Effects of periodic modulation on the nonlinear Landau-Zener tunneling

We study the Landau-Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.