Resonant Analytic Fields Applied to Generic Multi-state Systems
  Rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approach. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the Schroedinger equation. First, we introduce an extension of the rotating-wave approximation for multi-state systems. Under an assumption that a smooth transition is induced by the optimal field, we obtain three types of analytic control fields and demonstrate their validity and deficiency for generic systems represented by random matrices. Through the comparison, we conclude that the analytic field based on our coarse-grained approach outperforms the other ones for generic quantum systems with a large number of states. Finally, the further extension of the analytic field is introduced for realistic chaotic systems and its validity is shown in banded random matrix systems. 
Toshiya Takami and Hiroshi Fujisaki