  We propose a new way to generate an observable geometric phase by means of a
completely incoherent phenomenon. We show how to imprint a geometric phase to a
system by "adiabatically" manipulating the environment with which it interacts.
As a specific scheme we analyse a multilevel atom interacting with a broad-band
squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed
in time along a closed loop, the ground state of the system acquires a
geometric phase. We propose also a scheme to measure such geometric phase by
means of a suitable polarization detection.
