  We study the geometric phase acquired by an inertial atom whose trajectories
are parallel to a reflecting boundary due its coupling to vacuum fluctuations
of electromagnetic fields, by treating the atom as an open quantum system in a
bath of the fluctuating vacuum fields, and show that the phase is position
dependent as a result of the presence of the boundary which modifies the field
quantum fluctuations. Our result therefore suggests a possible way of detecting
vacuum fluctuations in experiments involving geometric phase.
