  Effects of a periodic driving field on Landau-Zener processes are studied
using a nonlinear two-mode model that describes the mean-field dynamics of a
many-body system. A variety of different dynamical phenomena in different
parameter regimes of the driving field are discussed and analyzed. These
include shifted, weakened, or enhanced phase dependence of nonlinear
Landau-Zener processes, nonlinearity-enhanced population transfer in the
adiabatic limit, and Hamiltonian chaos on the mean field level. The emphasis of
this work is placed on how the impact of a periodic driving field on
Landau-Zener processes with self-interaction differs from those without
self-interaction. Aside from gaining understandings of driven nonlinear
Landau-Zener processes, our findings can be used to gauge the strength of
nonlinearity and for efficient manipulation of the mean-field dynamics of
many-body systems.
