Characteristics Analysis and State Transfer for Non-Markovian Open Quantum Systems

Abstract

The weak-coupled two-level open quantum system described by non-Markovian time-convolution-less master equation is investigated in this paper. The system characteristics with respect to the decay rate β(t), coherence factor Coh and purity p in terms of the cut-off frequency ωc, coupling constant α and transition frequency ω0 are investigated, respectively. The appropriate parameters used in system simulation experiments are determined by analyzing results of different values of parameters for the effects of system performance. The control laws used to transfer the system states are designed on the basis of the Lyapunov stability theorem. Numerical simulation experiments are implemented under the Matlab environment. The features of the free evolution trajectory of the non-Markovian systems and the state transfer from a pure state to a desired pure state under the action of the proposed control laws are studied, respectively. By comparing the experimental results, the effectiveness of the proposed quantum Lyapunov control method applied to the state transfer in non-Markovian open quantum systems is verified. Meanwhile, the influences of different control parameters and cut-off frequencies on the system performance are analyzed.