Observable geometric phase induced by a cyclically evolving dissipative process

In [1], a new way to generate an observable geometric phase on a quantum system by means of a completely incoherent phenomenon has been proposed. The basic idea is to force the ground state of the system to evolve cyclically by 'adiabatically' manipulating the environment with which it interacts. The specific scheme analyzed in [1], consisting of a multilevel atom interacting with a broadband 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 at the ground state of the system is indeed due to a purely incoherent dynamics.