be regarded as a consequence of the presence of the detuning parameters (in the intensity-dependent coupling regime).

Sub-Poissonian statistics {#mandelparameter}
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In order to determine photon statistics of the field we use the Mandel’s $Q$ parameter which is defined by [@mandel]: $$\begin{aligned}
\label{mandel1}
 Q = \frac{\langle (\Delta \hat{n})^2\rangle - \langle \hat{n} \rangle}{\langle \hat{n} \rangle},
 \end{aligned}$$ where $\langle (\Delta \hat{n})^2\rangle=\langle \hat{n}^{2} \rangle-\langle \hat{n} \rangle^{2}$ and $\hat{n}=\hat{a}^{\dag}\hat{a}$. This parameter states that whenever $-1\leq Q <0 \;(Q>0)$ the statistics is sub-Poissonian (super-Poissonian) and $Q=0$ indicates the Poissonian statistics. By the way, the state vector of the system shows the nonclassical behavior when the photons statistics of field is sub-Poissonian.\
Our presented results in figure \[mandel\] show the time evolution of Mandel parameter versus the scaled time $\tau$, in which photon statistics of the cavity field (mode $1$) has been studied. In plotting this figure, the upside (downside) plots again correspond to the case $f_{i} (n_{i}) = 1$ ($f _{i}(n_{i}) = 1/\sqrt{n_{i}}$), also all parameters have been chosen like figure \[quant.ph-sq\]. Figure \[mandel\](a) is depicted for the case in which intensity-dependent coupling, deformed Kerr and detuning effects are all neglected, i.e., $(f_i(n_i)=1, \chi = 0 = \Delta_{2} = \Delta_{3})$. It is observed from the 