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Physical Review A

Optimal pulse sequences for population transfer in multilevel systems

Ignacio R. Solá, Vladimir S. Malinovsky, David J. Tannor

Published Oct 1, 1999• 74 citations
Publisher

Abstract

We study different mechanisms of adiabatic population transfer in N-level systems by means of optimal control algorithms. Using two-dimensional topographic maps of the yield of population transfer as a function of time delay and intensity of the pulses we analyze the global properties of the schemes and the conditions that lead to optimization. For three-level systems it is shown that the optimal pulse sequence is the well-known STIRAP (stimulated Raman adiabatic passage) scheme. For five-level systems a family of solutions ranging from the alternating STIRAP scheme to the new straddling STIRAP (S-STIRAP) scheme is obtained and the behavior of the solutions is compared. For four-level systems we obtain as optimal a S-STIRAP type sequence that behaves as an effective two-level system. For both odd and even numbers of N-level systems, the crucial role of the straddling pulse in reducing the population of all intermediate levels is demonstrated.

DOI
10.1103/physreva.60.3081

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Journal of Physics Conference Series•Mar 14, 2012•1 citation
We study different mechanisms of adiabatic population transfer in N-level systems by means of optimal control algorithms. Using two-dimensional topographic maps of the yield of population transfer as a function of time delay and intensity of the pulses we analyze the global properties of the schemes and the conditions that lead to optimization. For three-level systems it is shown that the optimal pulse sequence is the well-known STIRAP (stimulated Raman adiabatic passage) scheme. For five-level systems a family of solutions ranging from the alternating STIRAP scheme to the new straddling STIRAP (S-STIRAP) scheme is obtained and the behavior of the solutions is compared. For four-level systems we obtain as optimal a S-STIRAP type sequence that behaves as an effective two-level system. For both odd and even numbers of N-level systems, the crucial role of the straddling pulse in reducing the population of all intermediate levels is demonstrated.
Abstract We consider coherent population transfer in multilevel quantum systems driven by time-delayed pulse trains. We show how to choose the parameters of the trains so that the population dynamics tracks the behavior of a Λ-type three-level system under stimulated Raman adiabatic passage (STIRAP). Efficient population transfer can be achieved regardless of the order and with or without overlap of the pump and the Stokes sub-pulses of the trains. Generalized STIRAP schemes of population transfer in N -level system with sequential couplings are also examined. The mechanism of the population transfer and the robustness of the proposed schemes are discussed.
Population transfer in a three-level A system is simulated numerically and optimized. Almost complete population transfer from |1) to |3) is achieved by a genetic algorithm while the population in state |2) reached minimum over the entire evolution at the same time. The result shows that the optimal pulse sequence is the well-known stimulated Raman adiabatic passage (STIRAP) scheme. The detuning of pump pulse and Stokes pulse Δp and Δs with the opposite sign and the chirps χp and χs with the same sign are in favour of the complete and robust population transfer for few-cycle laser pulse. Rabi frequencies Ωp and Ωs have insensitive effects on the complete population transfer during a large scope of their ratio when they are large enough.
STIRAP (stimulated Raman adiabatic passage) has proven to be an efficient and robust technique for transferring population in a three-level system without populating the intermediate state. Here we show that the counterintuitive pulse sequence in STIRAP, in which the Stokes pulse precedes the pump, emerges automatically from a variant of optimal control theory we have previously called ``local'' optimization. Since local optimization is a well-defined, automated computational procedure, this opens the door to automated computation of generalized STIRAP schemes in arbitrarily complicated NNN-level coupling situations. If the coupling is sequential, a simple qualitative extension of STIRAP emerges: the Stokes pulse precedes the pump as in the three-level system. But, in addition, spanning both the Stokes and pump pulses are pulses corresponding to the transitions between the $N\ensuremath{-}2$ intermediate states with intensities about an order of magnitude greater than those of the Stokes and pump pulses. This scheme is amazingly robust, leading to almost 100% population transfer with significantly less population transfer to the $N\ensuremath{-}2$ intermediate states than in previously proposed extensions of STIRAP.
Population transfer in a three-level Λ system is simulated numerically and optimized. Almost complete population transfer from |1⟩ to |3⟩ is achieved by a genetic algorithm while the population in state |2⟩ reached minimum over the entire evolution at the same time. The result shows that the optimal pulse sequence is the well-known stimulated Raman adiabatic passage (STIRAP) scheme. The detuning of pump pulse and Stokes pulse Δ p and Δ s with the opposite sign and the chirps χ p and χ s with the same sign are in favour of the complete and robust population transfer for few-cycle laser pulse. Rabi frequencies Ω p and Ω s have insensitive effects on the complete population transfer during a large scope of their ratio when they are large enough.
The optimal control of population transfer for multi-level systems is investigated from the perspective of quantum geometry. Firstly, the general theoretical framework of optimizing the stimulated Raman adiabatic passage (STIRAP) scheme based on the dynamical quantum geometric tensor is given, and then the dynamical quantum geometric tensor and the nonadiabatic transition rate are calculated by taking the detuned ΛΛΛ-type three-level system and tripod-type four-level system for example. Secondly, the transfer dynamics of the particle population of the system are investigated in detail. For a three-level system, the optimal STIRAP scheme has an efficiency of over 98\% in transferring the population to the final state, while the transfer efficiency of traditional STIRAP is about 72\%. The superposition states with arbitrary proportions can be efficiently prepared for a four-level system due to the decoupling of the degenerate dark states. Finally, the influences of system parameters, such as the operation time of the Rabi pulses, the amplitude fluctuation and the single-photon detuning, on the transfer process are discussed. Especially, the phenomenon of the adiabatic resonance transfer is revealed. Choosing the pulse parameters in the resonance window can reduce the infidelity of the population transfer to below 10−310^{-3}10−3. It is found that the optimal STIRAP scheme by the dynamical quantum geometric tensor provides faster and more efficient transfer than the traditional STIRAP scheme.
We consider a five-level atomic system (M-system) driven by four near-resonant laser pulses and study the possibilities of population transfer via different combinations of Stimulated Raman Adiabatic Passage (STIRAP) and bright-STIRAP (b-STIRAP) processes. We examine these combinations analytically and numerically from the point of view of efficiency of population transfer. It is shown, in particular, that the combination of the processes above enhances the efficiency. Analytical expressions are obtained for the quasienergies of the system in two regimes differing by conditions imposed on resonance detunings. Interaction adiabaticity conditions are analyzed. We also study the necessary successions of turning on and off of pulses which ensure efficient transfer of atomic populations. The obtained analytical results agree well with direct numerical calculations.