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arXiv:1402.1299 · Physical Review A

Three-level superadiabatic quantum driving

Luigi Giannelli, E. Arimondo

Published Mar 17, 2014• 104 citations
arXivHTMLPDF

Abstract

The superadiabatic quantum driving, producing a perfect adiabatic transfer on a given Hamitonian by introducing an additional Hamiltonian, is theoretically analysed for transfers within a three-level system. Our starting point is the stimulated Raman adiabatic passage, realized through different schemes of laser pulses. We determine the superadiabatic correction for each scheme. The fidelity, robustness and transfer time of all the superadiabatic transfer schemes are discussed. We derive that all superadiabatic corrections are based on a $π$- (or near-$π$)-area pulse coupling between the initial and final states. The benefits in the protocol robustness overcome the difficulties associated to the actual implementation of the three-level superadiabatic transfer.

DOI
10.1103/physreva.89.033419

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The superadiabatic quantum driving, producing a perfect adiabatic transfer on a given Hamitonian by introducing an additional Hamiltonian, is theoretically analysed for transfers within a three-level system. Our starting point is the stimulated Raman adiabatic passage, realized through different schemes of laser pulses. We determine the superadiabatic correction for each scheme. The fidelity, robustness and transfer time of all the superadiabatic transfer schemes are discussed. We derive that all superadiabatic corrections are based on a πππ- (or near-πππ)-area pulse coupling between the initial and final states. The benefits in the protocol robustness overcome the difficulties associated to the actual implementation of the three-level superadiabatic transfer.
Abstract In many quantum technologies adiabatic processes are used for coherent quantum state operations, offering inherent robustness to errors in the control parameters. The main limitation is the long operation time resulting from the requirement of adiabaticity. The superadiabatic method allows for faster operation, by applying counterdiabatic driving that corrects for excitations resulting from the violation of the adiabatic condition. In this article we show how to construct the counterdiabatic Hamiltonian in a system with forbidden transitions by using two-photon processes and how to correct for the resulting time-dependent ac-Stark shifts in order to enable population transfer with unit fidelity. We further demonstrate that superadiabatic stimulated Raman passage can realize a robust unitary NOT-gate between the ground state and the second excited state of a three-level system. The results can be readily applied to a three-level transmon with the ladder energy level structure.
Reaching a given target quantum state with high fidelity and fast operation speed close to the quantum limit represents an important goal in quantum information science. Here we experimentally demonstrate superadiabatic quantum driving to achieve population transfer in a three-level solid-state spin system at ambient conditions. Starting from traditional stimulated Raman adiabatic passage (STIRAP), our approach implements superadiabatic corrections to the STIRAP Hamiltonian with several pulse shapes, including the paradigmatic Gaussian shapes and trigonometric pulse shapes that guarantee an operation speed equal to the quantum limit. It requires no intense microwave pulses or long transfer times and shows an enhanced robustness against pulse imperfections. Thereby, these results might provide a useful tool for quantum information processing and the coherent manipulation of quantum systems.
Abstract Stimulated Raman adiabatic passage (STIRAP) is a widely used technique for efficient population transfer between quantum states. However, the adiabatic nature of STIRAP requires slow evolution, leading to long operation times, which limits its practical applications. The superadiabatic method has been introduced to accelerate the STIRAP process, but it often necessitates additional couplings between the initial and target states, which may not be available in the original Hamiltonian. In this work, we present a novel approach to implement superadiabatic STIRAP (sa-STIRAP) between dressed states in a three-level quantum system. By modulating the amplitude and phase of the original driving fields, the initial and target states in dressed-state space can be effectively coupled. This approach provides a practical means of realizing sa-STIRAP in experimental setups, making it convenient to accelerate adiabatic quantum state transfer.
Stimulated Raman adiabatic passage (STIRAP) and its superadiabatic variant (sa-STIRAP) are pivotal techniques for high-fidelity quantum state transfer. However, STIRAP is inherently slow, while sa-STIRAP often requires additional, experimentally challenging couplings. Recent progress has shown that implementing these protocols in the dressed-state space can overcome these limitations by modulating the amplitude and phase of native driving fields, thereby enabling efficient population transfer without extra couplings. Nevertheless, the robustness of these dressed-state protocols against decoherence remains unclear. In this work, we investigate the decoherence resilience of both STIRAP and sa-STIRAP within the dressed-state framework. Through numerical simulations, we demonstrate that they exhibit significantly enhanced robustness to environmental noise compared to their standard three-level counterparts. Our results highlight the potential of dressed-state-based protocols for achieving robust, high-fidelity quantum state transfer in noisy environments.
Shortcuts to adiabaticity in various quantum systems have attracted much attention with their wide applications in quantum information processing and quantum control. In this paper, we concentrate on a stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counterdiabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counterdiabatic driving along with the unitary transformation and eventually modify the pump and Stokes pulses for achieving fast and high-fidelity population transfer. The required laser intensity and stability against parameter variation are further discussed, to demonstrate the advantage of shortcuts to adiabaticity.
Accurate control of a quantum system is a fundamental requirement in many areas of modern science ranging from quantum information processing to high-precision measurements. A significantly important goal in quantum control is to prepare a desired state as fast as possible with sufficiently high fidelity allowed by available resources and experimental constraints. Stimulated Raman adiabatic passage (STIRAP) is a robust way to realize high-fidelity state transfer but it requires a sufficiently long operation time to satisfy the adiabatic criteria. We here theoretically propose and then experimentally demonstrate a shortcut-to-adiabatic protocol to speed up the STIRAP. By modifying the shapes of the Raman pulses, we experimentally realize a fast and high-fidelity stimulated Raman shortcut-to-adiabatic passage that is robust against control parameter variations. The all-optical, robust, and fast protocol demonstrated here provides an efficient and practical way to control quantum systems.