Optimized adiabatic passage with dephasing

We study adiabatic population transfer with dephasing in two-level models driven by a chirped driving field. We show that the population transfer is maximized when the dynamics follows specific ellipses as trajectories in the parameter space. We determine the optimal parameters and estimate the losses in a closed form. These estimates show a similar robustness as for the standard lossless adiabatic processes with respect to variations of the parameters.