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Journal of Physics B Atomic Molecular and Optical Physics

Spin–spin correlations and entanglement in elastic electron scattering from hydrogen atoms

Klaus Bartschat

Published Sep 14, 2017• 1 citation
Publisher

Abstract

Abstract In two recent papers, Blum and Lohmann (2016 Phys. Rev. Lett. 116 033201) and Lohmann et al (2016 Phys. Rev. A 94 032331), the possibility of continuously varying the degree of entanglement between an elastically scattered electron and the valence electron of quasi-one electron targets was discussed. Here we present results for elastic electron scattering from atomic hydrogen in the energy regime of 1−10 eV and the full range of scattering angles 0 ° − 180 ° . We confirm previous calculations at very low energies, which predicted that the hydrogen target is not a promising candidate for Bell correlations through electron collisions. This finding remains unchanged in the near-resonance regime of incident electron energies just below 10 eV. In addition to the spin-correlation parameter P , we present the angle-integrated total cross section, as well as the angle-differential cross section at a few representative collision energies.

DOI
10.1088/1361-6455/aa8c8b

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In two recent papers [Blum and Lohmann, Phys. Rev. Lett. 116, 033201 (2016); Lohmann et al., Phys. Rev. A 94, 032331 (2016)], the possibility of continuously varying the degree of entanglement between an elastically scattered electron and the valence electron of an alkali-metal target was discussed. To estimate how well such a scheme may work in practice, we present results for elastic electron scattering from lithium in the energy regime of 1−−5eV1--5\phantom{\rule{4pt}{0ex}}\mathrm{eV}1−−5eV and the full range of scattering angles ${0}^{\ensuremath{\circ}}--{180}^{\ensuremath{\circ}}$. The most promising regime for Bell correlations in this particular collision system are energies between about 1.5 and 3.0 eV, in an angular range around ${110}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{\circ}}$. In addition to the relative exchange asymmetry parameter, we present the differential cross section that is important when estimating the count rate and hence the feasibility of experiments using this system.
Elastic collisions between initially unpolarized electrons and hydrogenlike atoms are discussed, aiming to analyze the entanglement properties of the correlated final spin system. Explicit spin-dependent interactions are neglected and electron exchange only is taken into account. We show the final spin system to be completely characterized by a single spin correlation parameter depending on scattering angle and energy. Its numerical value identifies the final spins of the collision partners to be either in the separable, entangled, or Bell correlated regions. We emphasize explicit examples for the mixed spin system in order to illustrate the abstract concepts. The analysis of published experimental and numerical data reveals the possibility to create tunable pairs of collision partners with any desired degree of spin entanglement.
Elastic collisions between initially unpolarized electrons and hydrogenlike atoms are discussed aiming to analyze the entanglement properties of the correlated final spin system. Explicit spin-dependent interactions are neglected and electron exchange only is taken into account. We show the final spin system to be completely characterized by a single spin correlation parameter depending on scattering angle and energy. Its numerical value identifies the final spins of the collision partners to be either in the separable, entangled, or Bell correlated regions. The symmetry of the scattering process allows for the construction of explicit examples applying methods of classical communication and local operations for illustrating the concepts of nonlocality versus separability. It is shown that strong correlations can be produced violating Bell's inequalities significantly. Furthermore, the degree of entanglement can be continuously varied simply by changing either the scattering angle and/or energy. This allows for the generation of tunable spin pairs with any desired degree of entanglement. It is suggested to use such nonlocally entangled spin pairs as a resource for further experiments, for example in quantum information processes.
We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the SSS-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The SSS-wave total and ortho-para conversion cross sections are calculated by making use of both 1S^{1}S1S and 3S^{3}S3S results. In the 3S^{3}S3S case, we see no indication of any resonances below the excitation threshold at 5.1 eV.
Abstract Generation of an entangled spin state as a result of a low-energy elastic collision of two protons is considered. The scattering process is described by a theoretical model that is in good agreement with the available experimental data on the angular differential cross sections of proton–proton collisions at low energies. The entanglement of the spin state of final protons as a function of the scattering angle is analyzed using Bell’s inequality and pair concurrence. The numerical results for different values of the collision energy are compared with the results without considering nuclear forces. It is shown that nuclear interaction significantly enhances the effects of spin entanglement.