singular (nonclassical states).\
In figure \[csi\] the time evolution of the CSI against the scaled time $\tau$ is illustrated for different chosen parameters similar to figure \[quant.ph-sq\], where the upside (downside) plots refer to the constant (intensity-dependent) coupling regime. The upside plot of figure \[csi\](a) shows that the quantum system is not sensitive to this nonclassical criterion when the atom-field coupling is constant, while in the presence of intensity-dependent coupling (downside plot), CSI always gets negative value with oscillatory behaviour. In figure \[csi\](b) where the effect of deformed Kerr medium is examined it is seen that, the deformed Kerr medium has no remarkable effect on the negativity of CSI, either in the presence or absence of the intensity-dependent coupling. In figure \[csi\](c) the effect of deformed Kerr medium together with the detuning parameters is shown. From the upside plot of this figure it is observed that, CSI varies between positive (classical behaviour) and negative (nonclassical behaviour) values. Also, from downside one, this quantity takes negative values in all time domain with fast oscillatory behaviour. Comparing the upside plots of figures \[csi\](b) and \[csi\](c) indicates that due to the presence of detuning, nonclassicality behaviour is revealed.\
By considering the presented results 