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    Quantum Stirling heat engine based on two-qubit quantum Rabi model with spin-spin coupling

    Luxin Xu1, Chunfeng Wu2,*, and Changliang Ren1,3,†

    • 1Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, Xiangjiang-Laboratory, Institute of Interdisciplinary Studies and Department of Physics, Hunan Normal University, Changsha 410081, China
    • 2Science, Mathematics and Technology, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
    • 3Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, Hunan Normal University, Changsha 410081, China

    • *Contact author: chunfeng_wu@sutd.edu.sg
    • †Contact author: renchangliang@hunnu.edu.cn

    Phys. Rev. A 112, 032226 – Published 26 September, 2025

    DOI: https://doi.org/10.1103/zqbv-j3jv

    Abstract

    Enhancing the efficiency of quantum heat engines (QHEs) is crucial for advancing fundamental research and quantum technologies. We explore a quantum Stirling cycle using a two-qubit quantum Rabi model with spin-spin coupling as a working medium. We propose parameter optimization strategies to maximize the efficiency of the heat engine, as there are multiple ways for the effective coupling constant to move toward its critical point. In the normal phase, enhancing the temperature ratio of hot-to-cold reservoirs and spin-mode coupling strength can boost QHE efficiency, while increasing the spin-spin coupling strength will reduce the efficiency. In the superradiant phase, when the temperature ratio is held constant, lowering the cold reservoir temperature moves the efficiency closer to the Carnot limit. Furthermore, when the cold reservoir temperature is fixed, increasing the ratio between spin-mode coupling and mode frequency will improve the efficiency. While the spin-spin coupling is fixed, the cycle with a higher-temperature ratio between the hot and cold reservoirs demands a higher ratio between the spin-mode coupling and mode frequency to improve efficiency. Our work deepens the understanding of QHE performance under various conditions and provides operative methods for optimizing the efficiency of QHE.

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