Off-resonant pumping for the transition from a continuous to a discrete spectrum and quantum revivals in systems in coherent states

We show that in parametrically driven systems and, more generally, in syste ms in coherent states, off-resonant pumping can cause a transition from a c ontinuum energy spectrum of the system to a discrete one, and result in qua ntum revivals of the initial state. The mechanism responsible for quantum r evivals in the present case is different from that in the nonlinear wavepac ket dynamics of systems such as Rydberg atoms. We interpret the reported ph enomenon as an optical analogue of Bloch oscillations realized in Fock spac e and propose a feasible scheme for inducing Bloch oscillations in trapped ions.