# Coherent control of electron-ion entanglement in multiphoton ionization

## TL;DR

This paper explores how to control and measure quantum entanglement between electrons and ions during ionization using ultrashort laser pulses.

## Contribution

The study introduces a method to manipulate and reconstruct electron-ion entanglement using time-delayed ultraviolet pulses and multi-electron simulations.

## Key findings

- Distinct scattering-phase differences were observed in electron configurations within the same partial wave channel.
- The purity of electron quantum states can be reconstructed and manipulated through photoelectron angular distributions.
- The framework provides experimentally feasible control of quantum entanglement in ultrafast ionization processes.

## Abstract

Quantitative control and measurement of quantum entanglement are essential for advancing quantum technologies. Photoionization induced by ultrashort laser pulses provides a unique platform for studying entanglement between photoelectrons and residual ions, representing one of the most intriguing quantum phenomena in attosecond physics. Although extensive studies have focused on the coherence properties within either the emitted electrons or the ions individually, the electron-ion entanglement has remained largely unexplored. In this work, we bridge this gap by investigating the resonance-enhanced multiphoton ionization of argon atoms driven by two time-delayed ultrashort ultraviolet pulses. Employing state-of-the-art first-principles multi-electron simulations, we demonstrate the ability to reconstruct and precisely manipulate the purity of electron quantum states through detailed analysis of the photoelectron angular distributions. Our results reveal distinct scattering-phase differences among various electron configurations within the same partial wave channel, providing unequivocal evidence of electron-ion correlation and entanglement. With the fast development of free-electron lasers, this study establishes an experimentally feasible framework for directly controlling quantum entanglement in ultrafast ionization processes, offering new insights and powerful methodologies for exploring complex electron dynamics in many-electron systems.