The SU(1, 1) Perelomov number coherent states and the non-degenerate parametric amplifier

Journal Article · Tue Apr 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4871445· OSTI ID:22250769

Granados, V. D. ^[1]; Mota, R. D. ^[2]

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1. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738 México D. F. (Mexico)
2. Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430, México D. F. (Mexico)

We construct the Perelomov number coherent states for an arbitrary su(1, 1) group operation and study some of their properties. We introduce three operators which act on Perelomov number coherent states and close the su(1, 1) Lie algebra. By using the tilting transformation we apply our results to obtain the energy spectrum and eigenfunctions of the non-degenerate parametric amplifier. We show that these eigenfunctions are the Perelomov number coherent states of the two-dimensional harmonic oscillator.

• OSTI ID: 22250769
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNIHILATION OPERATORS
EIGENFUNCTIONS
EIGENSTATES
ENERGY SPECTRA
HARMONIC OSCILLATORS
PARAMETRIC AMPLIFIERS
SU GROUPS