Abstract
The quantum system of the field initially defined by the k-photon-added Morse potential coherent states (MPCSs) of the radiation field interacting with a four-level atom (FLA) was studied. The physical and non-classical properties of the field defined by the MPCS system were quantified using the Mandel parameter. The effect of time-dependent coupling (TDC) on the atomic speed was examined. Moreover, the dynamic properties of the non-local correlation between the FLA and MPCS radiation field were studied and compared with those of the geometric phase. We also investigated the influence of the initial interaction conditions and different system parameters on the evolution of the non-local correlation, Mandel parameter, and geometric phase. The relationships between the geometric phase, Mandel parameter, and non-local correlation with TDC were explored.