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Two-photon algebra deformations

Preeti Parashar·Angel Ballesteros·Francisco J. Herranz
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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.

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Preeti Parashar, Angel Ballesteros, Francisco J. Herranz. 1999-07-26. Two-photon algebra deformations. https://arxiv.org/abs/math/9907170

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