Nonlinear Landau-Zener tunneling under higher-order dispersion

Abstract

We studied nonlinear Landau-Zener tunneling under the effect of higher-order dispersion, transformed the Gross-Pitaevskii (GP) equation with higher-order dispersion terms into a nonlinear two-energy level form using a two-mode approximation, and comprehensively analyzed the loop structure of the lowest-energy band and the nonlinear Landau-Zener tunneling. The results show that, when third-order dispersion coefficient is not zero, there is a spatial inversion symmetry breaking of the energy band structure and unbalanced Landau-Zener tunneling. By analyzing the fixed point's nature of the classical Hamiltonian, we obtain a law for the variation of the loop structure and adiabatic tunneling probability with the dispersion coefficient, consistent with our numerical analysis results. In addition, we analyzed the real-time evolution of solitons with transverse bias and observed the tunneling phenomenon. Consistent with our analysis, the adjustment of the dispersion term can effectively control optical tunneling, which provides an alternative idea for optical switching.