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

We propose an exact solution to a linear two-level system with the existence of a special hyperbolic secant external field and elucidate its transition dynamics. We then extend the model to the nonlinear case and show that the nonlinearity will significantly affect the transition dynamics. As nonlinearity increases, Landau-Zener-Stuckelberg-Majorana 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 the stationary phase approximation and find that transition probability will be blocked as the nonlinearity intensity is much larger than the external field frequency, which agrees with the numerical result.