Abstract
The present research paper considers a three-level atom (3LA) that interacts with a field mode primarily in a photon-added coherent state of Morse potential (PACSMP). The dynamics of entanglement, the photon statistics, and the quantum Fisher information are investigated. The statistics of field photons are discussed by evaluating the Mandel parameter. We check the influence of the energy dissipation and intensity-dependent function. Finally, we detect the relationship between the entanglement, the field's nonclassical characteristics, and atomic quantum Fisher information throughout the evolution of time. The findings illustrate the important role of the number of added photons and CSMP in affecting the entanglement's time evolution, the quantum Fisher information, and the Mandel parameter. Based on the obtained results, we reached significant physical phenomena, including the sudden birth and death of the nonlocal correlation between atom-Morse potential field structures.