Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir

doi:10.1088/1674-1056/aca207

中国物理B ›› 2023, Vol. 32 ›› Issue (3): 30503-030503.doi: 10.1088/1674-1056/aca207

Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir

Haoguang Liu(刘浩广)^1,2, Jizhou He(何济洲)¹, and Jianhui Wang(王建辉)^1,3,†

1 Department of Physics, Nanchang University, Nanchang 330031, China;
2 College of Science and Technology, Nanchang Aeronautical University, Nanchang 332020, China;
3 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China

收稿日期:2022-07-18 修回日期:2022-10-12 接受日期:2022-11-11 出版日期:2023-02-14 发布日期:2023-02-14
通讯作者: Jianhui Wang E-mail:wangjianhui@ncu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11875034) and the Opening Project of Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology.

Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir

Haoguang Liu(刘浩广)^1,2, Jizhou He(何济洲)¹, and Jianhui Wang(王建辉)^1,3,†

1 Department of Physics, Nanchang University, Nanchang 330031, China;
2 College of Science and Technology, Nanchang Aeronautical University, Nanchang 332020, China;
3 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China

Received:2022-07-18 Revised:2022-10-12 Accepted:2022-11-11 Online:2023-02-14 Published:2023-02-14
Contact: Jianhui Wang E-mail:wangjianhui@ncu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11875034) and the Opening Project of Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology.

摘要/Abstract

摘要： We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation — Carnot refrigeration cycle, employing a spin-$1/2$ system as the working substance. The thermal machine is alternatively driven by a hot boson bath of inverse temperature $\beta_{\rm h}$ and a cold boson bath at inverse temperature $\beta_{\rm c}(>\beta_{\rm h})$. While for the engine model the hot bath is constructed to be squeezed, in the refrigeration cycle the cold bath is established to be squeezed, with squeezing parameter $r$. We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators. We find that, in the high-temperature limit, the efficiency at maximum power is bounded by the analytical value $\eta_+=1-\sqrt{\text{sech}(2r)(1-\eta_{\rm C})}$, and the coefficient of performance at the maximum figure of merit is limited by $ \varepsilon_+=\frac{\sqrt{\text{sech}(2r)(1+\varepsilon_{\rm C}})}{\sqrt{\text{sech}(2r)(1+\varepsilon_{\rm C})-\varepsilon_{\rm C}}}-1$, where $\eta_{\rm C}=1-\beta_{\rm h}/\beta_{\rm c}$ and $\varepsilon_{\rm C}=\beta_{\rm h}/(\beta_{\rm c}-\beta_{\rm h})$ are the respective Carnot values of the engines and refrigerators. These analytical results are identical to those obtained from the Carnot engines based on harmonic systems, indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.

关键词: performance optimization, squeezed bath, quantum Carnot engine, quantum Carnot refrigerator

Abstract: We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation — Carnot refrigeration cycle, employing a spin-$1/2$ system as the working substance. The thermal machine is alternatively driven by a hot boson bath of inverse temperature $\beta_{\rm h}$ and a cold boson bath at inverse temperature $\beta_{\rm c}(>\beta_{\rm h})$. While for the engine model the hot bath is constructed to be squeezed, in the refrigeration cycle the cold bath is established to be squeezed, with squeezing parameter $r$. We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators. We find that, in the high-temperature limit, the efficiency at maximum power is bounded by the analytical value $\eta_+=1-\sqrt{\text{sech}(2r)(1-\eta_{\rm C})}$, and the coefficient of performance at the maximum figure of merit is limited by $ \varepsilon_+=\frac{\sqrt{\text{sech}(2r)(1+\varepsilon_{\rm C}})}{\sqrt{\text{sech}(2r)(1+\varepsilon_{\rm C})-\varepsilon_{\rm C}}}-1$, where $\eta_{\rm C}=1-\beta_{\rm h}/\beta_{\rm c}$ and $\varepsilon_{\rm C}=\beta_{\rm h}/(\beta_{\rm c}-\beta_{\rm h})$ are the respective Carnot values of the engines and refrigerators. These analytical results are identical to those obtained from the Carnot engines based on harmonic systems, indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.

Key words: performance optimization, squeezed bath, quantum Carnot engine, quantum Carnot refrigerator

中图分类号: (Nonequilibrium and irreversible thermodynamics)

05.70.Ln

Haoguang Liu(刘浩广), Jizhou He(何济洲), and Jianhui Wang(王建辉). Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir[J]. 中国物理B, 2023, 32(3): 30503-030503.

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Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir

Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir

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