  We study Rosen-Zener transition (RZT) in a nonlinear two-level system in
which the level energies depend on the occupation of the levels, representing a
mean-field type of interaction between the particles. We find that the
nonlinearity could affect the quantum transition dramatically. At certain
nonlinearity the 100% population transfer between two levels is observed and
found to be robust over a very wide range of external parameters. On the other
hand, the quantum transition could be completely blocked by a strong
nonlinearity. In the sudden and adiabatic limits we have derived analytical
expressions for the transition probability. Numerical explorations are made for
a wide range of parameters of the general case. Possible applications of our
theory to Bose-Einstern Condensates (BECs) are discussed.
