Evaluation of quantum entanglement state between photoelectron spin and emitted photon polarization in spin and polarization resolved XEPECS of $\rm Ti_{2}O_{3}$

TL;DR

This paper theoretically investigates the quantum entanglement between photoelectron spin and emitted photon polarization in Ti₂O₃, revealing how charge transfer and crystal field effects influence entanglement in a realistic model.

Contribution

It introduces a detailed theoretical model for spin-photon entanglement in Ti₂O₃, emphasizing the roles of charge transfer and crystal field effects on entanglement properties.

Findings

Quantum entanglement depends on the angular geometry of the process.

Entanglement decreases with stronger Ti 3d–O 2p hybridization.

Crystal field effects modify the degree of entanglement.

Abstract

We theoretically investigated the mechanism of quantum entanglement between the spin of photoelectrons and linear polarization of emitted X-ray photons in the 3$d\rightarrow\ $2$p$ XEPECS process for $\rm Ti_{2}O_{3}$. In the calculation, we used a realistic $\rm TiO_{6}$-type cluster model with the full multiplet structure of the Ti ion and the charge-transfer effect between the Ti 3$d$ and ligand O 2$p$ orbitals. We found that quantum entanglement occurs between the spin of photoelectrons and linear polarization of emitted X-ray photons and that it depends on the angular geometry in the XEPECS process. In addition, we found that the degree of spin and polarization entanglement decreases as the Ti 3$d\ $- O 2$p$ hybridization becomes stronger and as the crystal field modifies the electronic states in terms of the tangle, an index for the degree of entanglement. These results highlight the crucial role of the charge transfer and crystal field effects in determining entanglement properties in real material systems.