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The Journal of Chemical Physics

Optimal control of population transfer in an optically dense medium

Ningjun Wang, HERSCHEL A. RABITZ

Published Jan 22, 1996• 30 citations
Publisher

Abstract

We apply the optimal control technique (OCT) to design an optical pulse pair that controls the population transfer in a medium of three-level atoms. The absorption and reshaping of the controlling pulses by the medium are taken into account. The efficiency of the population transfer is improved significantly compared with designs that do not incorporate pulse absorption and reshaping.

DOI
10.1063/1.470777

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We apply the optimal control technique (OCT) to design an optical pulse pair that controls the population transfer in a medium of three-level atoms. The absorption and reshaping of the controlling pulses by the medium are taken into account. The efficiency of the population transfer is improved significantly compared with designs that do not incorporate pulse absorption and reshaping.
We apply an optimal control technique (OCT) to design a secondary coupling pulse that can control the amplification of a given primary optical pulse in a dense media of coherently prepared three-level \ensuremath{\lambda}-type atoms without population inversion. Effects of pulse absorption, amplification, and reshaping by the medium are incorporated in the OCT. We demonstrate numerically that shape-invariant as well as shape-distorted amplification without population inversion can be achieved by properly designing the shape of the coupling pulse. The maximum amplification obtainable is shown to be dependent on the initial atomic coherence as well as the upper bound of the coupling pulse intensity. The group velocity of the primary pulse can also be controlled by the coupling pulse. \textcopyright{} 1996 The American Physical Society.
In this paper, we suggest a straight-forward technique to control the atomic population inversion in a three-level dense medium based on the pulse shaping with a phase-jump. A strong stokes field and two weak probe fields excite the atomic medium via the V-type configuration. First, we reveal that the atomic population inversion is accomplished under a shaped pulse. Second, we show that this is significantly improved by including a phase-jump in the pulse profile. Finally, we suggest a typical combined shape and phase in order to control the dynamics of the atomic population inversion.
We demonstrate that Optimal Control Theory (OCT) with a state-dependent constraint which depends on the state of the system at each instant can reproduce the famous counterintuitive mechanism of Stimulated Raman adiabatic passage (STIRAP). We examine this behavior in a Λ-type three-level system and we show that could be applied for sequentially coupled many-level systems. We study the robustness of the two methods with respect to pulse fluctuations and the decays. We show that new OCT formulation appears to be more robust than STIRAP when a perturbation is introduced in the pulses. Such method is of great use for systems involving coherence loss such as molecular systems with dissociation or ionization limits. It also may find potential applications in the control of chemical reactions, quantum optics, and quantum information processing.
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.