Quantum correlations in the two-photon decay of few-electron ions

TL;DR

This paper theoretically investigates the polarization entanglement of two photons emitted during ionic decay, emphasizing relativistic and non-dipole effects, with detailed calculations for hydrogen-like and helium-like ions.

Contribution

It provides a comprehensive analysis of relativistic and non-dipole effects on photon entanglement in ionic decay, extending previous dipole approximation studies.

Findings

Relativistic effects significantly influence entanglement in high-Z ions.

Non-dipole contributions alter polarization correlations.

Detailed transition-specific calculations for hydrogen-like and helium-like ions.

Abstract

A theoretical study of the polarization entanglement of two photons emitted in the decay of metastable ionic states is performed within the framework of density matrix theory and second-order perturbative approach. Particular attention is paid to relativistic and non-dipole effects that become important for medium- and high-$Z$ ions. To analyze these effects, the degree of entanglement is evaluated both in the dipole approximation and within the rigorous relativistic theory. Detailed calculations are performed for the two-photon $2s_{1/2}\to 1s_{1/2}$ transition in hydrogen-like, as well as for the $1s_{1/2}\, 2s_{1/2} \; {}^1S_0 \to 1s_{1/2}^2 \; {}^1S_0$, $1s_{1/2} \, 2s_{1/2} \; {}^3S_1\to 1s_{1/2}^2 \; {}^1S_0$ and $1s_{1/2} \, 2p_{1/2} \; {}^3P_0\to 1s_{1/2}^2 \; {}^1S_0$ transitions in helium-like ions.