(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

Journal Article · Thu Mar 15 04:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2710651· OSTI ID:20929664

Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M Norbert ^[1]

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1. International Chair in Mathematical Physics and Applications (ICMPA-UNESCO), 072 B.P. 50 Cotonou (Benin)

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.

• OSTI ID: 20929664
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 48; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNIHILATION OPERATORS
APPROXIMATIONS
DEFORMATION
EIGENSTATES
EXACT SOLUTIONS
HAMILTONIANS
HARMONIC OSCILLATORS
QUANTUM MECHANICS
SPIN
SUPERSYMMETRY
VECTORS