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Physical Review A

Quantum spin correlations in Møller scattering of relativistic electron beams

Marta Włodarczyk, Paweł Caban, J. Ciborowski, Michał Drągowski, Jakub Rembieliński

Published Feb 6, 2017• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.95.022103

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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.
In this paper we present and discuss the relativistic correlation function in a bipartite system of two electrons, originating from the ${e}^{\ensuremath{-}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ scattering of a polarized electron beam on an unpolarized target. We also calculate and investigate the probabilities of the definite outcomes of spin-projection measurements performed by two observers. The presented results might help in experimentally verifying whether relativistic quantum theory is able to reproduce the behavior of real quantum systems.
We calculate the polarization correlation function in the Einstein-Podolsky-Rosen--type experiments with relativistic spin-1/21/21/2 particles. This function depends monotonically on the particle momenta. Moreover, we also show that the polarization correlation function violates the Clauser-Horn-Shimony-Holt inequality and the degree of this violation can depend on the particle momenta and the motion of observers.
The Polish-German project QUEST aims at studying relativistic quantum spin correlations of the Einstein-Rosen-Podolsky-Bohm type, through measurement of the correlation function and the corresponding probabilities for relativistic electron pairs. The results will be compared to theoretical predictions obtained by us within the framework of relativistic quantum mechanics, based on assumptions regarding the form of the relativistic spin operator. Agreement or divergence will be interpreted in the context of non-uniqueness of the relativistic spin operator in quantum mechanics as well as dependence of the correlation function on the choice of observables representing the spin. Pairs of correlated electrons will originate from the Mo/ller scattering of polarized 15 MeV electrons provided by the superconducting Darmstadt electron linear accelerator S-DALINAC, TU Darmstadt, incident on a Be target. Spin projections will be determined using the Mott polarimetry technique. Measurements (starting 2013) are planned for longitudinal and transverse beam polarizations and different orientations of the beam polarization vector w.r.t. the Mo/ller scattering plane. This is the first project to study relativistic spin correlations for particles with mass.
We show that a pair of massive relativistic spin-1/2 particles prepared in a maximally entangled spin state in general is not capable of maximally violating the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities without a postselection of the particles' momenta, representing a major difference in relation to nonrelativistic systems. This occurs because the quantization axis of the measurements performed on each particle depends on the particle velocity, such that it is not possible to define a reduced density matrix for the particles' spin. We also show that the amount of violation of the CHSH inequality depends on the reference frame and that in some frames the inequality may not be violated.