Heralding pure single photons: a comparision between counter-propagating   and co-propagating twin photons
  We investigate the possibility of generating pure heralded single photons through spontaneous parametric down-conversion comparing the counter-propagating geometry studied in [1] with more conventional co-propagating configurations which enhance the purity of the heralded photon state through the technique of group-velocity matching. We estimate the Schmidt number associated to the temporal modes as a function of the pump pulse duration for three particular configurations, showing how the different phase-matching conditions influences the degree of separability that can be achieved. 
E. Brambilla, T. Corti, and A. Gatti
quant-ph