Two-mode generalization of the Jaynes–Cummings and Anti-Jaynes–Cummings models

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Abstract

© 2017 Elsevier Inc. We introduce two generalizations of the Jaynes–Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes–Cummings interactions, while the second model is written as a simultaneous Jaynes–Cummings and Anti-Jaynes–Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novel problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.
Original languageAmerican English
Pages (from-to)121-134
Number of pages107
JournalAnnals of Physics
DOIs
StatePublished - 1 Dec 2017

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parametric amplifiers
harmonic oscillators
eigenvectors
energy spectra
oscillators
interactions
oscillations

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abstract = "{\circledC} 2017 Elsevier Inc. We introduce two generalizations of the Jaynes–Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes–Cummings interactions, while the second model is written as a simultaneous Jaynes–Cummings and Anti-Jaynes–Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novel problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.",
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Two-mode generalization of the Jaynes–Cummings and Anti-Jaynes–Cummings models. / Choreño, E.; Ojeda-Guillén, D.; Salazar-Ramírez, M.; Granados, V. D.

In: Annals of Physics, 01.12.2017, p. 121-134.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Two-mode generalization of the Jaynes–Cummings and Anti-Jaynes–Cummings models

AU - Choreño, E.

AU - Ojeda-Guillén, D.

AU - Salazar-Ramírez, M.

AU - Granados, V. D.

PY - 2017/12/1

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N2 - © 2017 Elsevier Inc. We introduce two generalizations of the Jaynes–Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes–Cummings interactions, while the second model is written as a simultaneous Jaynes–Cummings and Anti-Jaynes–Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novel problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.

AB - © 2017 Elsevier Inc. We introduce two generalizations of the Jaynes–Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes–Cummings interactions, while the second model is written as a simultaneous Jaynes–Cummings and Anti-Jaynes–Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novel problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.

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