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We study the quantum correlations induced by spontaneous parametricdown-conversion (SPDC) of a frequency comb. We derive a theoretical method tofind the output state corresponding to a pump with an arbitrary spectralprofile. After applying it to the relevant example of a spectrally chirpedpump, we run an optimization algorithm to numerically find the pump profilesmaximizing some target functions. These include the number of independentlysqueezed modes and the variances of nullifiers defining cluster states used inmany continuous-variable quantum information protocols. To assess theadvantages of pump-shaping in real experiments we take into account thephysical limitations of the pulse shaper.

Versatile engineering of multimode squeezed states by optimizing the pump spectral profile in spontaneous parametric down-conversion