Spectral Entanglement in Parametric Down-Conversion with Nondegenerate Frequencies

We analyze spectral entanglement of biphoton states in the non-degenerate scheme of spontaneous parametric down conversion. We show that, compared to the case of degenerate central frequencies of single and idler photons, non-degeneracy decreases the degree of entanglement. However, degradation of entanglement is inhomogeneous in dependence on the pump-pulse duration. Non-degeneracy affects first of all and mostly the region of long pump pulses. There is a well defined critical pump-pulse duration tau(cr) below which entanglement remains as high as in the case of degenerate frequencies. With a growing degree of non-degeneracy, the critical pulse duration tau(cr) diminishes. In other words, at any given value of the pump-pulse duration, always there is a finite spacing between the signal and idler frequencies vertical bar omega((0))(1) - omega((2))(2)vertical bar(cr) up to which a high spectral entanglement, found earlier for the case of degenerate frequencies, remains unchanged. We find that vertical bar omega((0))(1) - omega((0))(2)vertical bar(cr) is on the order of the bandwidth of the single-particle spectrum of SPDC with degenerate frequencies.