A transition in the spectral statistics of quantum optical model by different electromagnetic fields

In this paper, we have considered the effects of different quantized electromagnetic fields on the spectral statistics of two-level atoms. The Berry-Robnik distribution and the maximum likelihood estimation technique are used to analyze the effect of the mean photon numbers, the two level atoms numbers and also the quantum number of considered states on the fluctuation properties of different systems which are described by different sets of the Dicke Hamiltonian’s parameters. Our results describe the obvious effect of mean photon number on the spectral statistics and show more regular dynamics when this quantity reaches 700. Also, we observed universality in the spectral statistics of considered systems when the number of two level atoms approaches an unrealistic limit (NA ~ 200) and there are some suggestions about the effect of the quantum number of selected levels and the atom-field coupling constant on level statistics