In this manuscript, we study a new non-linear system which represents a
?-type five level atom interacting with a quantized four-mode
electromagnetic field. A non-linear Stark shift is introduced, through the
elimination of intermediate levels (two and four) using the adiabatic
elimination technique. By using the Schrodinger equation we obtain the
analytic solution this model. Some statistical aspects through the effective
Hamiltonian are presented such as the collapses-revivals phenomenon, degree
of purity, concurrence, and the squeezing phenomenon with respect to study
the effect of Stark shift parameters on these statistical aspects. For small
values of the Stark shift parameter, the collapse times increase and the
atomic inversion symmetry axis shifts upward, while the entanglement
decreases significantly. It has been noted that the system is affected by
the Stark shift parameter.