Optimal control of population inversion in open quantum systems

We consider an optimal control problem for the quantum population transfer in open quantum systems. Quantum optimal control using the Pontryagin maximum principle is specifically derived. The influences of surrounding environment are analytically and numerically studied. In particular, we demonstrate that the quantum optimal control ability remarkablely dependents on temperatures. Only at low temperatures, the derived control laws have active performance and the quantum decoherence time can be extended.