  We study the adiabatic evolution of a two-level model in the presence of an
external classical electric field. The coupling between the quantum model and
the classical field is taken in the electric dipole approximation. In this
regime, we show the absence of geometric phases in the interacting two-level
model in the presence of any periodic real time-dependent classical electric
field. We obtain a conservative scalar potential in the calculation of Berry's
phases of the instantaneous eigenstates of the model. For complex electric
fields, we recover the existence of geometric phases. In particular, the
geometric phases of the instantaneous eigenstates of the model in the presence
of a positive or of a negative frequency component of the monochromatic
electric field differ by an overall sign. As a check on our results, we map
this interacting two-level model onto a spin-1/2 model under the action of a
classical magnetic field. We confirm that the first one acquires Berry's phase
only in the rotating wave approximation [RWA].
