  In a prevous paper (Phys. Rev. Lett. 96, 150403 (2006)) we have proposed a
new way to generate an observable geometric phase on a quantum system by means
of a completely incoherent phenomenon. The basic idea was to force the ground
state of the system to evolve ciclically by "adiabatically" manipulating the
environment with which it interacts. The specific scheme we have previously
analyzed, consisting of a multilevel atom interacting with a broad-band
squeezed vacuum bosonic bath whose squeezing parameters are smoothly changed in
time along a closed loop, is here solved in a more direct way. This new
solution emphasizes how the geometric phase on the ground state of the system
is indeed due to a purely incoherent dynamics
