Abstract
We present a model of interaction between a four-level atom and the cavity field initially prepared in the coherent state in the presence of the phase damping effect. We discuss the atom-field entanglement and statistical properties under the damping effect in view of numerical calculations. We use the Mandel parameter as a quantifier of the statistical properties of the field; moreover, we study the different effects of the collective parameters in the master equation on the dynamical behavior of the field statistical properties and the entanglement measured by the negativity. Finally, we explore the link between the entanglement and statistical properties in view of the numerical results during the time evolution.