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Physical Review Letters

Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering

V. Dorier, Mariam Gevorgyan, Artur Mikhailovich Ishkhanyan, Claude Leroy, Hans Rudolf Jauslin, S. Guérin

Published Dec 13, 2017• 24 citations
Publisher

Abstract

We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.

DOI
10.1103/physrevlett.119.243902

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We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.
The stimulated Raman adiabatic passage 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 general approach to robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control. By controlling the dynamical process, we inversely design a family of Hamiltonians with non-divergent Rabi frequencies that can realize fast and accurate population transfer from the first to the third level, while the systematic errors are 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.
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.
Robust stimulated Raman exact passages are requisite for controlling nonlinear quantum systems, with wide applications, ranging from ultracold molecules to nonlinear optics to superchemistry. Inspired by shortcuts to adiabaticity, we propose the fast-forward scaling of stimulated Raman adiabatic processes with nonlinearity involved, describing the transfer from an atomic Bose-Einstein condensate to a molecular one by controllable external fields. The fidelity and robustness of atom-molecule conversion are shown to surpass those of conventional adiabatic passages, assisted by the fast-forward driving field. Finally, our results are extended to fractional stimulated Raman adiabatic processes for the coherent superposition of atomic and molecular states.
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.
Nonlinear quantum systems behave radically different from their linear counterparts and obstructions, identified as separatrix crossing and bifurcations in the phase space, can prevent their efficient control by standard approaches using adiabatic passage. We provide the exact resonant solution by solving the time-dependent nonlinear Schr\"odinger equation in terms of a Jacobi elliptic integral, interpreting the dynamics with the motion of a planar pendulum. This is referred to as nonlinear Rabi oscillation, which shows an obstruction to complete population transfer above a certain critical value of the nonlinearity strength, corresponding to an oscillating regime of the pendulum. Below this threshold, the so-called 2K2K2K pulse induces a complete population transfer, associated with a rotating regime of the pendulum, and representing the nonlinear counterpart of the $\ensuremath{\pi}$ pulse. We next propose a fast, robust, and high-fidelity control technique by a two-stage optimal inverse engineering strategy. It consists in dynamically compensating (diagonal) third-order nonlinearities, referred to as inverse linearization, combined with robust inverse optimization (RIO) developed for linear systems. We show that a moderate nonlinearity strength dramatically improves robustness.
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.