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arXiv:2209.07631 · Physical Review A

Optimal robust stimulated Raman exact passage by inverse optimization

Xavier Laforgue, Ghassen Dridi, S. Guérin

Published Mar 15, 2022• 23 citations
arXivHTMLPDF

Abstract

We apply the inverse geometric optimization technique to generate an optimal and robust stimulated Raman exact passage (STIREP) considering the loss of the upper state as a characterization parameter. Control field temporal shapes that are optimal with respect to pulse area, energy, and duration are found to form a simple sequence with a combination of intuitively (near the beginning and the end) and counterintuitively ordered pulse pairs. The resulting dynamics produces a loss which is about a third of that of the nonrobust optimal STIREP. Alternative optimal solutions featuring lower losses, larger pulse areas, and fully counterintuitive pulse sequences are derived.

DOI
10.1103/physreva.105.032807

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We apply the inverse geometric optimization technique to generate an optimal and robust stimulated Raman exact passage (STIREP) considering the loss of the upper state as a characterization parameter. Control field temporal shapes that are optimal with respect to pulse area, energy, and duration are found to form a simple sequence with a combination of intuitively (near the beginning and the end) and counterintuitively ordered pulse pairs. The resulting dynamics produces a loss which is about a third of that of the nonrobust optimal STIREP. Alternative optimal solutions featuring lower losses, larger pulse areas, and fully counterintuitive pulse sequences are derived.
Quantum control of lossy systems is known to be achieved by adiabatic passage via an approximate dark state relatively immune to loss, such as the emblematic example of stimulated Raman adiabatic passage (STIRAP) featuring a lossy excited state. By systematic optimal control study, via the Pontryagin maximum principle, we design alternative more efficient routes that, for a given admissible loss, feature an optimal transfer with respect to the cost defined as (i) the pulse energy (energy minimization) or (ii) the pulse duration (time minimization). The optimal controls feature remarkably simple sequences in the respective cases: (i) operating far from a dark state, of π-pulse type in the limit of low admissible loss, or (ii) close to the dark state with a counterintuitive pulse configuration sandwiched by sharp intuitive sequences, referred to as the intuitive/counterintuitive/intuitive (ICI) sequence. In the case of time optimization, the resulting stimulated Raman exact passage (STIREP) outperforms STIRAP in term of speed, accuracy, and robustness for low admissible loss.
Abstract Shortcuts to adiabaticity have been put forward for accelerating slow adiabatic passages in various quantum systems with tremendous applications for performing quantum information processing tasks. In this paper, we propose a hybrid protocol to achieve stimulated Raman exact passage (STIREP) by combining invariant-based inverse engineering, optimal control, and composite pulse approaches. We first derive the general solution and the corresponding pulse shapes by invariant-based inverse engineering. Counterintuitive and optimal (intuitive) pulse sequences are formulated in this context and incorporated into composite sequences. Such composite STIREP not only features robustness against the fluctuation of laser intensity, but also reduces the operation time and energy cost.
Stimulated Raman adiabatic passage (STIRAP) driven with pulses of optimum shape and delay has the potential of reaching fidelities high enough to make it suitable for quantum-information processing. The optimum pulse shapes are obtained upon reduction of STIRAP to effective two-state systems. We use the Dykhne-Davis-Pechukas (DDP) method to minimize nonadiabatic transitions and to maximize the fidelity of STIRAP. This results in a particular relation between the pulse shapes of the two fields driving the Raman process. The DDP-optimized version of STIRAP maintains its robustness against variations in the pulse intensities and durations, the single-photon detuning, and possible losses from the intermediate state.
We have looked at the laser-induced excitation of a level manifold coupled through a single excited level. This generalizes the ordinary Λ configuration to many levels. It is the original situation where stimulated Raman adiabatic passage (STIRAP) has been considered. We then apply optimal control theory to determine the pulse sequence which effects a predetermined superposition state with a minimal involvement of the excited state. The program is free to find its optimal pulse sequence, and we find that a generalization of the ordinary counterintuitive situation emerges. In addition to verifying the efficiency of the counterintuitive approach, the work justifies the separation into dark and bright subspaces, where time evolution in the former has to include the dynamical effects of adiabatic corrections.
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.