2020/03/12 by Rémi Robin, Robin, Rémi, Nicolas Augier +5 · 1 citation
Physics and Astronomy · #35Q41 #81P15 #81Q15 #81Q50 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Laser-Matter Interactions and Applications #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies
paper · doi:10.48550/arxiv.2003.05831
openalex publication_date 2020/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the physics literature it is common to see the rotating wave approximation andthe adiabatic approximation used "in cascade" to justify the use of chirped pulses for two-level quantum systems driven by one external field, in particular when the resonance frequency of the system is not known precisely. Both approximations need relatively long time and are essentially based on averaging theory of dynamical systems. Unfortunately, the two approximations cannot be done independently since, in a sense, the two time scales interact. The purpose of this paper is to study how the cascade of the two approximations can be justified and how large becomes the final time as the fidelity goes to one, while preserving the robustness of the adiabatic strategy. Our first result, based on high-order averaging techniques, gives a precise quantification of the uncertainty interval of the resonance frequency for which the population inversion works. As a byproduct of this result, we prove that it is possible to control an ensemble of spin systems by a single real-valued control, providing a non-trivial extension of a celebrated result of ensemble controllability with two controls by Khaneja and Li.