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arXiv:2508.19422 · Brazilian Journal of Physics

Revisiting the Jaynes–Cummings Model with Time-dependent Coupling

Thiago Takaji Tsutsui, Danilo Cius, A. Vidiella-Barranco, Antonio S. M. de Castro, Fabiano M. Andrade

Published Nov 19, 2025• 5 citations
arXivHTMLPDF
DOI
10.1007/s13538-025-01949-w

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Abstract In the Jaynes‐Cummings (JC) model, the time dependence in the coupling parameter allows changes in the forms of the Rabi oscillations. In the inverse problem approach (IPA), the time‐dependent coupling parameter is obtained from the resulting population inversion. In this work, the IPA is employed to obtain a time‐dependent coupling that reproduces the effects of ‐deformation in the population inversion of an undeformed JC. This is relevant because it may pave the way for simulating quantum deformation in the JC model and possibly enables an experimental verification in a setting where the coupling can be precisely controlled.
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.
We present a generalized Jaynes-Cummings model (JCM) with an intensity-dependent coupling interacting with a quantum group-theoretic coherent state. The field operators of the JCM Hamiltonian are identified as the elements of the suq{\mathrm{su}}_{\mathit{q}}suq​(1,1) quantum algebra in their Holstein-Primakoff realizations. We lay emphasis on the time evolution of field quadruatures and atomic population inversion of the generalized JCM. The revivals of radiation squeezing are obtained for any values of initial squeezing.