Counterdiabatic suppression of background state population in resonance leaking by controlling intermediate branching

The counterdiabatic principle [M. Demirplak and S. A. Rice, J. Phys. Chem. A 107, 9937 (2003)] is used in a pragmatic way to formulate a practical control strategy for perturbed population transfer. Interpreting the appearance of population in undesirable intruder or background states as phenomenological consequences of diabatic perturbations, such branching is suppressed as soon as it arises. By invoking a penalty term that is sensitive to any transitional population in undesirable levels, a correction field is created which effectively prevents diabatic behavior. This strategy is applied to the control of background state population in multiphoton excitations. For a model five-level system we show that leaking of a resonant three-photon transition to a background state can readily be suppressed by simple correction fields obtained from our intermediate-branching driven implementation of counterdiabatic control.