On the compatibility of the adiabatic and rotating wave approximations for robust population transfer in qubits

Rémi Robin (1) , Nicolas Augier (2) , Ugo Boscain (1, 3, 4) , Mario Sigalotti (1, 4)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 BIOCORE - Biological control of artificial ecosystems
3 CNRS - Centre National de la Recherche Scientifique
4 CaGE - Control And GEometry

In the physics literature it is common to see the rotating wave approximation and the 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 main result gives a precise quantification of the uncertainty interval of the resonance frequency for which the strategy works. We believe that this result, beside its mathematical interest, could be useful in experimental situations.

Mots clés: Spin dynamics; Adiabatic approximation; Rotating wave approximation

Domaines: Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Rémi Robin, Nicolas Augier, Ugo Boscain, Mario Sigalotti. On the compatibility of the adiabatic and rotating wave approximations for robust population transfer in qubits. 2020. ⟨hal-02504532v1⟩