Preparation of Schr\"odinger cat quantum state using parametric down-conversion interaction

The Schr\"odinger cat state is important in quantum optics because of its non-Gaussian properties. This paper proposes the use of degenerate parametric scattering and measurement of the number of photons in the pump mode to conditionally prepare the Schr\"odinger cat state. This method ensures the preparation of SC in systems with weak parametric non-linear interaction. Comparison with the existing whispering mode gallery microresonator from lithium niobate indicates the possible applicability of this method.