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.