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This article is cited in 3 scientific papers (total in 3 papers)
Quantization of some generalized Jaynes–Cummings models in a Kerr-like medium
A. J. Adanmitondea, G. Y. H. Avossevoua, F. A. Dossabc a Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi, Porto-Novo, République du Bénin
b Université Nationale des Sciences, Technologies, Ingénieries et Mathématiques d'Abomey, Abomey, République du Bénin
c Faculté des Sciences et Techniques de Natitingou,
Natitingou, République du Bénin
Abstract:
Based on fundamental principles of quantum mechanics, we present a method for a rigorous analytic construction of the spectra of the one- and two-photon Jaynes–Cummings models in a Kerr medium. To obtain an idea of the method, we consider a first generalized Jaynes–Cummings model with a real, linear superpotential using techniques of supersymmetric quantum mechanics. The Hamiltonian of this model is written as a combination of operators generating the underlying superalgebra whose elements are defined as differential matrix operators. Based on the formalism of supersymmetric quantum mechanics and the properties of sets of common observables, we derive solutions of the one- and two-photon models expressed in terms of confluent hypergeometric functions. Finally, using numerical analysis, we study the influence of the Kerr effect on the energy spectra of the physical system.
Keywords:
quantum mechanics, Jaynes–Cummings Hamiltonian, commuting operator, constant of motion, confluent hypergeometric function.
Received: 18.10.2019 Revised: 09.01.2020
Citation:
A. J. Adanmitonde, G. Y. H. Avossevou, F. A. Dossa, “Quantization of some generalized Jaynes–Cummings models in a Kerr-like medium”, TMF, 203:3 (2020), 451–466; Theoret. and Math. Phys., 203:3 (2020), 824–836
Linking options:
https://www.mathnet.ru/eng/tmf9835https://doi.org/10.4213/tmf9835 https://www.mathnet.ru/eng/tmf/v203/i3/p451
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Abstract page: | 260 | Full-text PDF : | 66 | References: | 34 | First page: | 9 |
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