Quantum correlations in the two-photon decay of few-electron 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 $1s_{1/2}2s_{1/2}{}^1{S}_0\to 1s_{1/2}^2{}^1{S}_0$, $1s_{1/2}2s_{1/2}{}^3{S}_1\to 1s_{1/2}^2{}^1{S}_0$ and $1s_{1/2}2p_{1/2}{}^3{P}_0\to 1s_{1/2}^2{}^1{S}_0$ transitions in helium-like ions.