This paper reviews the theoretical investigation of a three-level atom in the V configuration enclosed in a single-mode cavity with multiphoton transition under several applied conditions in the time dependent regime. The transition between the first and second atomic levels occurs through the number of q photons. A closed set of equations describes the temporal behavior of the atom-cavity system. The numerical solution of these equations is implemented by the fourth-order Runge-Kutta method. In a weak driving limit along with multiple other circumstances, the three-level atom illustrates a similar manner to an effective two-level one for each separate transition. The results of the three-level atomic simulations confirm the utilized constrains in the two-level atomic model according to the plotted curves in an appropriate way.
