of the system does not have sum squeezing property. However, after entering the intensity-dependent coupling, sum squeezing will be appeared in all times (the downside one). Figure \[sumsq\](b) indicates the effect of the deformed Kerr medium, from which it is found that the squeezing does not occur when the atom-field coupling is constant. On the contrary, in the intensity-dependent coupling regime, sum squeezing with oscillatory behavior is clearly observed at all times. Looking quantitatively at figures \[sumsq\](a) and \[sumsq\](b) implies the fact that, deformed Kerr medium has no remarkable effect in the negativity of sum squeezing. The effects of deformed Kerr medium and detuning parameters are simultaneously studied in figure \[sumsq\](c). As is seen, positive values of sum squeezing indicate the classical behaviour and so the state of quantum system does not possess this nonclassicality indicator. Comparing the downside plots of figures \[sumsq\](b) and \[sumsq\](c) shows that sum squeezing disappears when the detuning is considered.\
At last, one can conclude that while intensity-dependent coupling plays the important role to reach this nonclassical behaviour (negativity of sum squeezing parameter), the existence of the detuning destroys the sum squeezing of the state of the system even in the presence of intensity coupling. 