This book is on the study of the non-resonant interaction between a three-level type atom and a single mode cavity field. An effective model, where one of the three levels has been eliminated is introduced when the center-of-mass and the classical homogenous gravitational field are taken into account. Also, the homotopy analysis method is used on solving the explicit three-level model. Moreover, the idea of using the explicit time-dependence on the atom-field couplings, but for an extended model is presented. The nonlinearity effects and the intensity-dependent coupling are also explored. Numerical investigations are used to test the collapses-revivals, the anti-bunching of photons, the disentanglement of the atom from the field and the squeezing phenomena.