function which has been usually used in the contents of deformation of bosonic operators in quantum optics literature [@example-harmonious1; @example-harmonious2; @example-harmonious3].

Investigating the physical properties of the introduced state {#phyproperties}
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As we pointed out in the Introduction of the paper, in this section, we intend to examine the further physical properties with emphasising on some nonclassical features of the obtained state (in previous section) which are of special interest in the field of quantum optics and quantum information processing. To achieve this purpose, we check number-phase entropic squeezing, sub-Poissonian statistics, CSI and two different squeezing criteria, in detail. We will observe, the state has potential ability to show high nonclassicality behaviour in appropriate intervals of time. In this way, it may be noted that the unfinished work in [@usJOSA], in our opinion, will be truly completed.

Number-phase entropic uncertainty relation and entropy squeezing {#phase}
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It is well-known that the investigation of the dynamical behavior of phase distribution of the field photons is in fact an analysis of the variation of the phase relation between field photons and atoms [@nakano]. Phase distribution and squeezing in number/phase operator of various physical systems with known discrete spectrum $e_{n}$ have been reported 