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Scientific Reports

Polarized electron beams elastically scattered by atoms as a tool for testing fundamental predictions of quantum mechanics

Maurizio Dapor

Published Mar 29, 2018• 16 citations
Publisher

Abstract

Quantum information theory deals with quantum noise in order to protect physical quantum bits (qubits) from its effects. A single electron is an emblematic example of a qubit, and today it is possible to experimentally produce polarized ensembles of electrons. In this paper, the theory of the polarization of electron beams elastically scattered by atoms is briefly summarized. Then the POLARe program suite, a set of computer programs aimed at the calculation of the spin-polarization parameters of electron beams elastically interacting with atomic targets, is described. Selected results of the program concerning Ar, Kr, and Xe atoms are presented together with the comparison with experimental data about the Sherman function for low kinetic energy of the incident electrons (1.5eV-350eV). It is demonstrated that the quantum-relativistic theory of the polarization of electron beams elastically scattered by atoms is in good agreement with experimental data down to energies smaller than a few eV.

DOI
10.1038/s41598-018-23660-4

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Quantum information theory deals with quantum noise in order to protect physical quantum bits (qubits) from its effects. A single electron is an emblematic example of a qubit, and today it is possible to experimentally produce polarized ensembles of electrons. In this paper, the theory of the polarization of electron beams elastically scattered by atoms is briefly summarized. Then the POLARe program suite, a set of computer programs aimed at the calculation of the spin-polarization parameters of electron beams elastically interacting with atomic targets, is described. Selected results of the program concerning Ar, Kr, and Xe atoms are presented together with the comparison with experimental data about the Sherman function for low kinetic energy of the incident electrons (1.5eV-350eV). It is demonstrated that the quantum-relativistic theory of the polarization of electron beams elastically scattered by atoms is in good agreement with experimental data down to energies smaller than a few eV.
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.
An analysis of spin-polarization in low energy elastic scattering electrons by one electron s-state atoms is carried out allowing both for electron exchange and relativistic effects. First the collision matrix is written in terms of the asymptotic form of the solutions of the radial equations. Then arguments, based on the invariance of the Hamiltonian under time reversal, space rotation and space reflection are used to write down the most general form of this matrix. It is found that it can be expressed in terms of six independent amplitudes. Then expressions for the observable quantities, including the spin polarization of the electron and of the atom after the collision are derived. Finally, the analysis is specialized to the case where spin-polarization effects are caused by a spin-orbit interaction and these effects are considered in the neighbourhood of cusps and resonances in electron alkali atom scattering.
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.
The relativistic spin correlation function was calculated for a pair of electrons originating from M\o{}ller scattering of two polarized electron beams. The results were discussed in view of a possible measurement of the correlation function and the corresponding probabilities. The special case of scattering off a stationary target (both polarized and unpolarized) was also analyzed. It was shown that the Clauser-Horne-Shimony-Holt (CHSH) inequality may be violated in the relativistic energy range when both scattering electrons are highly polarized.
Abstract The dipole radiation emitted by an atom excited by a unidirectional electron beam has a nonuniform angular distribution which is simply related to the percentage polarization P of the radiation emitted perpendicular to the beam. P was first calculated using the OppenheimerPenney (O.-P.) theory. In this theory the probability of excitation of an upper quantum state and the probability of subsequent emission of a polarized photon from such a state are considered independently. P is finally expressed in terms of the cross-sections QM for excitation of states of definite component of angular momentum along the direction of the electron beam. In general, P is dependent on detailed numerical calculations of QM j, but the selection rule A = 0 removes this dependence at threshold. In the O.-P. theory allowance may be made for fine structure and hyperfine structure, but the theory is ambiguous when the f.s. or h.f.s. separations are comparable with the line width. A theory is therefore developed which is based on the calculation of the probability of a polarized photon being emitted by the complete system of atom + electron. The ambiguity of the O.-P. theory is removed by integration over line profiles, but the expressions reduce to O.-P. expressions when the f.s. or h.f.s. separations are much smaller or much larger than the line width. The Lyot line of hydrogen is an intermediate case for which the line widths and the h.f.s. separations are comparable. Assuming the validity of the Born approximation, a simple expression is obtained which allows the QM to be calculated from the angular distribution of the scattered electrons. Theoretical predictions are compared with experimental results. For the Na£) lines the predicted polarization is small enough to escape experimental detection. Polarizations observed by - Skinner & Appleyard in 1927 for various Hg lines rise to maxima with decreasing electron energy, and then tend to values close to zero at threshold. These experimental results at low energies appear to be inexplicable in terms of the reactions considered, but if the polarization curve above the maximum is extrapolated to threshold, the theory and experiment are found to be in reasonable agreement. Further experimental work is thought to be desirable
We have calculated cross sections for elastic and spin-flip scattering processes of electrons on positronium atoms in the para and ortho states in the energy region scrE\ensuremath{\le}0.05 eV; elastic and symmetric charge-exchange cross sections for the same system were calculated without spin interactions for the scattering energies scrE\ensuremath{\le}4 eV. This energy region has been treated for the first time. The calculations have been done by the adiabatic method, where this three-body problem reduces to the multichannel-scattering problem. Very high scattering cross sections were obtained, expecially near the threshold for spin-flip processes.