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Quantization of Some Generalized Jaynes-Cummings Models in a Kerr-Like Medium

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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.

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Acknowledgments

The authors thank a referee for the relevant comments that helped improve the work.

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Authors and Affiliations

  1. Institut de Mathématiques et de Sciences Physiques, Université d’Abomey-Calavi — Unité de Recherche en Physique Théorique, Porto-Novo, République du Bénin

    A. J. Adanmitonde & G. Y. H. Avossevou

  2. Université Nationale des Sciences, Technologies Ingénieries et Mathématiques d’Abomey, Abomey, République du Bénin

    F. A. Dossa

  3. Faculté des Sciences et Techniques de Natitingou, Natitingou, République du Bénin

    F. A. Dossa

Authors
  1. A. J. Adanmitonde
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  2. G. Y. H. Avossevou
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  3. F. A. Dossa
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Correspondence to A. J. Adanmitonde, G. Y. H. Avossevou or F. A. Dossa.

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The authors declare no conflicts of interest.

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 3, pp. 451–466, June, 2020.

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Adanmitonde, A.J., Avossevou, G.Y.H. & Dossa, F.A. Quantization of Some Generalized Jaynes-Cummings Models in a Kerr-Like Medium. Theor Math Phys 203, 824–836 (2020). https://doi.org/10.1134/S0040577920060082

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  • DOI: https://doi.org/10.1134/S0040577920060082

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