Universal Quartic Scaling Law for Kerr-Type Interactions: Projection-Law Factorization Across Nonlinear Quantum Platforms

• URL: http://arxiv.org/abs/2604.16816v1
• Date: Sat, 18 Apr 2026 04:11:26 GMT
• Title: Universal Quartic Scaling Law for Kerr-Type Interactions: Projection-Law Factorization Across Nonlinear Quantum Platforms
• Abstract summary: We present a universal projection-law factorization for quartic nonlinear coupling rates across physically distinct platforms.<n>A complete, step-by-step worked example for a superconducting quarton device predicts a cross-Kerr rate.<n>A formal error-propagation analysis establishes that the dominant uncertainty is the Josephson-energy extraction uncertainty.
• Score: 3.90378585979906
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a rigorous derivation and numerical validation of a universal projection-law factorization for quartic nonlinear coupling rates across physically distinct platforms. The central result is that observable Kerr-type interactions -- self-Kerr, cross-Kerr, and cross-phase modulation -- factorize into a dimensionless projection coefficient and an intrinsic quartic energy scale. This structure follows from canonical quantization of a quartic interaction projected onto a finite normal-mode basis. We state this result as a formal proposition with clearly enumerated assumptions, provide a proof sketch based on second quantization of the anharmonic potential, and enumerate the domain of validity. We then implement the scaling law as a lightweight computational toolkit (UEFT-Designer) with platform-specific kernels for superconducting circuits, photonic microcavities, and epsilon-near-zero (ENZ) structures. A complete, step-by-step worked example for a superconducting quarton device -- with full uncertainty propagation -- predicts a cross-Kerr rate $χ/2π= 361\pm 13\,\mathrm{MHz}$, agreeing with the independently measured value of $366\pm 0.5\,\mathrm{MHz}$ \cite{Ye2025} to within 1.4\%. A formal error-propagation analysis establishes that the dominant uncertainty is the Josephson-energy extraction uncertainty ($\sim\!2\%$), not the geometric projection factor. Cross-platform validation against five independent experiments spanning eight orders of magnitude in coupling strength confirms the universality of the factorization to within reported experimental uncertainties. The ghost-sector spectral correction introduced in earlier versions is reframed as an optional phenomenological self-energy model with no mandatory role in the validated scaling law.

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