The twin photons produced by a type-II spontaneous parametric down conversion are well know as a potential source of photons for quantum teleportation due to the strong entanglement in polarization. This strong entanglement in polarization, however, depends on the spectral composition of the pump photon and the nature of optical isotropy of the crystal. By exact numerical calculation of the concurrence, we have shown that how pump photons spectral width and the birefringence nature of the crystal directly affect the degree of polarization entanglement of the twin photons.

The realization of faithful transmission of information in quantum communication [_{2}O_{4} (BBO), nonlinear crystal are one of the common source of entangled state of the Bell type. There is an increasing interest in the spectral and spatial properties of the down-converted photons and, specifically, in achieving particular spatial and spectral profiles [

In parametric down-conversion type-I phase matching leads to two photons with same polarization. In this phase matching, if the down-conversion is degenerated, a pair of two photons with identical frequency emerges on a cone [

In Type-II parametric down-conversion we consider the case where the nonlinearity of the crystal does not depend on frequency so that the gain of the parametric interaction is constant. We also assume that the down-converted beams are constrained to be nearly collinear. The beam that pumps the crystals is pulsed laser which is much stronger than the down-converted beams. Under these conditions and taking into account that parametric down-conversion is very much ineffective, along the two directions, the state of the two photons can be written as [

Introducing the variables,

The degree of entanglement of a bipartite system, quantitatively, can be described using the von Neumann entropy [

We first examine how the degree of the entanglement of the down-converted photons depends on the spectral bandwidth of the pump photons,

The concurrence as a function of the ratio of the crystal transit times difference (

Humble and Grice [

The concurrence as a function of the pump spectral width

In conclusion, the Gaussian approximation for the phase matching function in type-II SPDC does not accurately predict the degree of polarization entanglement of the down-converted photons for a pump photon with broad spectral composition. This result may potentially be usefully to design a more effective experimental scheme for optimization of polarization entanglement of the twin photons in type-II SPDC.

This work is in part supported by US Department of Energy and Oak Ridge Institute for Science & Education and Middle Tennessee State University. The author thanks Travis S. Humble and Warren P. Grice.