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 nondipole 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 rigorous relativistic theory. Detailed calculations are performed for the two-photon $2{s}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}$ transition in hydrogenlike ions as well as for the $1{s}_{1/2} 2{s}_{1/2} {}^{1}{S}_{0}\ensuremath{\rightarrow}1{s}_{1/2}^{2} {}^{1}{S}_{0}$, $1{s}_{1/2} 2{s}_{1/2} {}^{3}{S}_{1}\ensuremath{\rightarrow}1{s}_{1/2}^{2} {}^{1}{S}_{0}$, and $1{s}_{1/2} 2{p}_{1/2} {}^{3}{P}_{0}\ensuremath{\rightarrow}1{s}_{1/2}^{2} {}^{1}{S}_{0}$ transitions in heliumlike ions.