Two-photon algebra deformations
Abstract
In order to obtain a classification of all possible quantum deformations of the two-photon algebra $h_6$, we introduce its corresponding general Lie bialgebra, which is a coboundary one. Two non-standard quantum deformations of $h_6$, 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- July 1999
- DOI:
- 10.48550/arXiv.math/9907170
- arXiv:
- arXiv:math/9907170
- Bibcode:
- 1999math......7170P
- Keywords:
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- Mathematics - Quantum Algebra
- E-Print:
- 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)