Two-photon algebra deformations
Abstract
In order to obtain a classification of all possible quantum deformations of the two-photon algebra , we introduce its corresponding general Lie bialgebra, which is a coboundary one. Two non-standard quantum deformations of , together with their associated quantum universal R-matrix, are presented; each of them contains either a quantum harmonic oscillator subalgebra or a quantum gl(2) subalgebra. One-boson representations for these quantum two-photon algebras are derived and translated into Fock--Bargmann realizations. In this way, a systematic study of `deformed' states of light in quantum optics can be developed.
Cite
@article{arxiv.math/9907170,
title = {Two-photon algebra deformations},
author = {Preeti Parashar and Angel Ballesteros and Francisco J. Herranz},
journal= {arXiv preprint arXiv:math/9907170},
year = {2007}
}
Comments
12 pages, LaTeX. Contribution to Symmetries in Quantum Mechanics and Quantum Optics. Edited by A. Ballesteros et al. Universidad de Burgos, pp. 235--246, (1999)