show that the temporal changes in the phonon occupation number manifestly sets apart the population decay rates from the single-particle scattering rates.