State transfer based on decoherence-free target state by Lyapunov-based control

We propose a Lyapunov-based control approach for state transfer based on the decoherence-free target state. The expected target state is constructed to be a decoherence-free state in a decoherence-free subspace （DFS） by an external laser field I, so that the system state can be decoupled from the environment, and no more decoherence process will occur. With the decoherence-free target state, we design a Lyapunov-based control field II to steer the given initial state to the decoherence-free state of open quantum systems as completely as possible, and decouple the system state from the environment at the same time. In the end, it is verified that the state transfer control designed comes true on a A-type four-level atomic system, and the system can stay on the decoherence-free target state without coupling to environment.