In this paper, we investigate the time evolution of the atomic operators of a two-Ievel atom interacting with the field via a two –photon Process within and without the rotating-wave approximation (RWA) by means of non-relativestic QED. We also verified that the virtual photon field is the cause for quantum chaos embodied by the periodic decay and revival effect of the atom using the numerical and analytic methods, and discussed the reason of neglecting the influence of the virtual photon field on the revival time.