Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems

We construct fast and stable control schemes for two- and three-level quantum systems. These schemes result in an almost perfect population transfer even in the presence of an additional, unwanted and uncontrollable transition. Such schemes are developed by first using the techniques of 'shortcuts to adiabaticity' and then introducing and examining a measure of the scheme's sensitivity to an unwanted transition. We optimize the schemes to minimize this sensitivity and provide examples of shortcut schemes which lead to a nearly perfect population inversion even in the presence of unwanted transitions.