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The present paper reports on results of quantum dynamics calculations forStark-chirp rapid-adiabatic passage (SCRAP) in two-level systems with electricfields computed with the optimal control theory. The Pontryagin maximumprinciple is used to determine the robust optimal control fields in thepresence of time-varying and spatially-inhomogeneous perturbing electricfields. The concept of a non-adiabatic correction to the Bloch vector dynamicsis introduced and discussed. The existence of a non-zero geometric phase isproved for certain adiabatic paths, which correspond to the complete populationreturn in the rapid-adiabatic passage. A connection is shown between thegeometric phase and a measure of the non-adiabatic effects in the timeevolution of the state vector during SCRAP. Different cost functionals used inthe optimal control scheme are shown to correlate with different topologies ofthe paths followed by the parameters of the Hamiltonian, which tightly relatesto the values of the geometric phase acquired by the adiabatic wavefunction.

Optimal control theory for rapid-adiabatic passage techniques in inhomogeneous external fields