Chaos in generalized Jaynes-Cummings model

The possibility of chaos formation is studied in terms of a generalized Jaynes-Cummings model which is a key model in the quantum electrodynamics of resonators. In particular, the dynamics of a three-level optical atom which is under the action of the resonator field is considered. The specific feature of the considered problem consists in that not all transitions between the atom levels are permitted. This asymmetry of the system accounts for the complexity of the problem and makes it different from the three-level systems studied previously. We consider the most general case, where the interaction of the system with the resonator depends on the system coordinate inside the resonator. It is shown that, contrary to the commonly accepted opinion, the absence of resonance detuning does not guarantee the system state controllability. In the course of evolution the system performs an irreversible transition from the purely quantum-mechanical state to the mixed state. It is shown that the asymmetry of the system levels accounts for the fact that the upper excited level turns out to be the most populated one.