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

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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. © 2014 AIP Publishing LLC.
Original languageAmerican English
JournalJournal of Mathematical Physics
DOIs
StatePublished - 23 Apr 2014

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