Universal Quartic Scaling Law for Kerr-Type Interactions: Projection-Law Factorization Across Nonlinear Quantum Platforms
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914528391856128 |
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| author | Liu, Xiaochen Yong, Ken-Tye |
| author_facet | Liu, Xiaochen Yong, Ken-Tye |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16816 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Quartic Scaling Law for Kerr-Type Interactions: Projection-Law Factorization Across Nonlinear Quantum Platforms Liu, Xiaochen Yong, Ken-Tye Quantum Physics Optics 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. |
| title | Universal Quartic Scaling Law for Kerr-Type Interactions: Projection-Law Factorization Across Nonlinear Quantum Platforms |
| topic | Quantum Physics Optics |
| url | https://arxiv.org/abs/2604.16816 |