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The Journal of Chemical Physics

Is adiabatic passage population transfer a solution to an optimal control problem?

Y. B. Band, O. Magnes

Published Nov 1, 1994• 30 citations
Publisher

Abstract

We demonstrate that stimulated Raman adiabatic passage (STIRAP) of population from a ground state to an excited state of an atom or molecule is not an optimal control solution to the problem of maximizing the population in the excited state.
DOI
10.1063/1.468246

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The stimulated Raman adiabatic passage (STIRAP) shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity, in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a generally robust approach to speed up STIRAP with invariant-based shortcut to adiabaticity. By controlling the dynamical process, we inversely design a family of Hamiltonians that can realize fast and accurate population transfer from the first to the third level, while the systematic error is largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.
We derive STIRAP (stimulated Raman adiabatic passage) shortcuts to adiabaticity maximizing population transfer in a three-level $\mathrm{\ensuremath{\Lambda}}$ quantum system, using spin-to-spring mapping to formulate the corresponding optimal control problem on the simpler system of a classical driven dissipative harmonic oscillator. We solve the spring optimal control problem and obtain analytical expressions for the impulses, the durations of the zero control intervals, and the singular control, which are the elements composing the optimal pulse sequence. We also derive suboptimal solutions for the spring problem, one with less impulses than the optimal and others with smoother polynomial controls. We then apply the solutions derived for the spring system to the original system, and compare the population transfer efficiency with that obtained for the original system using numerical optimal control. For all dissipation rates used, the efficiency of the optimal spring control approaches that of the numerical optimal solution for longer durations, with the approach accomplished earlier for smaller decay rates. The efficiency achieved with the suboptimal spring control with less impulses is very close to that of the optimal spring control in all cases, while that obtained with polynomial controls lies below, and this is the price paid for not using impulses, which can quickly build a nonzero population in the intermediate state. The analysis of the optimal solution for the classical driven dissipative oscillator is not restricted to the system at hand but can also be applied in the transport of a coherent state trapped in a moving harmonic potential and the transport of a mesoscopic object in stochastic thermodynamics.
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.
Abstract The population transfer of a NaH molecule from the ground state X 1 Σ + to the target state A 1 Σ + via stimulated Raman adiabatic passage (STIRAP) is investigated. The results show that the intensity, delay time and detuning have a significant effect on population transfer. A large population transfer is observed with increased pump and Stokes intensity, especially when the pump and Stokes intensity match. Population transfer also depends on the delay time between the pump laser pulse and the Stokes laser pulse. The detuning of the two pulses influences the population transfer. Efficient population transfer can be realized under the resonant or two-photon resonant condition.
We consider combined stimulated Raman adiabatic passage (STIRAP) and fast-forward field (FFF) control of selective vibrational population transfer in a polyatomic molecule. The motivation for using this combination control scheme is 2-fold: (i) to overcome transfer inefficiency that occurs when the STIRAP fields and pulse durations must be restricted to avoid excitation of population transfers that compete with the targeted transfer and (ii) to overcome transfer inefficiency resulting from embedding of the actively driven subset of states in a large manifold of states. We show that, in a subset of states that is coupled to background states, a combination of STIRAP and FFFs that do not individually generate processes that are competitive with the desired population transfer can generate greater population transfer efficiency than can ordinary STIRAP with similar field strength and/or pulse duration.
The rovibrational dynamics of an extended ladder stimulated Raman adiabatic passage (STIRAP) system through permanent dipole moment transitions is investigated theoretically using the time-dependent quantum-wave-packet method for the ground electronic state of the HF molecule. The calculated results show that nearly 100% of the population can be transferred to the target state through (1+2), (1+3), and (2+2) STIRAP schemes. By choosing a suitable excitation pathway, the effects of the background states on the final population of the target state can be removed. For the multiphoton STIRAP process, the one-photon overtone pump scheme is more efficient than the two-photon pump scheme in controlling the population transfer to the target state.