English

Two-photon algebra deformations

Quantum Algebra 2007-05-23 v1

Abstract

In order to obtain a classification of all possible quantum deformations of the two-photon algebra h6h_6, we introduce its corresponding general Lie bialgebra, which is a coboundary one. Two non-standard quantum deformations of h6h_6, 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.

Keywords

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)