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Journal of the Optical Society of America B

Characterization of polarization-entangled processes in photon–photon scattering: a comparison of differential cross sections for unentangled and entangled final states

Michael A. Stroscio, Mitra B. Dutta

Published Jul 25, 2025• 0 citations
Publisher

Abstract

Polarization-entangled photons are routinely produced using complex nonlinear media. In using such systems to produce polarization-entangled photons, it is assumed that the entanglement effects are not altered by such nonlinear media. However, this assumption is generally accepted but there remains the need to ensure that the nonlinear media do not alter the entanglement of the photons. To address the polarization entanglement of photons in the absence of a complex nonlinear medium, such as a nonlinear crystal or an atomic system, this paper calculates branching ratios of entangled and unentangled photons from the fundamental process of photon–photon scattering in vacuum as opposed to in a complex nonlinear medium. Herein, the Dyson–Feynman formalism of quantum electrodynamics is used to examine selected entanglement effects manifested in the well-known process of photon–photon scattering in vacuum. Based on known partial scattering amplitudes for processes where two photons of specified polarizations interact via an intermediate fermion loop to form a final state of two photons with allowed polarization states, polarization-entangled photon affects are analyzed for cases where both initial and final states are described by specific entangled states, extending previous analyses. The current analysis compares the cases where unentangled photons scatter in a vacuum into final states of (a) unentangled photons, (b) maximally entangled photons (symmetric Bell state), and (c) antisymmetric Bell state. This comparison reveals that the probability of scattering into a state of maximally entangled polarization-entangled states is of the same order as that of scattering into unentangled final-state photons.

DOI
10.1364/josab.564488

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Polarization-entangled photons are routinely produced using complex nonlinear media. In using such systems to produce polarization-entangled photons, it is assumed that the entanglement effects are not altered by such nonlinear media. However, this assumption is generally accepted but there remains the need to ensure that the nonlinear media do not alter the entanglement of the photons. To address the polarization entanglement of photons in the absence of a complex nonlinear medium, such as a nonlinear crystal or an atomic system, this paper calculates branching ratios of entangled and unentangled photons from the fundamental process of photon–photon scattering in vacuum as opposed to in a complex nonlinear medium. Herein, the Dyson–Feynman formalism of quantum electrodynamics is used to examine selected entanglement effects manifested in the well-known process of photon–photon scattering in vacuum. Based on known partial scattering amplitudes for processes where two photons of specified polarizations interact via an intermediate fermion loop to form a final state of two photons with allowed polarization states, polarization-entangled photon affects are analyzed for cases where both initial and final states are described by specific entangled states, extending previous analyses. The current analysis compares the cases where unentangled photons scatter in a vacuum into final states of (a) unentangled photons, (b) maximally entangled photons (symmetric Bell state), and (c) antisymmetric Bell state. This comparison reveals that the probability of scattering into a state of maximally entangled polarization-entangled states is of the same order as that of scattering into unentangled final-state photons.
A Stokes parameter representation for two-photon systems is developed to calculate cross sections for both entangled and classically correlated mixed states scattering off unpolarized and polarized Compton electrons. The cross section of Compton scattering for pairs of maximally entangled annihilation photons, generated by the disintegration of para-positronium, is compared with classical analogs. An analysis of the symmetrical properties and basis independence of these systems is conducted to elucidate the observed differences. We propose a method to establish an upper bound for identifying correlations influenced by entanglement. Furthermore, we calculate the cross section for Compton scattering of annihilation photons from spin-polarized electrons. A qualitative analysis reveals a contradiction to the contemporary assumption that Compton scattering acts as an entanglement kill switch. These findings contribute to a broader understanding of photon systems and their behavior in various scattering scenarios. Although the primary focus of this article is on Compton scattering, the formalism can be adapted to other interactions, provided that the Mueller matrix representation of the interaction is available. Published by the American Physical Society 2024
The central topic of the Thesis concerns light scattering experiments with entangled photons. Specifically, we study the effect of scattering processes on polarization-entanglement of twin-photons. The main idea is that scattering generally couples polarization and spatial degrees of freedom of photons. The details of this coupling depend on the characteristics of the scattering medium. Such coupling, in turn, can reduce the entanglement of twin-photons, if the photon pairs are detected in a momentum-insensitive way. We have investigated a broad range of optical scattering media ranging from milk to polymer fibers. By manipulating the parameters of these samples we were able to generate a broad range of quantum states, proving for the first time that scattering processes are a substantial tool for mixed-state engineering. This is of great importance for quantum information since any real-world application thereof has to deal with mixed (as opposed to pure) states.
In this paper, the 16 Stokes parameters of a two-photon system are organized into a $4\ifmmode\times\else\texttimes\fi{}4$ Stokes matrix. This formalism is then applied to analyze the polarization properties of annihilation photons produced by electron-positron annihilation, with a particular focus on their evolution during Compton scattering interactions. The study demonstrates that when one of the subsystems undergoes Compton scattering, quantum entanglement preserves the polarization symmetry between the scattered and noninteraction photons, while in the absence of entanglement, this symmetry is lost. Moreover, the method simplifies the calculation of the joint differential cross section for multiple scattering scenarios and provides a means to characterize the polarization properties of the individual subsystems. These findings highlight the impact of quantum correlations on scattering behavior, and they offer a framework for further investigation into the polarization dynamics of entangled photon pairs.
It is found that the differential cross section of photon-photon scattering is a function of the degree of polarization entanglement of the two-photon state. A reduced general expression for the differential cross section of photon-photon scattering is derived by applying simple symmetry arguments. An explicit expression is obtained for the example of photon-photon scattering due to virtual electron-positron pairs in quantum electrodynamics. It is shown how the effect in this explicit example can be explained as an effect of quantum interference and that it fits with the idea of distance-dependent forces.
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We study entanglement dynamics among helicity degrees of freedom in quantum electrodynamics (QED) scattering processes. For generic initial states, we consider scattering at fixed momentum, corresponding to a generalized measurement described by a positive operator-valued measure, resulting in a post-measurement state. Such processes are modeled in terms of quantum maps, whose spectral structure fully determines the associated entanglement dynamics. For scattering involving fermions only, maximal entanglement present in the initial state is always preserved. Moreover, iterating the corresponding quantum maps on arbitrary initial states, we obtain the fixed points of the maps, which, in the largest number of cases, are asymptotic (pure) maximally entangled states. The structure of the maps also accounts for the entanglement dynamics in processes involving both fermions and photons. The defining properties of these maps originate from discrete symmetries of the QED interaction.