# Nonlinear coherence effects in transient-absorption ion spectroscopy with stochastic extreme-ultraviolet free-electron laser pulses

## TL;DR

This study demonstrates time-resolved nonlinear EUV absorption spectroscopy on multiply charged neon ions using phase-locked free-electron laser pulses, revealing transient spectral features and AC Stark shifts explained by a quantum model.

## Contribution

It introduces a novel approach to observe nonlinear coherence effects in transient ions with phase-locked FEL pulses and models the enhanced ionic coupling during pulse overlap.

## Key findings

- Observation of time-dependent spectral changes in doubly charged neon ions.
- Detection of 10-meV-scale spectral shifts due to the AC Stark effect.
- Explanation of the phenomena using a time-dependent quantum model.

## Abstract

We demonstrate time-resolved nonlinear extreme-ultraviolet absorption spectroscopy on multiply charged ions, here applied to the doubly charged neon ion, driven by a phase-locked sequence of two intense free-electron laser pulses. Absorption signatures of resonance lines due to 2$p$--3$d$ bound--bound transitions between the spin-orbit multiplets $^3$P$_{0,1,2}$ and $^3$D$_{1,2,3}$ of the transiently produced doubly charged Ne$^{2+}$ ion are revealed, with time-dependent spectral changes over a time-delay range of $(2.4\pm0.3)\,\text{fs}$. Furthermore, we observe 10-meV-scale spectral shifts of these resonances owing to the AC Stark effect. We use a time-dependent quantum model to explain the observations by an enhanced coupling of the ionic quantum states with the partially coherent free-electron-laser radiation when the phase-locked pump and probe pulses precisely overlap in time.