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

TL;DR

This paper develops polynomial algebras as symmetry structures for multi-mode boson systems in non-linear optics, enabling exact solutions including Bethe ansatz methods for models like BEC.

Contribution

It introduces higher order polynomial algebras as dynamical symmetries and constructs their representations to solve complex multi-mode boson systems exactly.

Findings

Derived polynomial algebras for multi-mode boson systems

Constructed unitary representations and differential operator realizations

Obtained exact solutions including Bethe ansatz for BEC models

Abstract

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.