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We investigate ways to optimize adiabaticity and diabaticity in the Landau-Zener model with non-uniform sweeps. We show how diabaticity can be engineered with a pulse consisting of a linear sweep augmented by an oscillating term. We show that the oscillation leads to jumps in populations whose value can be accurately modeled using a model of multiple, photon-assisted Landau-Zener transitions, which generalizes work by Wubs et al. [New J. Phys. 7, 218 (2005)]. We extend the study on diabaticity using methods derived from optimal control. We also show how to preserve adiabaticity with optimal pulses at limited time, finding a non-uniform quantum speed limit.
We consider fast high-fidelity quantum control by using a shortcut to adiabaticity (STA) technique and optimal control theory (OCT). Three specific examples, including expansion of cold atoms from the harmonic trap, atomic transport by moving harmoni
We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing. We correct
We examine structural and dynamical properties of quantum resonances associated with an avoided crossing and identify the parameter shifts where these properties attain maximal or extreme values, first at a general level, and then for a two-level sys
Fast and robust quantum control protocols are often based on an idealised approximate description of the relevant quantum system. While this may provide a performance which is close to optimal, improvements can be made by incorporating elements of th
In a recent publication [Phys. Rev. A 79, 065602 (2009)] it was shown that an avoided-crossing resonance can be defined in different ways, according to level-structural or dynamical aspects, which do not coincide in general. Here a simple $3$-level s