Polynomial algebras and exact solutions of general quantum non-linear optical models II: Multi-mode boson systems

Details Polynomial algebras and exact solutions of general quantum non-linear optical models II: Multi-mode boson systems Polynomial algebras and exact solutions of general quantum non-linear optical models II: Multi-mode boson systems

2010-04-08

arxiv.org/abs/1004.1235v2

J. Phys. A: Math. Theor. 43 (2010) 375211 (12pp)

Physics

Mathematical Physics

LaTex 14 pages, no figure; Version 2, to appear in J. Phys. A: Math. Theor

Scientific paper

10.1088/1751-8113/43/37/375211

We present higher order polynomial algebras which are the dynamical symmetry algebras of a wide class of multi-mode boson systems in non-linear optics. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to the multi-mode boson systems, including the BEC models as special cases.

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