https://doi.org/10.1140/epjd/e2012-30099-y
Regular Article
X-entangled biphotons: Schmidt number for 2D model
1
Laboratoire PhLAM, Université Lille 1,
59655
Villeneuve d’Ascq,
France
2
B.I.Stepanov Institute of Physics, NASB, Nezavisimosti ave. 68, 220072
Minsk,
Belarus
3
IFN-CNR and Dipartimento di Alte Tecnologie, Universita
dell’Insubria, Via Valleggio
11, 22100
Como,
Italy
a e-mail: dmitri.horoshko@gmail.com
Received:
9
February
2012
Received in final form:
8
June
2012
Published online:
12
September
2012
We calculate the Schmidt number for a two-dimensional model of the nonfactorable spatiotemporal wave-function of biphotons produced in type-I spontaneous parametric down-conversion with degenerate and collinear phase-matching taking into consideration a major part of the broad spectral and angular bandwidth of the down-converted light. We deduce an analytical expression for the Schmidt number as a function of the filter bandwidth in the limit of spectrally narrow pump and consider a possibility of tailoring a Gaussian model for the description of this kind of entanglement.
Key words: Topical issue: High Dimensional Quantum Entanglement. Guest editors: Sonja Franke-Arnold, Alessandra Gatti and Nicolas Treps
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2012