the intensity-dependent coupling, i.e. $f_{i} (n_{i}) = 1$ and the downside plots correspond to the intensity-dependent coupling regime by using the nonlinearity function $f_{i} (n_{i})=1/\sqrt{n_{i}}$. In figure \[quant.ph-sq\](a) Kerr effect is absent ($\chi = 0$) and the exact resonant case is assumed ($\Delta_{2} = \Delta_{3} =0$). Figure \[quant.ph-sq\](b) shows the effect of deformed Kerr medium ($\chi = 0.4 \lambda$), by considering the nonlinearity function $ g_{i}(n_{i})  = 1/\sqrt{n_{i}}$, in the absence of the detuning parameters. The influence of deformed Kerr medium in the presence of detuning parameters has been depicted in figures \[quant.ph-sq\](c). From the upside plot of figure \[quant.ph-sq\](a) which corresponds to the constant coupling regime, no Kerr medium and in the resonance condition, it is observed that the state of the system possesses the entropy squeezing until it becomes positive after nearly $\tau=35$. By entering the effect of intensity-dependent coupling (downside plot of figure \[quant.ph-sq\](a)), remarkable constant amount of entropy squeezing ($\simeq -0.81954$) is appeared at all times. Considering both upside plots of figures \[quant.ph-sq\](a) and \[quant.ph-sq\](b) shows that, they are nearly the same, both qualitatively and quantitatively. Looking at the downside plot of figure \[quant.ph-sq\](b) indicates that, deformed Kerr medium can strengthen the entropy squeezing. In this 