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arXiv · 1208.2326

A connection between optimal control theory and adiabatic passage techniques in quantum systems

E. Assémat·D. Sugny
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Abstract

This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum Principle. In a three-level quantum system, we show that the Stimulated Raman Adiabatic Passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.

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E. Assémat, D. Sugny. 2012-08-11. A connection between optimal control theory and adiabatic passage techniques in quantum systems. https://doi.org/10.1103/physreva.86.023406

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