Optimal control of non-Markovian dynamics in open quantum systems

We study the optimal control problem in a non-Markovian open quantum system. The quantum system of interest is coupled to its local environment, which is dissipative in nature and tends to decay the quantum system. Based on the non-Markovian master equation, we study the non-Markovian effects on the system dynamics. The non-Markovian environment has dual effects on the quantum system: the dissipation and the backaction. The dissipation effect makes the system lose of quantum features, whereas the backaction revives it. We further design quantum control laws to control the system. The optimal control principle is studied to steer to quantum state to a target state. Finally, as an example, we used the optimal control method to control the quantum decoherence.