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

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

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

Fingerprint

Coherent States
parametric amplifiers
eigenvectors
Eigenfunctions
harmonic oscillators
algebra
energy spectra
Tilting
Energy Spectrum
Harmonic Oscillator
operators
Lie Algebra
Arbitrary
Operator

Cite this

@article{a26d1f5f06ea441fa7257b49be5c3525,
title = "The SU(1, 1) perelomov number coherent states and the non-degenerate parametric amplifier",
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. {\circledC} 2014 AIP Publishing LLC.",
author = "D. Ojeda-Guill{\'e}n and Mota, {R. D.} and Granados, {V. D.}",
year = "2014",
month = "4",
day = "23",
doi = "10.1063/1.4871445",
language = "American English",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",

}

TY - JOUR

T1 - The SU(1, 1) perelomov number coherent states and the non-degenerate parametric amplifier

AU - Ojeda-Guillén, D.

AU - Mota, R. D.

AU - Granados, V. D.

PY - 2014/4/23

Y1 - 2014/4/23

N2 - 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.

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. © 2014 AIP Publishing LLC.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84902294366&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84902294366&origin=inward

U2 - 10.1063/1.4871445

DO - 10.1063/1.4871445

M3 - Article

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

ER -