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CRC Press eBooks

The Jaynes-Cummings model and raising and lowering operators

Véronique Hussin, L M Nieto

Published Nov 30, 2003• 0 citations
Publisher

Abstract

Ladder operators acting on the energy eigenstates of the Jaynes-Cummings model in the rotating wave approximation are constructed using the fact that they satisfy some reasonable additionnal properties. In fact, we show that it is possible to write the Jaynes-Cummings Hamiltonian as a product of such ladder operators. It may be relevant for the study of new sets of coherent states for this model.

DOI
10.1201/9781482269079-107

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Ladder operators acting on the energy eigenstates of the Jaynes-Cummings model in the rotating wave approximation are constructed using the fact that they satisfy some reasonable additionnal properties. In fact, we show that it is possible to write the Jaynes-Cummings Hamiltonian as a product of such ladder operators. It may be relevant for the study of new sets of coherent states for this model.
Classes of (p,q)-deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q)-arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translates into (p,q)-deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.
Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translates into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.
General sets of coherent states and the JaynesndashndashndashCummings model
In this paper we define, in the context of dynamical algebras, a set of operators that are suitable for studying any relevant quantity related to the two-level Jaynes–Cummings model (JCM). We study the usual JCM with and without the rotating wave approximation (RWA), and then we add the presence of an external field. In this last case we find that in the strong driving regime there are significant differences between the results obtained with the RWA and without it. This holds even for the case in which the usual requirements for applying the RWA without an external driving are fulfilled.