Abstract:
Building on our prior proposal of photonic Schrödinger cat-like states (SCLSs) in spontaneous parametric down-conversion (SPDC) [arXiv:2405.14526], this work derives the optimal crystal length required for their practical generation. We present analytical and approximate formulas that link crystal and pump parameters directly to the optimal interaction length. These results provide a critical design tool for determining the optimal crystal length, enabling the practical generation of entangled cat states in $\chi^{(2)}$ nonlinear media.
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