Resumen: We present a general qubit-boson interaction Hamiltonian that describes the Jaynes–Cummings model and its extensions as a single Hamiltonian class. Our model includes non-linear processes for both the free qubit and boson field as well as non-linear, multi-boson excitation exchange between them. It shows an underlying algebra with supersymmetric quantum mechanics features allowing an operator based diagonalization that simplifies the calculations of observables. As a practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases covering the standard Jaynes–Cummings model and some of its extensions including Stark shift, Kerr-like, intensity dependent coupling, multi-boson exchange and algebraic deformations. Idioma: Inglés DOI: 10.1038/s41598-021-95259-1 Año: 2021 Publicado en: Scientific reports (Nature Publishing Group) 11 (2021), 16467 [15 pp.] ISSN: 2045-2322 Factor impacto JCR: 4.997 (2021) Categ. JCR: MULTIDISCIPLINARY SCIENCES rank: 19 / 74 = 0.257 (2021) - Q2 - T1 Factor impacto SCIMAGO: 1.005 - Multidisciplinary (Q1)