Optimal Lyapunov quantum control of two-level systems: Convergence and extended techniques

Taking a two-level system as an example, we show that a strong control field may enhance the efficiency of optimal Lyapunov quantum control but could decrease its control fidelity. A relationship between the strength of the control field and the control fidelity is established. An extended technique, which combines free evolution and external control, is proposed to improve the control fidelity. We analytically demonstrate that the extended technique can be used to design a control law for steering a two-level system exactly to one predetermined eigenstate of the free Hamiltonian. In such a way, the convergence of the extended optimal Lyapunov quantum control can be guaranteed.