  We investigate a special time-dependent quantum model which assumes the
Landau-Zener driving form but with an overall modulation of the intensity of
the pulsing field. We demonstrate that the dynamics of the system, including
the two-level case as well as its multi-level extension, is exactly solvable
analytically. Differing from the original Landau-Zener model, the nonadiabatic
effect of the evolution in the present driving process does not destroy the
desired population transfer. As the sweep protocol employs only the finite
driving fields which tend to zero asymptotically, the cutoff error due to the
truncation of the driving pulse to the finite time interval turns out to be
negligibly small. Furthermore, we investigate the noise effect on the driving
protocol due to the dissipation of the surrounding environment. The losses of
the fidelity in the protocol caused by both the phase damping process and the
random spin flip noise are estimated by solving numerically the corresponding
master equations within the Markovian regime.
