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

D. Ojeda-Guillén; R. D. Mota; V. D. Granados

doi:10.1063/1.4871445

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

D. Ojeda-Guillén, R. D. Mota, V. D. Granados

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Abstract

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.

Original language	English
Article number	042109
Journal	Journal of Mathematical Physics
Volume	55
Issue number	4
DOIs	https://doi.org/10.1063/1.4871445
State	Published - 23 Apr 2014

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AB - 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.

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

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