State transfer and coherence maintain based on DFS in open quantum systems

To maintain state coherence in an open quantum systems, the decoherence-free subspace (DFS) is an effective method. The target state is usually needed to be in DFS. In the case the target state is not in DFS, we first design external control field I to construct a DFS included target state. Then another control field II is used to transfer the state of the system to be controlled to the expected target state. As is well known, invariant set contains all stable states of the system. Control Hamiltonian is designed to shrink invariant set and increase the transition probability from the system state to target state. In such a way, the state transfer and coherence maintain are completed. Numerical simulation is given for a four-level energy open quantum system to demonstrate the effectiveness of the control strategy proposed.