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

The Schrödinger cat (SC) states are important in quantum optics because of their non-Gaussian properties. We propose a novel method of 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 the modern high-$Q$ optical microresonators.