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 special hyperbolic secant external field and elucidate its transition dynamics. then extend model nonlinear case show that nonlinearity will significantly affect As increases, Landau–Zener–Stückelberg–Majorana interference fringes can be constructive up energy level in adiabatic limit splits into three levels. For fast-sweeping fields, we derive analytic expression for dynamics under stationary phase approximation find probability blocked as intensity is much larger than frequency, which agrees numerical result.