X-entanglement of PDC photon pairs: the nonfactorable spatiotemporal structure of biphoton correlation

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). Here we turn our attention to the genuine quantum properties of PDC, and we demonstrate the hyperbolic geometry underlying the spatio-temporal structure of the PDC entanglement and its non-factorability with respect to space and time [2]. As for the X-waves encountered in nonlinear optics, the X-shape of the bi-photon correlation is imposed by the phase-matching mechanism governing the PDC process, and following this analogy we coined the name of X-entanglement. This represents a entirely new concept, because investigations on the quantum state of of PDC have been performed to date mostly in a purely either temporal or spatial framework. Our approach, which takes into account the nonfactorability of the state in space and time, leads to relevant elements of novelty, namely i) the possibility of tailoring the temporal bandwidth of the bi-photons by manipulating their spatial degrees of freedom, or viceversa and ii) the extreme relative localization of the X-entanglement in time and space, with bi-photon correlation times and lengths in the femtosecond and micrometer range, respectively. It should be stressed that both the non-factorability and the extreme localization are not present in the detection schemes used so far, which usually select small angular portions of the PDC fluorescence. In the metrology domain, our researches have high potentialities for e.g. ultra-precise measurements of time delays and clock synchronizations, due to the ultra-short localization in time of the entangled photons. [1] For a review see C.Conti and S.Trillo in Localized-Waves, p. 243, H.E.Hernandez- Figuroa, M.Zamboni-Rached and E.Recami eds. [2] E. Brambilla, L. Caspani, O. Jedrkiewicz, L.A. Lugiato and A. Gatti, X-entanglement of PDC photon pairs, e-print arXiv:0812.3533v1