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

TL;DR

This paper investigates the link between optimal control theory and adiabatic passage methods in quantum systems, revealing that certain adiabatic pulses correspond to solutions of specific optimal control problems through geometric Hamiltonian analysis.

Contribution

It establishes a geometric framework connecting adiabatic passage techniques with optimal control theory in multi-level quantum systems, highlighting the role of Hamiltonian singularities.

Findings

Stimulated Raman Adiabatic Passage linked to Hamiltonian singularity

Adiabatic pulses are solutions to optimal control problems for specific cost functionals

Extension of analysis from three-level to four-level 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.