  Single-photon pairs created in the nonlinear process of spontaneous
parametric downconversion form the backbone of fundamental and applied
experimental quantum information science. Many applications benefit from
careful spectral shaping of the single-photon wave-packets. In this paper we
tailor the joint spectral wave-function of downconverted photons by modulating
the nonlinearity of a poled crystal without affecting the phase-matching
conditions. We designed a crystal with a Gaussian nonlinearity profile and
confirmed successful wave-packet shaping by two-photon interference
experiments. We numerically show how our method can be applied for attaining
one of the currently most important goals of single-photon quantum optics, the
creation of pure single photons without spectral correlations.
