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Spin Correlations in e+e − Pair Creation by Two-Photons and Entanglement in QED

Nattapong Yongram

Published Aug 14, 2016• 4 citations
OpenAlex

Abstract

Spin correlations of e + e − pair productions of two colliding photons are investigated and explicit expressions for their corresponding probabilities are derived and found to be energy (speed) dependent, for initially linearly and circularly polarized photons, different from those obtained by simply combining the spins of the relevant particles, for initially polarized photons. These expressions also depend on the angles of spin of e + (and/or of e −), for initially linearly polarized photons, but not for circularly polarized photons, as a function of the energy. It is remarkable that these explicit results obtained from quantum field theory show a clear violation of Bell's inequality of Local Hidden Variables theories at all energies beyond that of the threshold one for particle production, in support of quantum field theory in the relativistic regime. We hope that our explicit expression will lead to experiments, of the type described in the bulk of this paper, which can monitor energy (and speed) in polarization correlation experiments.

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Spin correlations of e + e − pair productions of two colliding photons are investigated and explicit expressions for their corresponding probabilities are derived and found to be energy (speed) dependent, for initially linearly and circularly polarized photons, different from those obtained by simply combining the spins of the relevant particles, for initially polarized photons. These expressions also depend on the angles of spin of e + (and/or of e −), for initially linearly polarized photons, but not for circularly polarized photons, as a function of the energy. It is remarkable that these explicit results obtained from quantum field theory show a clear violation of Bell's inequality of Local Hidden Variables theories at all energies beyond that of the threshold one for particle production, in support of quantum field theory in the relativistic regime. We hope that our explicit expression will lead to experiments, of the type described in the bulk of this paper, which can monitor energy (and speed) in polarization correlation experiments.
Abstract This paper provides explicit and detailed quantum field theory (QFT) computations of polarizations correlations of emerging particles in several processes in QED, Electroweak Theory, and even in particle productions from strings, and hence are based on dynamical theries. The novel properties observed in the computations of such polarizations correlations, as predicted by QFT, is that they depend on the speed of the colliding particles, and, in some cases, even on coupling parameters ratios as well as on mass ratios of the underlying theory. These investigations clearly show that arguments based simply on combining spins to generate probabilities of such polarization correlations are not reliable. The novel properties obtained, with details of derivations provided here, hopefully would call for experiments on polarizations correlations which would monitor speeds of colliding particles, and, would, in turn, lead to new tests of the fundamental interactions of QFT such as of QED and of the Electroweak Theory.
In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the distribution of the joint measurement outcomes on the two sides. So it is a function of both hidden variable and settings. In this case, Bell's inequalities fail. Our further analysis shows that Bell's locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, thus violation of Bell's inequalities cannot rule out the existence of local hidden variable. In order to explain the results of EPR-type experiments, we suppose that polarization entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any non-local influence on it. Then several experiments are suggested to reveal the components of polarization entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with a same quantum state will behave in the same way under the same measuring condition.
Entanglement is studied in the framework of Dyson's S-matrix theory in relativistic quantum field theory, which leads to a natural definition of entangled states of a particle-antiparticle pair and the spin operator from a Noether current. As an explicit example, the decay of a massive pseudo-scalar particle into a pair of electron and positron is analyzed. Two spin operators are extracted from the Noether current. The Wigner spin operator characterizes spin states at the rest frame of each fermion and, although not measurable in the laboratory, gives rise to a straightforward generalization of low-energy analysis of entanglement to the ultrarelativistic domain. In contrast, if one adopts a (modified) Dirac spin operator, the entanglement measured by spin correlation becomes maximal near the threshold of the decay, while the entanglement is replaced by the classical correlation for the ultrarelativistic electron-positron pair by analogy to the case of neutrinos, for which a hidden-variables type of description is possible. Chiral symmetry differentiates the spin angular momentum and the magnetic moment. The use of weak interaction that can measure helicity is suggested in the analysis of entanglement at high energies instead of a Stern-Gerlach apparatus, which is useless for the electron. A difference between the electron spin at high energies and the photon linear polarization is also noted. The Standard Model can describe all of the observable properties of leptons.
In derivating of Bell’s inequalities, the probability distribution is supposed to be a function only of a hidden variable. We point out that the true implication of the probability distribution of Bell’s correlation function is the distribution of joint measurement outcomes on the two sides. It is therefore a function of both the hidden variable and the settings. In this case, Bell’s inequalities fail. Our further analysis shows that Bell’s locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, and hence violation of Bell’s inequalities cannot rule out the existence of local hidden variable. To explain the results of EPR-type experiments, we suppose that a polarization-entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any nonlocal influence on it. Then several experiments are suggested to reveal the components of the polarization-entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with the same quantum state behave the same under the same measuring conditions.
A bstract A photon linear collider, the two-photon collision mode of an e + e − linear collider, uses high-energy laser photons backscattered off the incoming electrons and positrons. The colliding-photon polarization is fully controllable through the polarizations of the initial electron and positron beams and laser photons. We investigate the impact of colliding-photon polarization on the observability of quantum entanglement in top-quark pair production at a photon linear collider. Constructing the spin density matrix of the tt‾t\overline{t }tt two-qubit system from the helicity amplitudes, we demonstrate that a photon linear collider is an ideal machine to probe quantum entanglement and Bell nonlocality across the broad phase space of the process.
Spin Correlation and Quantum Entanglement of Fermion Pairs in Transversely Polarized e−e+e^-e^+e−e+ Collisions
We systematically study the spin correlations and quantum entanglement in transversely polarized electron-positron collisions. We find that the sss-channel QED process e−e+→ffˉe^-e^+\to f\bar fe−e+→ffˉ​ produces a maximally entangled state in the entire phase space when the initial beams are transversely polarized, while the quantum magic varies in different phase space points for the maximally entangled Bell states. For electroweak processes, the spin configuration of final states depends on chiral couplings, and the entanglement is also greatly enhanced by transverse polarization as in the QED process. For Bhabha scattering with additional ttt-channel contributions, the transverse polarization still increases the final state entanglement, although with some dilution. The sensitive dependence of final spin states on the transverse polarization makes the beam polarization a powerful tool for generating and controlling quantum entanglement in collider experiments, opening up new opportunities for quantum information studies at high-energy colliders.