Environment-assisted non-Markovian speedup dynamics control

For the damped Jaynes-Cummings model in the weak system-environment coupling regime, a scheme to manipulate the non-Markovian dynamics has been previously proposed in the controllable environment. We here mainly focus on the two-Lorentzian model and the band-gap model, which are composed by adding a new Lorentzian spectrum to the original single-Lorentzian spectrum. By manipulating the parameters of the new added Lorentzian spectrum, i.e., changing the weights of the two Lorentzians, and tuning the spectral width of the new second Lorentzian, the dynamical crossover from Markovian to non-Markovian is achieved in the weak system-environment coupling regime. In addition, according to the controllable non-Markovian dynamics behavior, the roles of the parameters of the environment on the speedup evolution of the system are discussed.