Journal of Physics Conference Series

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

F. Fratini, A. Surzhykov, Thorsten Jahrsetz, Malte C. Tichy, Andreas Buchleitner, S. Fritzsche

Published Nov 5, 2012• 0 citations

Abstract

The photon-photon polarization entanglement in the two-photon decay of metastable ionic states has been analyzed in the framework of the density matrix and second-order perturbation theory. Emphasis is placed especially upon the relativistic and non-dipole effects along the hydrogen- and helium-isoelectronic sequence.

DOI: 10.1088/1742-6596/388/8/082034

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Journal of Physics Conference Series

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

F. Fratini, A. Surzhykov, Thorsten Jahrsetz, Malte C. Tichy, Andreas Buchleitner, S. Fritzsche

Published Nov 5, 2012• 0 citations

Publisher

Abstract

DOI: 10.1088/1742-6596/388/8/082034

Related papers

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

F. Fratini, Malte C. Tichy, Thorsten Jahrsetz +3 more

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.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.

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Angular correlations in the two-photon decay of aligned hydrogenlike ions

Lesya Borowska, A. Surzhykov, Th. Stöhlker +1 more

The two-photon decay of highly charged hydrogenlike ions is studied within the framework of second-order perturbation theory, based on Dirac's equation. Attention has been paid to the angle-angle correlations between the two emitted photons. In particular, the density matrix theory is applied in order to explore how these angle-angle correlations are affected by the alignment of the excited states of the ions. Detailed computations have been carried out for the $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition in hydrogenlike uranium ${\mathrm{U}}^{91+}$ ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the $3{d}_{5∕2}$ state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.The two-photon decay of highly charged hydrogenlike ions is studied within the framework of second-order perturbation theory, based on Dirac's equation. Attention has been paid to the angle-angle correlations between the two emitted photons. In particular, the density matrix theory is applied in order to explore how these angle-angle correlations are affected by the alignment of the excited states of the ions. Detailed computations have been carried out for the $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition in hydrogenlike uranium ${\mathrm{U}}^{91+}$ ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the $3{d}_{5∕2}$ state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.

Physical Review ADec 29, 20068 citations

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.

Z

increases. Detailed computations on the photon-photon angular distribution have been carried out for the $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ and $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transitions in neutral hydrogen (H) as well as for hydrogenlike xenon

({\mathrm{Xe}}^{53+})

and uranium

({\mathrm{U}}^{91+})

ions, and are compared with previous nonrelativistic results by Au [Phys. Rev. A 14, 531 (1976)]).

The angular and polarization properties of the photon pair emitted in the two--photon decay of

2s

hyperfine states in hydrogenlike ions are investigated within the relativistic Dirac framework and second order perturbation theory. The studied transitions are

2s_{1/2}\,(F=1,0)\to1s_{1/2}\,(F=1,0)

in Hydrogen atom and

2s_{1/2}\,(F=4,3)\to1s_{1/2}\,(F=4,3)

in hydrogenlike Uranium ion. Two different emission patterns are found: For non-spin-flip transitions, the angular correlation (

i.e.

the angular distribution of the emitted photons) is of the type

\sim 1+\cos^2θ

, while the linear polarizations of the emitted photons are approximately parallel one another; For spin-flip transitions, the angular correlation is of the type

\sim 1-1/3\cos^2θ

, while the linear polarizations of the emitted photons are approximately orthogonal one another.

{\mathrm{U}}^{91+}

ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the

3{d}_{5∕2}

state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.