We consider the scattering of entangled two-photon states from collections of small particles. We also study the related Mie problem of scattering from a sphere. In both cases, we calculate the entropy of entanglement and investigate the influence of the entanglement of the incident field on the entanglement of the scattered field.
We are interested in the entanglement entropy of the final state of two particles in an elastic scattering. One can expect that the entanglement is yielded by the interaction between the particles. Within an S-matrix theory, by using the partial wave expansion of the S-matrix elements for two-particle states, we calculate a density matrix in a high energy elastic scattering, and obtain the entanglement entropy formula, which is described by physical observables. In the derivation of this formula, there appear divergences due to the infinite volume of two-particle Hilbert space. In order to avoid such divergences, we suggest a volume-regularization. Then we concretely evaluate the entanglement entropy for proton-proton scattering by using experimental data.
We perform a theoretical study on the two-photon scattering effect of a single Mie scatterer, and investigate its dependence on the rotation angle of the scatterer, and the wavelength and polarization of incident light. Different regions of the two-photon correlation map are recognized by investigating two parameters, i.e., the visibility of two-photon superposition that represents the path information of different two-photon paths, and the balance factor of the double-side single-photon scattering amplitude that indicates the possibility of the single-photon scattering process. It is shown that the two-photon scattering pattern is a result of two-photon interference from the incoherent to fully coherent regime, together with a contribution from a single-photon-like correlation. In the coherent two-photon interference region, it is found that the transition from destructive to constructive interference emerges by rotating the scatterer, as well as by changing the polarization of incident light. These results demonstrate the rich features of the two-photon scattering effect for a single Mie scatterer, and open new possibilities to explore nano scatterers for controlling two-photon interference, and their applications in communications, sensing, and imaging.
We study the entanglement entropy between the two outgoing particles in an elastic scattering process. It is formulated within an S-matrix formalism using the partial wave expansion of two-body states, which plays a significant role in our computation. As a result, we obtain a novel formula that expresses the entanglement entropy in a high energy scattering by the use of physical observables, namely the elastic and total cross sections and a physical bound on the impact parameter range, related to the elastic differential cross-section.
We compute the entanglement entropy variation between initial (separable or entangled in the momenta) and final states ΔSE in an elastic scattering of a bipartite system composed by two interacting scalar particles. We perform a quantum field theoretical calculation to one loop order and verify that $ΔS_E $ changes as we vary the energy of incoming particles and the coupling strength in a non-trivial way.