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Optica Acta International Journal of Optics

Second-order Solution in the Photon Anticorrelation Effect for Stimulated Annihilation of Electron-positron Pairs

Vlasta Peřinová, Jan Peřina, M. Bertolotti, Concita Sibilia

Published Feb 1, 1982• 3 citations
Publisher

Abstract

The second-order iterative solution for the antinormal characteristic function has been obtained for the stimulated annihilation process of electron-positron pairs. It is shown that the first-order solution, obtained recently, is sufficient to define the anticorrelation effect in this process. Some estimates are given concerning possible realizations.

DOI
10.1080/713820829

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The second-order iterative solution for the antinormal characteristic function has been obtained for the stimulated annihilation process of electron-positron pairs. It is shown that the first-order solution, obtained recently, is sufficient to define the anticorrelation effect in this process. Some estimates are given concerning possible realizations.
A relation between the normal generating and characteristic functions, recently obtained by Rockower and Abraham, is shown to be valid in a space of generalized functions if antinormal ordering is adopted. This is demonstrated for the quadratic non-linear interaction for which we derive the change of quantum statistics caused by the dynamics of the process as well as by the initial statistical state of the field. The possibilities that the uncertainty might increase and that anticorrelation might occur are discussed. The analyticity of the generating function is applied to demonstrate a smoothing process when calculating the normal generating function and to show that a recent statement of Timmermans and Zijlstra concerning the restricted validity of cumulants is incorrect.
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.
This paper shows the various parameters to be considered, duringelectron - positron annihilation. Many of the theories suggest that directionof gamma ray emission cannot be predicted. This is normally justifiedby using quantum mechanics. This paper gives an alternative explanation tounpredictability of gamma ray direction. This explanation does not require thelogic of quantum mechanics. It requires modification of classical mechanics toaccount of the forces between colliding particles.The logic of this paper is thatin case of pair production involving gamma ray and electron- positron pair, theclassical mechanics calculation itself shows perfect conservation of directionand magnitude of momentum. There, a little recoiling of the nucleus is observedfor conserving momentum. Hence it must be possible to use classicalmechanics for the process of electron- positron annihilation process also.
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.