State transfer control in non-Markovian open quantum systems

The weak-coupled two-level open quantum system described by non-Markovian time-convolution-less master equation is investigated in this paper. Based on the Lyapunov stability theorem, the system control laws used to transfer state are designed. The characteristics of the purity changes in the non-Markovian open quantum systems are studied. The effectiveness of the control system is ensured by adjusting the parameters of control laws. Three simulation experiments are implemented under the Matlab environment, they are the states transfer from the eigenstate to the superposition state, from the superposition state to the superposition state, and from the mixed state to the superposition state, respectively. Numerical experimental results show that the target state can be reached from different initial states under the action of the control laws designed, and demonstrate the effectiveness of quantum Lyapunov control method proposed.