Quantum optics

In the paper [23] I studied a generalized 3-level Janes-Cummings model for atoms interacting with radiation in a resonator. In such kind of models the self-consistent field in the resonator is classical while the atom is quantum. It was shown that if the atom levels are equidistant and dipole transitions are possible between all levels then the exchange of energy between the 2-mode resonant field and atoms is chaotic. This model gives the first example of such quantum optical system where the chaos appears in the rotating wave approximation and can take place for arbitrary small coupling constant $\Lambda = (16\pi\rho d^2/\hbar \omega)^{1/2}<<1$ between atoms and the the resonator field. Such unusual situation appears due to degeneracy of unperturbed system and unapplicability of the Kolmogorov-Arnold-Moser theorem in this case. The investigation of such kind of models but with quantized field showed that in the chaotic regime the statistics of levels is described by Wigner-Dyson distribution [35].