Photon pairs with tailor-made entanglement obtained from the two-photon decay of atomic hydrogen

From the work by W. Perrie et al. Phys. Rev. Lett. 54 1790 (1985)], it is known that the photon pairs that are emitted in the 2s_1∕2→1s_1∕2 (two-photon) decay of atomic hydrogen are quantum mechanically correlated, i.e., entangled. However, less information is available about the degree of polarization entanglement between the two photons if an arbitrary geometry is considered for collecting the photons. In this paper, we study the effect of the decay geometry on the degree of polarization entanglement between the two emitted photons. Results are shown for the 2s_1∕2→1s_1∕2 and 3d_5∕2→1s_1∕2 two-photon transitions of atomic hydrogen. The outlined theory is general and can be applied also to heavier elements. To demonstrate the influence of relativistic and multipole effects, results are also shown for the 3d_5∕2→1s_1∕2 transition of hydrogenlike uranium.