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

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.

19 pages, 6 figures

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Cited by in corpus (6)

• Optimal Efficiency of a Noisy Quantum Heat Engine
• Optimal shortcuts of Stimulated Raman Adiabatic Passage in the presence of dissipation
• Optimal STIRAP shortcuts using the spin to spring mapping
• Minimum time generation of a uniform superposition in a qubit with only transverse field control
• Optimal shape of STIRAP pulses for large dissipation at the intermediate level
• On the optimality of optical pumping for a closed $\Lambda$-system with large decay rates of the intermediate excited state