Dynamical transitions in a modulated Landau-Zener model with finite driving fields

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.