Microscopic insight into the pump–probe relaxation dynamics of superconductors: Model study of MgB2 relaxation within nonlinear response theory

Here we present a quantum‐statistical formulation of relaxation dynamics of superconductors related to pump–probe (PP) spectroscopy. The method is based on the perturbation expansion of the non‐equilibrium density matrix for calculation of multi‐time correlation functions, and the corresponding response function. As a model for our study, the high‐temperature superconductor MgB2 has been selected. Knowledge of the electronic structure and of the corresponding Eliashberg function of electron–phonon (EP) interactions enabled us to distinguish non‐equilibrium processes in a sequence of interactions with laser pulses on a microscopic level. Temperature‐dependent relaxation dynamics as a function of delay time between the pump and probe pulses have been derived. We have shown that an abrupt increase of the relaxation time at Tc is the direct consequence of sudden changes in the character of EP coupling in transition from an adiabatic to a stabilized superconducting anti‐adiabatic state, as it predicts the anti‐adiabatic theory of electron–vibration interactions. The BCS model, which is based on adiabatic character of EP coupling, is basically unable to reflect the enormous sudden increase of the relaxation time at Tc. Differences in the optical pump–optical probe and the optical pump–terahertz probe settings of PP relaxation dynamics are discussed within diagrammatic perturbation theory.