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
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.
Journal of the Optical Society of America B•Jul 25, 2025•0 citations