Shannon’s idea which is related to classical information theory and following the path of [@pb], we may define the (Shannon) entropies associated with the number and phase probability distribution by the following relations: $$\begin{aligned}
\label{shannonent}
  \hspace{-1cm}R_{n}(t) &=& - \sum_{n_{1}=0}^{+\infty} \sum_{n_{2}=0}^{+\infty}  \mathcal{P}_{n}(n_{1},n_{2}) \ln \mathcal{P}_{n}(n_{1},n_{2}), \nonumber \\
  \hspace{-1cm}R_{\theta}(t) &=& - \int \limits_{\theta_{0}}^{\theta_{0}+2\pi} d\theta_{1} \int \limits_{\theta_{0}}^{\theta_{0}+2\pi} d\theta_{2} \; \mathcal{P}_{\theta}(\theta_{1},\theta_{2}) \ln \mathcal{P}_{\theta}(\theta_{1},\theta_{2}),
  \end{aligned}$$ where $\mathcal{P}_{n}(n_{1},n_{2})=\langle n_{1},n_{2}|\hat{\rho}_{F}|n_{1},n_{2} \rangle$ and $\hat{\rho}_{F}=\mathrm{Tr}_{\mathrm{Atom}} \left( |\psi(t) \rangle \langle \psi(t)| \right)$. The sum of the entropic uncertainty relations for the number and phase in (\[shannonent\]) can specify the lower bound for entropy which is given by $R_{n}+R_{\theta} \geq \ln 2\pi$. Considering this inequality, we suggest two quantities as follows: $$\begin{aligned}
\label{entsq}
 S_{n}(t)&=&\frac{1}{\sqrt{2\pi}} \exp(R_{n}(t))-1, \nonumber \\
 S_{\theta}(t)&=&\frac{1}{\sqrt{2\pi}} \exp(R_{\theta}(t))-1.
 \end{aligned}$$ These quantities indicate that when $-1<S_{n}(t)<0$ ($-1<S_{\theta}(t)<0$), the number (phase) component of the field entropy is squeezed. It is worthwhile to declare that the negativity of $S_{n(\theta)}(t)$ and in other words, entropy squeezing is another expression of the fact that $R_{n(\theta)}(t)$ is below its minimum value.\
Figure \[quant.ph-sq\] shows the time evolution of the entropy squeezing in phase against the scaled time $\tau$ for initial mean number of photons fixed at $|\alpha_{1}|^{2} = 10=|\alpha_{2}|^{2}$. The upside plots concern with the absence of 