Resonance overlap in the semiclassical Jaynes-Cummings model

The authors investigate the transition to chaos in the semiclassical Jaynes-Cummings model without the rotating wave approximation employing the Chirikov criterion of overlapping resonances. As an integrable approximation they use a degenerate version of the model, in which the energy difference between two levels vanishes. The authors give a canonical formulation of the problem in terms of appropriate action-angle variables. Due to a simple structure of resonances the authors obtain a very good agreement between the critical values of parameters at the border of chaos derived from theoretical and numerical calculations.