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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2601.17208 |
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| _version_ | 1866912845219758080 |
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| author | Urzúa, Alejandro R. |
| author_facet | Urzúa, Alejandro R. |
| contents | This work presents a pedagogical and self-contained derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model in the dispersive regime. A perturbative unitary transformation removes nonresonant atom-field terms, revealing dispersive frequency shifts leading to an atom-induced effective beam-splitter interaction between the field modes. The resulting Hamiltonian is diagonalized through a simple geometric rotation in the two-mode bosonic space, providing a transparent interpretation of the underlying dynamics. The exposition emphasized clarity and physical insight, making effective Hamiltonian methods accessible for teaching and learning in multimode light-matter interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17208 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A pedagogical derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model Urzúa, Alejandro R. Quantum Physics Physics Education This work presents a pedagogical and self-contained derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model in the dispersive regime. A perturbative unitary transformation removes nonresonant atom-field terms, revealing dispersive frequency shifts leading to an atom-induced effective beam-splitter interaction between the field modes. The resulting Hamiltonian is diagonalized through a simple geometric rotation in the two-mode bosonic space, providing a transparent interpretation of the underlying dynamics. The exposition emphasized clarity and physical insight, making effective Hamiltonian methods accessible for teaching and learning in multimode light-matter interactions. |
| title | A pedagogical derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model |
| topic | Quantum Physics Physics Education |
| url | https://arxiv.org/abs/2601.17208 |