Adiabatic passage for a lossy two-level quantum system by a complex time method

Using a complex time method with the formalism of Stokes lines, we establish a generalization of the Davis–Dykhne–Pechukas formula which gives in the adiabatic limit the transition probability of a lossy two-state system driven by an external frequency-chirped pulse-shaped field. The conditions that allow this generalization are derived. We illustrate the result with the dissipative Allen–Eberly and Rosen–Zener models. (paper)