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

Abstract

We study the quantum correlations induced by spontaneous parametric down-conversion of a frequency comb. We derive a theoretical method to find the output state corresponding to a pump with an arbitrary spectral profile. After applying it to the relevant example of a spectrally chirped pump, we run an optimization algorithm to numerically find the pump profiles maximizing some target functions. These include the number of independently squeezed modes and the variances of nullifiers defining cluster states used in many continuous-variable quantum information protocols. To assess the advantages of pump shaping in real experiments, we take into account the physical limitations of the pulse shaper.