A pedagogical derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model

• URL: http://arxiv.org/abs/2601.17208v1
• Date: Fri, 23 Jan 2026 22:35:15 GMT
• Title: A pedagogical derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model
• Authors: Alejandro R. Urzúa,
• Abstract summary: This work presents a derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model in the dispersive regime.<n>A perturbative unitary transformation removes nonresonant atom-field terms, revealing dispersive frequency shifts.<n>The resulting Hamiltonian is diagonalized through a simple geometric rotation in the two-mode bosonic space.
• Score: 51.56484100374058
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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