  We analyse the geometric phase due to the Stark shift in a system composed of
a bosonic field, driven by time-dependent linear amplification, interacting
dispersively with a two-level (fermionic) system. We show that a geometric
phase factor in the joint state of the system, which depends on the fermionic
state (resulting form the Stark shift), is introduced by the amplification
process. A clear geometrical interpretation of this phenomenon is provided. We
also show how to measure this effect in an interferometric experiment and to
generate geometric "Schrodinger cat"-like states. Finally, considering the
currently available technology, we discuss a feasible scheme to control and
measure such geometric phases in the context of cavity quantum electrodynamics.
