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Entropy

Optimal Pulse Design for Dissipative-Stimulated Raman Exact Passage

Kaipeng Liu, Dominique Sugny, Xi Chen, S. Guérin

Published May 12, 2023• 10 citations
Publisher

Abstract

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.

DOI
10.3390/e25050790

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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.
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.
Abstract We conduct a systematic study to optimize the stimulated Raman adiabatic passage (STIRAP) processes using Pontryagin’s principle. Pontryagin’s principle enables the incorporation of time- and fidelity-based optimization strategies into the traditional adiabatic processes. By incorporating an integral term of the intermediate state population into the cost function of either evolution time or target state fidelity, we can achieve either time-optimal or high-fidelity state transfer while maintaining minimal intermediate state occupation. This optimization method can also be superior to the shortcuts to adiabaticity control in either transfer speed or state fidelity, depending on the chosen cost function. Our method provides a systematic optimization strategy for the STIRAP process. Moreover, this approach is robust against the decoherence effect of the system caused by its surrounding environment, thereby enhancing the overall control performance and stability.
The standard stimulated Raman adiabatic passage (STIRAP) protocol enables high-fidelity quantum state transfer in an ideal three-level system via adiabatic following of a dark state. However, in practical systems with more energy levels, control pulses with finite spectral selectivity often couple the three-level subspace to the remaining subspace, introducing leakage that fundamentally limits the transfer performance. Here, we adopt a multilevel chain model for STIRAP that explicitly incorporates this leakage subspace. Using Pontryagin's maximum principle, we formulate a leakage-penalized quantum optimal control problem with the control pulses constrained to experimentally feasible Gaussian pulse families. We derive explicit gradients of the objective functional with respect to the pulse parameters, enabling efficient low-dimensional optimization that suppresses leakage while preserving the counterintuitive STIRAP pulse ordering. Numerical simulations for a superconducting transmon platform demonstrate that the optimized control pulses significantly enhance the target-state transfer fidelity and improve robustness against amplitude miscalibration and detuning drifts.
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.
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.
Stimulated Raman adiabatic passage (STIRAP) is a widely-used technique of coherent state-to-state manipulation for many applications in physics, chemistry, and beyond. The adiabatic evolution of the state involved in STIRAP, called adiabatic passage, guarantees its robustness against control errors, but also leads to problems of low efficiency and decoherence. Here we propose and experimentally demonstrate an alternative approach, termed stimulated Raman "user-defined" passage (STIRUP), where a parameterized state is employed for constructing desired evolutions to replace the adiabatic passage in STIRAP. The user-defined passages can be flexibly designed for optimizing different objectives for different tasks, e.g. minimizing leakage error. To experimentally benchmark its performance, we apply STIRUP to the task of coherent state transfer in a superconducting Xmon qutrit. We found that STIRUP completed the transfer more then four times faster than STIRAP with enhanced robustness, and achieved a fidelity of 99.5%, which is the highest among all recent experiments based on STIRAP and its variants. In practice, STIRUP differs from STIRAP only in the design of driving pulses; therefore, most existing applications of STIRAP can be readily implemented with STIRUP.