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 τ 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 τ 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 |ω (0) 1 − ω (0) 2|cr up to which a high spectral entanglement, found earlier for the case of degenerate frequencies, remains unchanged. We find that |ω (0) 1 − ω (0) 2|cr is on the order of the bandwidth of the single-particle spectrum of SPDC with degenerate frequencies.
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Document Type: Research Article
Publication date: 2009-12-01
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