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Influence of atom-photon correlations on atom-atom entanglement

F. Lastra, Sascha Wallentowitz

Published Nov 18, 2009• 0 citations
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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 $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ (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 $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ and $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ 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 $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition of hydrogenlike uranium.
We study the distribution of the stationary correlations in a system of two nonidentical as well as identical two-level atoms separated by an arbitrary distance and interacting with a squeezed vacuum. We investigate how the interatomic distance and the squeezing mean number of photons influence the way that one of the atoms is quantum correlated with the environment. Both for nonidentical and identical atoms, the approach of the two atoms can maximize the entanglement and quantum discord between the pair of atoms. For nonidentical atoms, the bigger the mean number of photons, the stronger the stationary correlations, i.e., entanglement of formation (EOF) and quantum discord (QD) between the qubit and the environment as the increase of distance. The increase of EOF and QD with the environment is always accompanied by a decrease of the correlations between the subsystems with regard to the interatomic distance no matter what the mean number of photons is. For identical atoms, the stationary correlations EOF and QD between each partition behave similarly with respect to the distance when the mean number of photons is very small.