Effects of periodic modulation on the nonlinear Landau--Zener tunneling

We study the Landau-Zener tunneling of a nonlinear two-level systemby applying a periodic modulation on its energy bias. We find thatthe two levels are splitting at the zero points of the zero orderBessel function for high-frequency modulation. Moreover, we obtainthe effective coupling constant between two levels at the zeropoints of the zero order Bessel function by calculating the finaltunneling probability at these points. It seems that the effectivecoupling constant can be regarded as the approximation of the higherorder Bessel function at these points. For the low-frequencymodulation, we find that the final tunneling probability is afunction of the interaction strength. For the weak inter-levelcoupling case, we find that the final tunneling probability is moredisordered as the interaction strength becomes larger.