An implementation of the polynomial Lie algebra methods for solving a class of nonlinear models in quantum optics

V. P. Karassiov; A. A. Gusev; S. I. Vinitsky

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An implementation of the polynomial Lie algebra methods for solving a class of nonlinear models in quantum optics

V. P. Karassiov·A. A. Gusev·S. I. Vinitsky

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Abstract

We develop some calculation schemes to determine dynamics of a wide class of integrable quantum-optical models using their symmetry adapted reformulation in terms of polynomial Lie algebras $su_{pd}(2)$. These schemes, based on "diagonal" representations of model evolution operators (via diagonalizing Hamiltonians with the help of the $su_{pd}(2)$ defining relations), are implemented in the form adapted for numerical calculations. Their efficiency is demonstrated on the example of the second-harmonic-generation model.

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V. P. Karassiov, A. A. Gusev, S. I. Vinitsky. 2001-05-31. An implementation of the polynomial Lie algebra methods for solving a class of nonlinear models in quantum optics. https://arxiv.org/abs/quant-ph/0105152

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