Sorkin parameter for type-I spontaneous parametric down-conversion biphotons and matter waves
F. C. V. de Brito, Carlos H. S. Vieira, I. G. da Paz, Jonas B. Araujo, Marcos Sampaio · Physical Review A · 2021
Type-I spontaneous parametric down-converted biphotons can be described approximately by a double-Gaussian wave function in configuration space. Using an effective propagator in the Fresnel approximation, the time evolution and transversal spreading of the two-particle biphoton wave function allow us to evaluate the Sorkin parameter $\ensuremath{\kappa}$, which results from nonclassical path contributions of the kink type and loops to double- and triple-slit interferometry. This simple unidimensional model for the evaluation of $\ensuremath{\kappa}$ predicts that kinked nonclassical paths may lead to $\ensuremath{\kappa}\ensuremath{\approx}{10}^{\ensuremath{-}5}$ for degenerate biphotons. We show that such a model reproduces well the Sorkin parameter for matter waves found in more involved approaches in the literature. Moreover, we establish a hierarchy of approximations based on the shape of the nonclassical paths for matter waves and compare their size with leading relativistic corrections to the propagator.