Abstract

Mastering the techniques involving sources of entangled photon pairs has become vital for the implementations of many quantum networks and quantum computing schemes. So far, parametric down-conversion (PDC) demonstrated the most efficient room-temperature source of entangled photon pairs, employed in successful implementation of quantum communication schemes. At the very heart of such technologies lies the quantum interference between photonic wave functions, which depends crucially on the spatio-temporal mode structure of the photons. In this work, this issue is addressed from a peculiar and novel point of view, that is, the non factorability in space and time of the PDC bi-photon entanglement. The idea is driven by recent investigations in nonlinear optics [1] that outlined how in nonlinear media the angular dispersion relations impose a hyperbolic geometry involving temporal and spatial degrees of freedom in a non-factorable way. The wave object that captures such a geometry is the so-called X-wave (the X being formed by the asymptotes of the hyperbola). The statistical counterpart of the X-wave was recently showed to emerge in the X-shaped structure of the classical first order coherence function [2].

© 2009 IEEE