Non-equilibrium Bethe-Salpeter equation for transient photo-absorption spectroscopy

TL;DR

This paper develops a first-principles non-equilibrium Bethe-Salpeter equation approach to accurately simulate transient photo-absorption spectra in Pump&Probe experiments, incorporating an adiabatic approximation validated against full NEGF simulations.

Contribution

It introduces a non-equilibrium Bethe-Salpeter equation framework with an adiabatic approximation for transient spectroscopy, compatible with existing ab-initio codes.

Findings

The non-equilibrium BSE effectively captures spectral features across various experimental conditions.

The adiabatic approximation remains robust even under nonadiabatic conditions.

Benchmarking shows good agreement with full NEGF simulations.

Abstract

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