by one of us in [@honar]. Also, the number-phase entropic uncertainty relation and the number-phase Wigner function of generalized coherent states associated with a few solvable quantum systems that have non-degenerate spectra are examined [@honarasaphase]. Here, we intend to investigate the [*entropy squeezing*]{} for considered bipartite system in terms of entropies of [*number*]{} and [*phase*]{} operators, in which the phase properties of a photon field are evaluated by using the Pegg-Barnett approach [@pb]. According to this method, all observables corresponding to the phase properties are defined in an $(s+1)$-dimensional space, in which they constitute the eigenvalue equations with $(s+1)$ eigenstates (orthonormal phase states). Based on the Pegg-Barnett formalism, a complete set of $(s +1)$ orthonormal phase states (of a single-mode field) is defined by $$\begin{aligned}
\label{pb1mode}
  |\theta_{p} \rangle = \frac{1}{\sqrt{s+1}}\sum_{n=0}^{s}\exp(in\theta_{p})| n \rangle,
  \end{aligned}$$ where $\{| n \rangle\}_{n=0}^{s}$ are the number states and $\theta_{p}$ gets the following values: $$\begin{aligned}
\label{thetap}
  \theta_{p}=\theta_{0}+\frac{2\pi p}{s+1},\;\;\;\;p=0,1,...,s,
  \end{aligned}$$ with $\theta_{0}$ as an arbitrary value. It is useful to state that in calculating the required expectation values, the parameter $s$ tends finally to infinity. Moreover, since we are dealing with the two-mode field in the present atom-field interaction, it is necessary to generalize the orthonormal phase states. 