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arXiv:math-ph/0207031 · Journal of Mathematical Physics

Some integrable systems in nonlinear quantum optics

Maciej Horowski, Anatol Odzijewicz, Agnieszka Tereszkiewicz

Published Jan 17, 2003• 25 citations
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Abstract

In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states related to these systems is constructed and described. Some applications are also presented.
DOI
10.1063/1.1530756

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We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general procedure to map these deformed algebras to appropriate Lie algebras. This is used, for the non compact cases, to obtain the annihilation operator coherent states, by finding the canonical conjugates of these operators. Generalized coherent states, in the Perelomov sense also follow from this construction. This allows us to explicitly construct coherent states associated with various quantum optical systems.