Original citationDaems, D., Ruschhaupt, A., Sugny, D. and Guérin, S. (2013) Access to the full text of the published version may require a subscription. Rights

We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two-and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the wellknown technique of ''-pulse transfer'' in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the ''-pulse transfer.'' This geometrical picture also allows one to analyze the population transfer by adiabatic passage.

We present a method for optimization of the technique of adiabatic passage between two quantum states by composite sequences of frequency-chirped pulses with specific relative phases: composite adiabatic passage (CAP). By choosing the composite phases appropriately the nonadiabatic losses can be canceled to any desired order with sufficiently long sequences, regardless of the nonadiabatic coupling. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp. The accuracy of the CAP technique and its robustness against parameter variations make CAP suitable for high-fidelity quantum information processing.