# Analytic modeling of structures in attosecond transient-absorption spectra

## TL;DR

This paper derives analytical formulas to explain key features in attosecond transient-absorption spectra, enhancing understanding of electron dynamics on subfemtosecond timescales.

## Contribution

It introduces closed-form analytical expressions for spectral features in ATAS based on a three-level adiabatic model, validated against numerical Schrödinger equation results.

## Key findings

- Analytical formulas accurately predict spectral features.
- The formulas clarify the physical origins of oscillating fringes and sidebands.
- Validation shows strong agreement with numerical simulations.

## Abstract

Attosecond transient-absorption spectroscopy (ATAS) is an established method for exploring electron dynamics on the subfemtosecond time-scale. ATAS spectra contain certain ubiquitous features, such as oscillating fringes, light-induced structures and hyperbolic sidebands, representing physical processes. We derive closed analytical expressions describing these features, based on a three-level system responding adiabatically to the influence of an infrared field in conjunction with an extreme ultraviolet pulse, and use He to illustrate the theory. The validity of the formulas is substantiated by comparing their predictions with spectra calculated numerically by the time-dependent Schr\"odinger equation. The closed analytical forms and the details of their derivation resolve the origins of the features.