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arXiv · 1311.6867

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

D. Ojeda-Guillen·R. D. Mota·V. D. Granados
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Abstract

We construct the Perelomov number coherent states for any three $su(1,1)$ Lie algebra generators 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. We show that the most general $SU(1,1)$ coherence-preserving Hamiltonian has the Perelomov number coherent states as eigenfunctions, and we obtain their time evolution. We apply our results to obtain the non-degenerate parametric amplifier eigenfunctions, which are shown to be the Perelomov number coherent states of the two-dimensional harmonic oscillator.

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D. Ojeda-Guillen, R. D. Mota, V. D. Granados. 2013-11-27. The SU(1,1) Perelomov number coherent states and the non-degenerate parametric amplifier. https://doi.org/10.1063/1.4871445

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