Geometric phase induced by a cyclically evolving squeezed vacuum reservoir

We propose a method 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. The prototypical example consider is a multilevel atom surrounded by 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