We design, by invariant-based inverse engineering, driving fields that invert the population of a two-level atom in a given time, robustly with respect to dephasing noise and/or systematic frequency shifts. Without imposing constraints, optimal protocols are insensitive to the perturbations but need an infinite energy. For a constrained value of the Rabi frequency, a flat π pulse is the least sensitive protocol to phase noise but not to systematic frequency shifts, for which we describe and optimize a family of protocols.
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Lu et al. (2013) studied this question.
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