Switchable dynamics in the deep-strong-coupling regime

We investigate theoretically the dynamics of the system that consists of a cascade three-level emitter interacting with a single-mode resonator in the deep-strong-coupling regime. We show that the dynamical evolution of the system can only occur in a certain parity chain decided by the initial state, in which the photon population and the initial state probability present periodic collapses and revivals. In particular, we find that the evolution of the dynamics can be controlled by feeding the time-control pulses into the system. Control pluses with specific arrival times can suddenly switch off and on the time evolutions of the system populations and initial state probability when the system is originally in a symmetry superposition state. Physically, the switch-off of the evolution originates from the symmetry-breaking of the state, i.e, $(|g0\rangle+|f0\rangle)/\sqrt{2}\rightarrow(|g0\rangle-|f0\rangle)/\sqrt{2}$. This work offers an all-optical approach to manipulate the dynamics of the system, which might have potential application in modern quantum technology.