Modelling parametric down-conversion yielding spectrally pure photon pairs

Pair creation by spontaneous parametric down-conversion (SPDC) has become a reliable source for single-photon states, used in many kinds of quantum information experiments and applications. In order to be spectrally pure, the two photons within a generated pair should be as frequency-uncorrelated as possible. For this purpose most experiments use narrow bandpass filters, having to put up with a drastic decrease in count rates. This article elaborates (theoretically and by numerical evaluation) the alternative method to engineer a setup such that the SPDC-generated quantum states are intrinsically pure. Using pulsed pump lasers and periodically poled crystals this approach makes bandpass filtering obsolete and allows for significantly higher output intensities and therefore count rates in the detectors. After numerically scanning all common wavelength regimes, polarisation configurations and three different non-linear crystals, we present a broad variety of setups which allow for an implementation of this method.