Adiabatic transition histories of population transfer in the Λ system

The superadiabatic basis scheme developed by Berry [Proc. R. Soc. London 429, 61 (1990)] is used to analyze adiabatic population transfer in the {Λ} system in what is known as the counterintuitive pulse scheme. For a specific choice of pulses, we find that the diabatic loss is given by the exponentially small (8-4{}2)exp(-2/{ε}), where {ε} is a small parameter describing the adiabaticity of the process. We thus establish the connection between population transfer in the {Λ} system and general adiabatic transition theory. We project numerical solutions onto superadiabatic basis states for the real three-level system and show how the history of population transfer has a very compact and universal history in one particular superadiabatic basis.