Generalizedn-level Jaynes–Cummings and Dicke models, classical rationalr-matrices and algebraic Bethe ansatz
T. Skrypnyk · Journal of Physics A Mathematical and Theoretical · 2008
We construct integrable n -level generalizations of Jaynes–Cummings and Dicke models corresponding to the simple (reductive) Lie algebras of rank n . We show that for each such Lie algebra there exist many integrable Jaynes–Cummings and Dicke-type models each of which is associated with the reductive subalgebras containing Cartan subalgebra and is obtained via reduction from Jaynes–Cummings or Dicke-type models with a maximal number of bosons. We diagonalize the constructed Jaynes–Cummings and Dicke-type Hamiltonians in the physically most interesting case of using a nested algebraic Bethe ansatz.