Azimuthal angular entanglement between decaying particles in ultra-peripheral ion collisions

Ultra-peripheral collisions (UPCs) involving relativistic heavy ions are a unique laboratory to study quantum correlations. The intense electromagnetic fields generate high rates of photonuclear interactions, including events involving multiple photon exchange. Multiple photon exchange can result in the production of multiple vector mesons and/or nuclear excitations. These interactions share a common impact parameter, so the photons have the same linear polarization. The shared polarization entangles the particles, leading to unique quantum correlations. The decays of these vector excitations are sensitive to this polarization, allowing for the study of these correlations. This letter will compare classical and quantum calculations of the correlations between these azimuthal directions. The two approaches predict vert different angular correlations. The differences are akin to those seen with polarized photons in tests of Bells inequality. Uniquely, UPC photoproduction can produce final states containing three or more particles, all entangled with the same polarization. These more complex states exhibit additional unique phenomenology, allowing new tests of multi-particle entanglement.

💡 Research Summary

Ultra‑peripheral collisions (UPCs) of relativistic heavy ions provide a uniquely clean environment in which strong electromagnetic fields act as sources of quasi‑real photons. Because the impact parameter b is large, the ions do not undergo hadronic interactions, yet each ion’s electric field is linearly polarized along b. When several photons are exchanged in a single encounter, all of them share this common polarization direction. Consequently, any particles produced by these photons – vector mesons such as ρ⁰, ϕ, J/ψ or nuclear excitations like the Giant Dipole Resonance (GDR) – inherit the same linear polarization. The decay products of these short‑lived states are self‑analyzing: the azimuthal angle θ of a daughter particle with respect to b follows a cos²θ distribution.

The paper first derives the classical expectation for the azimuthal correlation between two such decay products. Treating each particle independently, the joint probability is the convolution of two cos²θ distributions, yielding
  P(θ₁₂)=½