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.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.

Journal of Physics A Mathematical and TheoreticalOct 20, 200817 citations

A GENERALIZED JAYNES-CUMMINGS MODEL WITH INTENSITY-DEPENDENT COUPLING

Peng Zhou, jinjia peng

Chinese Science BulletinJan 1, 19910 citations

Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models

Colin V. Coane, Francesco Iachello

We demonstrate how supersymmetries of Hamiltonians for coupled Bose-Fermi systems can be used to place the Hamiltonians of the Jaynes-Cummings model and Dicke model under the rotating wave approximation in matrix form and provide explicit analytic solutions for their eigenvalues. We then use this supersymmetry to place the Liouvillians of the associated Markovian open systems in matrix form and provide explicit solutions for their eigenvalues. These results are a consequence of the fact that the Hamiltonian of the Jaynes-Cummings model commutes with the linear Casimir invariant of the superalgebra $u(1|1)$ and that the Hamiltonian of the Dicke model commutes both with the linear invariant of $\sum_{i} u_{i}(1|1)$ and with the invariant of an additional $su(2)$ algebra. Our methods apply to various coupled Bose-Fermi systems with $u(1|1)$ and more generally with $u(n|m)$ dynamical superalgebras, and may provide efficient tools for studying more complicated examples.We demonstrate how supersymmetries of Hamiltonians for coupled Bose-Fermi systems can be used to place the Hamiltonians of the Jaynes-Cummings model and Dicke model under the rotating wave approximation in matrix form and provide explicit analytic solutions for their eigenvalues. We then use this supersymmetry to place the Liouvillians of the associated Markovian open systems in matrix form and provide explicit solutions for their eigenvalues. These results are a consequence of the fact that the Hamiltonian of the Jaynes-Cummings model commutes with the linear Casimir invariant of the superalgebra $u(1|1)$ and that the Hamiltonian of the Dicke model commutes both with the linear invariant of $\sum_{i} u_{i}(1|1)$ and with the invariant of an additional $su(2)$ algebra. Our methods apply to various coupled Bose-Fermi systems with $u(1|1)$ and more generally with $u(n|m)$ dynamical superalgebras, and may provide efficient tools for studying more complicated examples.

quant-pharXiv:2606.12682Journal of Physics A Mathematical and TheoreticalJun 12, 20260 citations

u(1|1)

and that the Hamiltonian of the Dicke model commutes both with the linear invariant of

\sum_{i} u_{i}(1|1)

and with the invariant of an additional

su(2)

algebra. Our methods apply to various coupled Bose-Fermi systems with

u(1|1)

and more generally with

u(n|m)

dynamical superalgebras, and may provide efficient tools for studying more complicated examples.