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Theory of Computing Systems

Positron/Electron Annihilation via the Two-Photon Pathway

Isabelle Gauthier

Published Jan 1, 2011• 0 citations

Abstract

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.

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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.

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.

Recent experimental measurements of the time interval between detection of the two photons emitted in positron-electron annihilation have indicated that collapse of the spatial part of the photon's wave function, due to detection of the other photon, does not occur. Although quantum nonlocality actually occurs in photons produced through parametric down-conversion, the recent experiments give strong evidence against measurement-induced instantaneous spatial localization of high-energy $\ensuremath{\gamma}$ photons. A quantum-mechanical analysis of the Einstein-Podolsky-Rosen problem is presented, which may help to explain the observed differences between photons produced through parametric down-conversion and photons produced through positron-electron annihilation. The results are found to concur with the recent experiments involving $\ensuremath{\gamma}$ photons.

Recent experimental measurements of the time interval between detection of the two photons emitted in positron-electron annihilation have indicated that collapse of the spatial part of the photon's wave function, due to detection of the other photon, does not occur. Although quantum nonlocality actually occurs in photons produced through parametric down-conversion, the recent experiments give strong evidence against measurement-induced instantaneous spatial localization of high-energy $\ensuremath{\gamma}$ photons. A quantum-mechanical analysis of the Einstein-Podolsky-Rosen problem is presented, which may help to explain the observed differences between photons produced through parametric down-conversion and photons produced through positron-electron annihilation. The results are found to concur with the recent experiments involving $\ensuremath{\gamma}$ photons.

Correlations between the behavior of pairs of particles are generated in the following experimental situation. An on-line source emits a stream of two-particle systems, where each system is in one and the same quantum state. After emission, the particles – call then (I) and (II) – move off in opposite directions. Each particle then encounters one of several possible barriers that either it passes or doesn't. A short distance behind each barrier is a detector set to register the presence of the particle, should it get that far. Finally, the detectors are connected by a timed relay and counter that registers a “coincidence count” should the two detectors fire within a set, brief time interval. When the experiment is run with various different barriers, detection rates accumulate for each barrier singly, and coincidence rates (the correlations) for the various pairs of barriers.