Dynamical algebraic connection between the Stark and Kerr effects
J. L. Gruver, J. Aliaga · Physical Review A · 1997
We show that the Stark and Kerr Hamiltonians are deeply connected in the framework of dynamical algebras. We found that the algebras for both Hamiltonians are the same when physically relevant magnitudes, such as the population inversion and the $n$th order coherence function are considered as elements of a Lie algebra under commutation with the Hamiltonians. By analyzing the equations of motion we were able to find a set of conditions for the characteristic magnitudes of both Hamiltonians that leads to the same dynamical behavior for all the elements of the group. Finally, we conclude that the results of this paper can be generalized to any extension of the Jaynes-Cummings model, where any of the different elements of the group are present.