Formation of Optical Schrödinger Cat-Like States via a Non-Linear Optical Process

We demonstrate the generation of Schrödinger cat-like states in spontaneous parametric down-conversion (SPDC) with a fully quantized, depleted pump. Unlike undepleted-pump models, our approach reveals key quantum features: significant squeezing, super-Poissonian statistics, entanglement, and resilience to dissipation. These results enable robust, strongly non-Gaussian states for continuous-variable quantum technologies using conventional $\chi^{(2)}$ media at moderate intensities.