Abstract
Recently, the Mth coherent state (Mth CS) has been defined to be the resultant state of applying the number operator M times on the coherent state (CS) (Othman, Int. J. Theor. Phys. 58: 2451, 2019). In this article, we study the interaction between a two-level atom and a quantized single-mode field with intensity-dependent coupling in a Kerr medium. The Mth CS is assumed to be the interacting field with the atom. We study the dynamical behavior of the inversion, Q Mandel, linear squeezing, amplitude squared squeezing, and field entropy for different parameters and M values. We find that a certain pattern in the dynamics is induced with the Mth CS that is not present with the CS. We term this pattern as the "resolution phenomenon". It is related to a semi-regular pattern being apparent in a specific region while after or before this region the pattern is overlapping. We also discover, in general, that the Mth CS of large M values for a given dynamic tends to have more periodicity, wider peaks, less growing/decaying rates, and more covering its range. Many other classical/nonclassical features are discussed for the concerning measurements. Finally, in the end, we propose some potential applications.