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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.17200 |
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| _version_ | 1866917983557779456 |
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| author | Taniguchi, Kento Noguchi, Atsushi Oka, Takashi |
| author_facet | Taniguchi, Kento Noguchi, Atsushi Oka, Takashi |
| contents | Strongly driven nonlinear systems are frequently encountered in physics, yet their accurate control is generally challenging due to the intricate dynamics. In this work, we present a non-perturbative, semi-analytical framework for tailoring such systems. The key idea is heuristically extending the Floquet theory to nonlinear differential equations using the Harmonic Balance method. Additionally, we establish a novel constrained optimization technique inspired by the Lagrange multiplier method. This approach enables accurate engineering of effective potentials across a broader parameter space, surpassing the limitations of perturbative methods. Our method offers practical implementations in diverse experimental platforms, facilitating nonclassical state generation, versatile bosonic quantum simulations, and solving complex optimization problems across quantum and classical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17200 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-Analytical Engineering of Strongly Driven Nonlinear Systems Beyond Floquet and Perturbation Theory Taniguchi, Kento Noguchi, Atsushi Oka, Takashi Quantum Physics Atomic Physics Strongly driven nonlinear systems are frequently encountered in physics, yet their accurate control is generally challenging due to the intricate dynamics. In this work, we present a non-perturbative, semi-analytical framework for tailoring such systems. The key idea is heuristically extending the Floquet theory to nonlinear differential equations using the Harmonic Balance method. Additionally, we establish a novel constrained optimization technique inspired by the Lagrange multiplier method. This approach enables accurate engineering of effective potentials across a broader parameter space, surpassing the limitations of perturbative methods. Our method offers practical implementations in diverse experimental platforms, facilitating nonclassical state generation, versatile bosonic quantum simulations, and solving complex optimization problems across quantum and classical applications. |
| title | Semi-Analytical Engineering of Strongly Driven Nonlinear Systems Beyond Floquet and Perturbation Theory |
| topic | Quantum Physics Atomic Physics |
| url | https://arxiv.org/abs/2502.17200 |