  We study, in the framework of open quantum systems, the geometric phase
acquired by a uniformly accelerated two-level atom undergoing nonunitary
evolution due to its coupling to a bath of fluctuating vacuum electromagnetic
fields in the multipolar scheme. We find that the phase variation due to the
acceleration can be in principle observed via atomic interferometry between the
accelerated atom and the inertial one, thus providing an evidence of the Unruh
effect.
