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arXiv:1006.0665 · Physical Review A

Photon correlations in positron annihilation

Isabelle Gauthier, Margaret Hawton

Published Jun 23, 2010• 6 citations
arXivHTMLPDF

Abstract

The two-photon positron annihilation density matrix is found to separate into a diagonal center-of-energy factor implying maximally entangled momenta, and a relative factor describing decay. For unknown positron injection time, the distribution of the difference in photon arrival times is a double exponential at the para-Ps decay rate, consistent with experiment [V. D. Irby, Meas. Sci. Technol. 15, 1799 (2004)].

DOI
10.1103/physreva.81.062121

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The two-photon positron annihilation density matrix is found to separate into a diagonal center-of-energy factor implying maximally entangled momenta, and a relative factor describing decay. For unknown positron injection time, the distribution of the difference in photon arrival times is a double exponential at the para-Ps decay rate, consistent with experiment [V. D. Irby, Meas. Sci. Technol. 15, 1799 (2004)].
When a positron/electron pair annihilate via the two-photon pathway, the emitted photons are momentum correlated. This correlation ensures that they move along a straight line path in opposite directions. An experiment performed in 2004 by Dr. V.D. Irby measured the time interval between \ndetection of the photons. He observed a decay in the number of counts with increasing detection time interval, which he described using a Lorentzian, the line width of which at full-width half-maximum is \nmeasured to be 120ps. The data collected by Irby is interesting because current theory predicts that because the source is so localized (the effective source width used by Irby is safely within 5rnrn) the photons should be detected within a time interval of ?t=d/c where d is the thickness of the source. This time interval corresponds to 17ps. This thesis fits the results to an exponential, and shows that this exponentially decaying nature of the coincidence time interval is characteristic of the entanglement of the two photons. We find that the wavefunctions of the photons decoheres in space according to how long the particle pair took to decay (which is exponential), and that the probability of simultaneous \ndetection depends on the exponential of the product of the lifetime of positronium and the detection time interval.
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.
The entanglement of photons originating from electron-positron annihilation has not been experimentally proven.owever, the independent experiments performed so far unanimously confirm that the correlation between the linear polarizations of back-to-back photons from electron-positron annihilation is consistent with the assumption that these photons are entangled in the polarization.Yet, unexpectedly, recent experiments differ as regards the correlation of polarization direction of back-to-back photons after the decoherence induced by the scattering of one of these photons on the electron in the scattering material.In one of the experiments, the correlation before and after the decoherence of the photon state is the same, and in the other experiment, the scattering of one photon leads to a significant decrease in this correlation.Here we discuss this puzzle.Decoherent states were ensured provided by forcing one of the annihilation photons to scatter earlier before measuring the polarization correlation based on Compton kinematics.The comparison is made between the experimental setups used for the different measurements, and the results obtained are briefly discussed, highlighting the parameters that are important in performing such measurements.Finally, the main features of the J-PET detector are presented, along with the schemes for performing similar studies, so that the conclusive results can be used as remarks to solve the puzzle in question.Solving the decoherence puzzle will have crucial consequences for basic studies of entanglement, as well as for the proposed application of the photon polarization in positron emission tomography.If the correlation of the polarization of back-to-back photons from the electron-positron annihilation is the same before and after the scattering of these photons, then it will not be useful for the reduction of scatter fraction in positron emission tomography diagnostics.
IntroductionIn this experiment we will explore whether photons emitted from the decay of positronium, a positron-electron composition, are quantum entangled. When talking about quantum entangled particles it is impossible to fully represent the quantum state of one particle independently of another such that if we know one photon from an entangled pair is horizontally polarized then the other must be vertically polarized. We will use this concept along with knowledge from previous experiments on positron-electron annihilation and Compton scattering to try to determine the truth of this model.ProcedureIn this experiment we used two NaI detectors, photo-multiplier tubes (PMT), pre-amplifiers, and amplifiers. Along with two single channel analyzers, a logic gate, a coincidence detector, a high-voltage supply, and a multi-channel analyzer (MCA) and of course two aluminum targets, a sodium-22 radioactive source, and loads of lead bricks. Our source was encased in the center of our detector configuration such that radiation from the source was focused towards both aluminum targets placed opposite of each other with respect to the source. Both detectors were then stationed so that photons coming from the source were detected after a 90 degree Compton scattering from the target. This ninety degree correlation is necessary for proof of quantum entanglement as we expect no coincidences to occur when both detectors are in the same plane do to quantum pairs anti-correlated polarization causing expected scattering to be related by this ninety degree angle. The picture below shows the basic geometry of this set up.
We present a new experimental study of the quantum entanglement of photon pairs produced in positron-electron annihilation at rest. Each annihilation photon has an energy that is five orders of magnitude higher than the energy of photons in optical experiments. It provides a unique opportunity for controlled Compton pre-scattering of initial photons before the polarization measurements. The experimental setup includes a system of Compton polarimeters to measure the angular correlations of annihilation photons in initial and thus prepared pre-scattered states. For the first time, a direct comparison of the polarization correlations of initial and pre-scattered annihilation photons has been carried out. The angular distributions of scattered in polarimeters photons turned out to be the same for both types of events. Moreover, the correlation function in the Bell's inequality is also the same for both states. We discuss the implications of our results for quantum measurement theory and for the quantum-entangled positron emission tomography.