Nonequilibrium Bethe-Salpeter equation for transient photoabsorption spectroscopy

In this work, we propose an accurate first-principles approach to calculate the transient photoabsorption spectrum measured in pump-and-probe experiments. We formulate a condition of adiabaticity and thoroughly analyze the simplifications brought about by the fulfillment of this condition in the nonequilibrium Green's function (NEGF) framework. Starting from the Kadanoff-Baym equations, we derive a nonequilibrium Bethe-Salpeter equation (BSE) for the response function that can be implemented in most of the already existing ab initio codes. In addition, the adiabatic approximation is benchmarked against full NEGF simulations in simple model Hamiltonians, even under extreme, nonadiabatic conditions in which it is expected to fail. We find that the nonequilibrium BSE is very robust and captures important spectral features in a wide range of experimental configurations.