Dynamical transition in a nonlinear two-level system driven by a special hyperbolic-secant external field

Abstract We propose a simplification of the exact solution model in a linear system, which creates a transparent passage for dynamical transition. We extend this model to the nonlinear system and show that the transition dynamics will be determined by the nonlinear parameter and an unique parameter of external field. Asnon-linearity increases, Landau-Majorana-Stückelberg- Zener (LMSZ) interference fringes can be constructive and the up energy level in the adiabatic limit splits into three levels. For fast-sweeping fields, we derive an analytic expression for dynamics transition under stationary phase approximation and show that transition probability will be blocked as the non-linearity is much larger than external field parameter, which agrees with numerical results.