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Chinese Physics Letters

Optimal Control of Population Transfer in Three-Level System with Genetic Algorithms

Xiangyun Zhang, Zhenrong Sun, Guoliang Chen, Zugeng Wang, Zhizhan Xu, Ruxin Li

Published Oct 1, 2004• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/21/10/018

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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.
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.
It introduced several methods to transfer population,including two-level system and three-level system, and gave some comparisons on transfer efficiency and transfer velocity of them in theory. It is shown that population transfer by coherent pulse sequence is better than incoherence one. Numerical simulation results showed that when using Stimulated Raman Adiabatic Rapid Passage (STIRAP), in which the pump laser pulse fully overlaps the Stokes pulse with the Stokes preceding the pump, population can be transferred completely and rapidly. Robust control of population transfer among Zeeman sublevels in the ground states of three-level system is investigated using adiabatic rapid passage in theory. The laser pulse widths are supposed to be short compared to the lifetime of the excited level, which means adiabatic. We demonstrated that techniques of STIRAP can be found to optimize population transfer in the ground states of three-level Λ system.
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.
Adiabatic passage induced by chirped laser pulses in three-level $\ensuremath{\Lambda}$ systems is investigated. Two different strategies for efficient population transfer (equal and opposite sign of the chirp) are analyzed. The role of detuning, crucial for the attempt to reduce the population of the intermediate state, is demonstrated. The scheme of adiabatic passage by laser pulses with chirps of different sign is not symmetric with respect to the sign of the one-photon detuning. Blue detuning results in a smaller transient population of the intermediate state than does red detuning. The results are explained on the basis of dressed states. Numerical results for a fully off-resonant adiabatic passage scheme, based on two pulses with the same sign of the chirps, are also considered. The robustness of the schemes in terms of the Rabi frequency, chirp rate, detuning, and time delay of the pulses is explored.
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.