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 systems in coherent states, off-resonant pumping can cause a transition from a continuum energy spectrum of the system to a discrete one, and result in quantum revivals of the initial state. The mechanism responsible for quantum revivals in the present case is different from that in the nonlinear wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported phenomenon as an optical analogue of Bloch oscillations realized in Fock space and propose a feasible scheme for inducing Bloch oscillations in trapped ions