In this work 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 [1,2]. As for the macroscopic X-waves, the X-shape of the biphoton correlation is imposed by the phase-matching mechanism governing the PDC process, and following this analogy we coined the name of X-entanglement [1] A. Gatti, E. Brambilla, L. Caspani, O. Jedrkiewicz, and L.A. Lugiato, Phys. Rev. Lett. 102, 223601 (2009) ; e-print arXiv:0812.3533v1 [2] L. Caspani, E. Brambilla and A. Gatti, Tailoring the spatio-temporal structure of biphoton entanglement in type I PDC , Phys. Rev A, 81, 033808 (2010)
X-entanglement: the non-factorable spatio-temporal structure of biphoton correlation
BRAMBILLA, ENRICO;Caspani L.;JEDRKIEWICZ, OTTAVIA;LUGIATO, LUIGI
2010-01-01
Abstract
In this work 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 [1,2]. As for the macroscopic X-waves, the X-shape of the biphoton correlation is imposed by the phase-matching mechanism governing the PDC process, and following this analogy we coined the name of X-entanglement [1] A. Gatti, E. Brambilla, L. Caspani, O. Jedrkiewicz, and L.A. Lugiato, Phys. Rev. Lett. 102, 223601 (2009) ; e-print arXiv:0812.3533v1 [2] L. Caspani, E. Brambilla and A. Gatti, Tailoring the spatio-temporal structure of biphoton entanglement in type I PDC , Phys. Rev A, 81, 033808 (2010)
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