2014•Journal of Mathematical PhysicsOpen access

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

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

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.

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Key concepts: Degenerate energy levels, Coherent states, Eigenfunction, Parametric oscillator, Mathematics, Harmonic oscillator, Lie group, Parametric statistics