Preparation of the Schrödinger cat quantum state using parametric down-conversion interaction

Schrödinger cat (SC) states are important in quantum optics because of their non-Gaussian properties. We propose a novel, to the best of our knowledge, method for the conditional generation of bright (multi-photon) SC states that uses degenerate parametric down-conversion and heralding measurement of the photon number in the pump mode. We show that this method, in principle, could be implemented using modern high- Q optical microresonators.