  Geometric phases are well known in classical electromagnetism and quantum
mechanics since the early works of Pantcharatnam and Berry. Their origin relies
on the geometric nature of state spaces and has been studied in many different
systems such as spins, polarized light and atomic physics. Recent works have
explored their application in interferometry and quantum computation. Earlier
works suggest how to observe these phases in single quantum systems
adiabatically driven by external classical devices or sources, where, by
classical, we mean any system whose state does not change considerably during
the interaction time: an intense magnetic field interacting with a spin 1/2, or
a birefringent medium interacting with polarized light. Here we propose a
feasible experiment to investigate quantum effects in these phases, arising
when this classical source drives not a single quantum system, but two
interacting ones. In particular, we show how to observe a signature of field
quantization through a vacuum effect in Berry's phase. To do so, we describe
the interaction of an atom and a quantized cavity mode altogether driven by an
external quasi-classical field.
