CSI may be generally led to the violation of Bell inequalities [@walls]. Also, it is shown that, the violation of CSI can be observed in a two-photon interference experiment with a light source in a pair coherent state [@ghosh]. Moreover, concerning the importance of the squeezing phenomenon, it is worthwhile to illustrate that two-mode squeezed state can be regarded as the output state of an ideal two-photon device [@caves]. In addition, it is reported that, in particular there exists a close link between sum squeezing phenomenon and sum-frequency generation (combination of two photons with different frequencies $\omega_{a}$ and $\omega_{b}$, and generation of a photon with frequency $\omega_{c}=\omega_{a}+\omega_{b}$, by the presence of a nonlinear medium and through the second-order susceptibility $\chi^{(2)}$ [@boyd]) that has been explored by Hillery [@hillery]. All above explanations which attracted a great deal of attention in recent researches motivate one to explore the considered nonclassicality features for the complicated atom-field interaction system which has been analytically solved by us [@usJOSA].\
The paper is organized as follows. In the next section, a brief review of obtaining the state vector of the atom-field system will be given, which has been extensively explained in [@usJOSA]. In section \[phyproperties\], after investigating 