Where are photons created in parametric down-conversion? On the control of the spatio-temporal properties of biphoton states

In spontaneous parametric down-conversion, pairs of photons are known to be created coherently and with equal probability over the entire length of the crystal. Then, there is no particular position in the crystal where a photon pair is created. We make the seemingly contradictory observation that the time delay between the photons in the pair depends on the distance from the crystal to the collection lens, as if the photons were actually collected preferentially from a particular position in the crystal. We resolve this contradiction by showing that the spatio-temporal correlations critically affect the temporal properties of the pair of photons. The theoretical model we present matches all our experimental results. We expect this to have important implications for experiments that require indistinguishable photons.