Amplification of the parametric dynamical Casimir effect via optimal control

We introduce different strategies to enhance photon generation in a cavity within the Rabi model in the ultrastrong coupling regime. We show that a bang-bang strategy allows one to enhance the effect up to 1 order of magnitude with respect to simply driving the system in resonance for a fixed time. Moreover, up to about another order of magnitude can be gained by exploiting quantum optimal control strategies. Finally, we show that such optimized protocols are robust with respect to systematic errors and noise, paving the way to future experimental implementations of such strategies.