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arXiv:2011.14655 · Journal of Physics Communications

Amplification of polarization correlations in Compton scattering of hard x-ray Bell states

Peter Caradonna

Published Nov 1, 2020• 0 citations
arXivHTMLPDF

Abstract

Abstract The theoretical cross section for Compton scattering of maximally entangled Bell photons has yet to be rigorously confirmed by experiments. Test cases of Bell states for use in Compton scattering experiments can now be expanded given reports of creating all 4 Bell states in the hard x-ray regime by the process of spontaneous parametric down-conversion. We outline an experiment and apply a matrix method to parameterize Compton scattering theory using the phase matching angles. When the azimuths of two hypothetical photon counters are recorded at angles of 0 degrees and 90 degrees, and the ratio of their counting rates determined, azimuthal ratios are expected to be 600 times larger compared to 511 keV Bell photons.

DOI
10.1088/2399-6528/abcb45

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This theoretical research aims to examine areas of the Compton cross section of entangled annihilation photons for the purpose of testing for possible break down of theory, which could have consequences for predicted optimal capabilities of Compton PET systems. We provide maps of the cross section for entangled annihilation photons for experimental verification. We introduce a strategy to derive cross sections in a relatively straight forward manner for the Compton scattering of a hypothetical separable, mixed and entangled states. To understand the effect that entanglement has on the cross section for annihilation photons, we derive the cross section so that it is expressed in terms of the cross section of a hypothetical separable state and of a hypothetical forbidden maximally entangled state. We find lobe-like structures in the cross section which are regions where entanglement has the greatest effect. We also find that mixed states do not reproduce the cross section for annihilation photons, contrary to a recent investigation which reported otherwise. We review the motivation and method of the most precise Compton scattering experiment for annihilation photons, in order to resolve conflicting reports regarding the extent to which the cross section itself has been experimentally verified.
Abstract An experimental setup for studying the Compton scattering of annihilation photons in various (entangled and decoherent) quantum states is presented. Two entangled γ-quanta with an energy of 511 keV and mutually orthogonal polarizations are produced by positron-electron annihilation in a thin aluminum plate and are emitted in opposite directions. To measure both photons, the setup provides two equivalent arms of Compton polarimeters. A Compton polarimeter consists of a plastic scintillation scatterer and an array of NaI(Tl) detectors for measuring photons deflected at an angle of 90°. The intermediate scatterer of the GAGG scintillator with SiPM readout is inserted into one of the arms to create a tagged decoherence process prior to the measurement of annihilation photons in polarimeters. The performance of Compton scatterers and NaI(Tl) counters is discussed. The polarization modulation factor and the analyzing power of Compton polarimeters are evaluated from the angular distributions of scattered gammas. The Compton scattering of photons in entangled and decoherent states is compared reliably for the first time.
In positron annihilation, exploration of the polarization correlations of the emerging gamma quanta has gained interest, since they offer a possibility to improve signal-to-background in medical imaging using positron emission tomography. The annihilation quanta, which are predicted to be in an entangled state, have orthogonal polarizations and this property may be exploited to discriminate them from two uncorrelated gamma photons contributing to the background. Recent experimental studies of polarization correlations of the annihilation quanta after a prior Compton scattering of one of them, had rather different conclusions regarding the strength of the correlation after the scattering, showing its puzzling nature. The scattering was described as a decoherence process. In the present work, we perform for the first time, a study of the polarization correlations of annihilation quanta after decoherence via Compton scattering in the angular range 0∘−50∘ using single-layer gamma ray polarimeters. In addition, we compare the measured polarization correlations after Compton scattering at 30∘ with an active and a passive scatterer element. The measured azimuthal correlation of back-to-back annihilation quanta is consistent with the Pryce-Ward formulation, as confirmed by Monte Carlo simulations. Further, the results indicate that the correlation, expressed in terms of the polarimetric modulation factor, shows no significant difference at small scattering angles (0∘−30∘) compared to the correlation measured for direct photons, while a moderate indication of a lower modulation is observed for 50∘ scattering angle. The measured modulation is larger at all scattering angles than the one expected from the simulation of orthogonally polarized, independent annihilation quanta.
We present a theoretical study of the evolution of polarization entanglement and quantum coherence in 511 keV photon pairs produced by para-positronium decay during successive Compton scattering events. We start with a maximally entangled Bell state and employ the generalized Stokes-Mueller formalism to derive the two-photon density matrix following single-, double-, and triple-Compton scattering, explicitly considering both polar and azimuthal scattering geometries. Using this framework, we quantify the degradation of quantum correlations through concurrence (as a measure of entanglement) and the l1l_1l1​-norm (as a measure of coherence). Our results demonstrate that entanglement is highly sensitive to the scattering geometry and disappears near right-angle scattering, while quantum coherence remains finite even in regimes where entanglement vanishes completely. These findings provide a unified description of polarization-dependent decoherence in annihilation photon pairs and clarify the distinct roles of entanglement and coherence in realistic two-photon interactions. These results are relevant for quantum-enhanced positron emission tomography and highlight the persistence of quantum resources in scattering-dominated media.
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Abstract The experimental setup for study of Compton scattering of entangled and decoherent annihilation gammas is described. These gammas are born in two-photon positron-electron annihilation. Polarizations of annihilation gammas are mutually orthogonal, while the polarization of each photon is indefinite. If one of the photons of the pair interacts with matter, the pair becomes decoherent and photons acquire the determined polarization states. The kinematics of Compton scattering depends on the polarization states and can be different for entangled and decoherent pairs of annihilation photons. The angular correlations of scattered gammas for both, entangled and decoherent states are measured and compared. It is shown, that the kinematics of Compton scattering are similar for both cases.