Optimal control in laser-induced population transfer for two- and three-level quantum systems
- 1 May 2002
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 43 (5), 2107-2132
- https://doi.org/10.1063/1.1465516
Abstract
We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two- and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the well-known technique of “π-pulse transfer” in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the “π-pulse transfer.” This geometrical picture also allows one to analyze the population transfer by adiabatic passage.This publication has 18 references indexed in Scilit:
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