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arXiv:1611.06180 · Physical Review A

Spin entanglement in elastic electron scattering from lithium atoms

Klaus Bartschat, Samantha Fonseca dos Santos

Published Apr 19, 2017• 7 citations
arXivHTMLPDF

Abstract

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 $1--5\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ 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.

DOI
10.1103/physreva.95.042707

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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∘−−180\ensuremath∘{0}^{\ensuremath{\circ}}--{180}^{\ensuremath{\circ}}0\ensuremath∘−−180\ensuremath∘. 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∘\ifmmode±\else\textpm\fi10\ensuremath∘{110}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{\circ}}110\ensuremath∘\ifmmode±\else\textpm\fi10\ensuremath∘. 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.
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.
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.
We present measurements of differential elastic cross sections for various alkali-alkali pairs, as well as the angular dependence of the probability of electron spin exchange in these collisions. The resolution is sufficient to reveal interference structure in the angular dependence of both quantities. We describe our apparatus, which polarizes one incident beam and analyzes the polarization of the scattered atoms, and discuss the measurement and data-reduction procedures. Results are presented in the range 0.1-0.2 eV for the systems Na-Cs, Na-Rb, Na-K, K-Cs, and K-Rb.
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.
The results of a joint experimental and theoretical study concerning elastic electron scattering by laser-excited 138 Ba( ... 6s6p 1 P 1 ) atoms are described. These studies demonstrate several important aspects of elastic electron collisions with coherently excited atoms, and are the first such studies. From the measurements, collision and coherence parameters, as well as cross sections associated with an atomic ensemble prepared with an arbitrary in-plane laser geometry and linear polarization (with respect to the collision frame), or equivalently with any magnetic sublevel superposition, have been obtained at 20 eV impact energy and at 10°, 15° and 20° scattering angles. The convergent close-coupling (CCC) method was used within the non-relativistic LS -coupling framework to calculate the magnetic sublevel scattering amplitudes. From these amplitudes all the parameters and cross sections at 20 eV impact energy were extracted in the full angular range in 1° steps. The experimental and theoretical results were found to be in good agreement, indicating that the CCC method can be reliably applied to elastic scattering by 138 Ba( ... 6s6p 1 P 1 ) atoms, and possibly to other heavy elements when spin-orbit coupling effects are negligible. Small but significant asymmetry was observed in the cross sections for scattering to the left and to the right. It was also found that elastic electron scattering by the initially isotropic atomic ensemble resulted in the creation of significant alignment. As a byproduct of the present studies, elastic scattering cross sections for metastable 138 Ba atoms were also obtained.