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光子驱动量子点制冷机

李唯 符婧 杨贇贇 何济洲

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光子驱动量子点制冷机

李唯, 符婧, 杨贇贇, 何济洲

Quantum dot refrigerator driven by photon

Li Wei, Fu Jing, Yang Yun-Yun, He Ji-Zhou
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  • 提出了由两个二能级量子点、一个光子库与两个导体端构成的光子驱动量子点制冷机模型. 基于主方程, 导出了制冷机的制冷率和制冷系数的表达式, 获得了制冷机处于紧耦合时所满足的条件. 接着, 数值模拟出该制冷机处于紧耦合和一般情况下制冷率与制冷系数之间的性能特征图, 确定了制冷机性能的优化范围. 最后, 以最大制冷率、最大制冷率下的制冷系数、最大制冷系数和最大制冷系数下的制冷率作为优化目标, 分析了光子库温度、跃迁系数和温比对制冷机性能的影响.
    A model of quantum dot refrigerator driven by photon, which consists of two two-level quantum dots, a photon reservoir and two leads, is proposed in this paper. Comparing with previous studies, we consider the transitions of electrons between different energy levels in a single quantum dot, which is more practical.Based on the theory of master equation and the assumption of weak coupling, we derive the expression of the cooling rate and the coefficient of performance of the refrigerator and obtain the condition of the tight coupling of the refrigerator operation. Next, we plot numerically the performance characteristic curves between the cooling rate and the coefficient of performance in the case of the tight coupling and in the general case. We find that the curves between the cooling rate and the coefficient of performance are opened loops for tight coupling, but they are closed loops in the general case. And we gain the conclusions that the refrigerator can be reversible under the condition of the tight coupling, while it can be irreversible in the general case. Then the optimally operating range of the refrigerator is determined. Finally, the effect of the temperature of the photon reservoir, transition coefficient, and temperature ratio on the performance of refrigerator under the conditions of the maximum cooling rate are studied, and also the coefficient of performance under the maximum cooling rate, the maximum coefficient of performanceand the cooling rate under the maximum coefficient of performanceare analyzed in detail.
      通信作者: 何济洲, hjzhou@ncu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11365015)资助的课题
      Corresponding author: He Ji-Zhou, hjzhou@ncu.edu.cn
    • Funds: Supported by the National Natural Science Foundations of China (Grant No. 11365015)
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    Giazotto F, Heikkila T T, Luukanen A, Savin A M, Pekola J P 2006 Rev. Mod. Phys. 78 217Google Scholar

    [2]

    Koumoto K, Mori T 2013 Thermoelectric Nanomaterials: Materials Design and Applications (Vol. 182) (Berlin: Springer Press) pp255-285

    [3]

    Maciá E 2015 Thermoelectric Materials: Advances and Applications (Jenny: Stanford Publishing)

    [4]

    Pichanusakorn P, Bandaru P 2010 Mater. Sci. Eng. R 67 19Google Scholar

    [5]

    Benenti G, Casati G, Saito K, Whitney R S 2017 Phys. Reports 694 1Google Scholar

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    Sothmann B, Sánchez R, Jordan A N 2014 Nanotechnology 26 032001Google Scholar

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    Sánchez R, Büttiker M 2011 Phys. Rev. B 83 085428Google Scholar

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    Dare A M, Lombardo P 2017 Phys. Rev. B 96 115414Google Scholar

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    Zhang Y C, Gin G X, Chen J C 2015 Phys. Rev. E 91 052118Google Scholar

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    Sothmann B, Sánchez R, Jordan A N, Büttiker M 2012 Phys. Rev. B 85 205301Google Scholar

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    Zhang Y C, Zhang X, Ye Z L, Gin G X, Chen J C 2017 Appl. Phys. Lett. 110 153501Google Scholar

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    Jordan A N, Sothmann B, Sánchez R, Buttiker M 2013 Phys. Rev. B 87 075312Google Scholar

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    Prance J R, Smith C G, Griffiths J P, Chorley S J, Anderson D, Jones G A C, Farrer I, Ritchie D A 2009 Phys. Rev. Lett. 102 146602Google Scholar

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    Sothmann B, Sánchez R, Jordan A N, Büttiker M 2013 N. J. Phys. 15 095021Google Scholar

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    Choi Y J, Jordan A N 2015 Physica E 74 465Google Scholar

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    Su S H, Zhang Y C, Chen J C, Shih T M 2016 Sci. Rep. 6 21425Google Scholar

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    Wohlman O E, Imry Y, Aharony A 2015 Phys. Rev. B 91 054302Google Scholar

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    Szukiewicz B, Eckern U, Wysokinski K I 2016 New J. Phys. 18 023050Google Scholar

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    Whitney R S, Sánchez R, Haupt F, Splettstoesser J 2016 Physica E 75 257Google Scholar

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    Lim J S, Sanchez D, Lopez R 2018 New J. Phys. 20 023038Google Scholar

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    Walldorf N, Jauho A P, Kaasbjerg K 2017 Phys. Rev. B 96 115415

    [22]

    Jiang J H, Entin-Wohlman O, Imry Y 2013 New J. Phys. 15 075021Google Scholar

    [23]

    Su H, Shi Z C, He J Z 2015 Chin. Phys. Lett. 32 100501Google Scholar

    [24]

    Lin Z B, Li W, Fu J, Yang Y Y, He J Z 2019 Chin. Phys. Lett. 36 060501Google Scholar

    [25]

    Josefsson M, Svilans A, Burke A M, Hoffmann E A, Fahlvik S, Thelander C, Leijnse M, Linke H 2018 Nature Nanotechnol. 13 920Google Scholar

    [26]

    Thierschmann H, Sanchez R, Sothmann B, Arnold F, Heyn C, Hansen W, Buhmann H, Molenkamp L W 2015 Nature Nanotechnol. 10 854Google Scholar

    [27]

    Roche B, Roulleau P, Ulien T J, Jompol Y, Farrer I, Ritchie D A, Glattli D C 2015 Nature Commun. 6 6738Google Scholar

    [28]

    Hartmann F, Pfeffer P, Hofling S, Kamp M, Worschech L 2015 Phys. Rev. Lett. 114 146805Google Scholar

    [29]

    Cleuren B, Rutten B, van den Broeck C 2012 Phys. Rev. Lett. 108 120603Google Scholar

    [30]

    Levy A, Alicki R, Kosloff R 2012 Phys. Rev. Lett. 109 248901Google Scholar

    [31]

    Wang J H, Lai Y M, Ye Z L, He J Z, Ma Y L, Liao Q H 2015 Phys. Rev. E 91 050102Google Scholar

    [32]

    van den Broeck C 2005 Phys. Rev. Lett. 95 190602Google Scholar

    [33]

    Yuan Y, Wang R, He J Z, Ma Y L, Wang J H 2014 Phys. Rev. E 90 052151Google Scholar

    [34]

    Sheng S Q, Tu Z C 2014 Phys. Rev. E 89 012129Google Scholar

  • 图 1  光子驱动量子点制冷机模型图

    Fig. 1.  A model of a quantum dot refrigerator driven by photon.

    图 2  紧耦合条件下制冷率与制冷系数在不同温度${T_{\rm{S}}}$下的关系

    Fig. 2.  The relation curves of the cooling rate and the coefficient of performance at different temperature ${T_{\rm{S}}}$ under the condition of tight coupling.

    图 3  紧耦合条件下制冷率与制冷系数在不同跃迁系数${\varGamma _{n{\rm{r}}}}$下的关系

    Fig. 3.  The relation curves of the cooling rate and the coefficient of performance at different transition coefficient ${\varGamma _{n{\rm{r}}}}$ under the condition of tight coupling.

    图 4  一般情况下制冷率与制冷系数在不同温度${T_{\rm{S}}}$下的关系

    Fig. 4.  The relation curves of the cooling rate and the coefficient of performance at different temperature ${T_{\rm{S}}}$ in the general case.

    图 5  一般情况下制冷率与制冷系数在不同跃迁系数${\varGamma _{n{\rm{r}}}}$下的关系

    Fig. 5.  The relation curves of the cooling rate and the coefficient of performanceat different transition coefficient ${\varGamma _{n{\rm{r}}}}$ in the general case.

    图 6  在不同温度${T_{\rm{S}}}$下, 两个优化性能参数${\dot Q}_{\rm{R}}^{\max }$${\eta ^{{Q_{\rm{R}}}}}$随温比的变化

    Fig. 6.  The curves of two optimal performance parameters ${\dot Q}_{\rm{R}}^{\max }$ and ${\eta ^{{Q_{\rm{R}}}}}$ changing with the temperature ratio at different temperature ${T_{\rm{S}}}$

    图 7  在不同跃迁系数${\varGamma _{n{\rm{r}}}}$下, 两个优化性能参数${\dot Q}_{\rm{R}}^{\max }$${\eta ^{{Q_{\rm{R}}}}}$随着温比的变化

    Fig. 7.  The curves of two optimal performance parameters ${\dot Q}_{\rm{R}}^{\max }$ and ${\eta ^{{Q_{\rm{R}}}}}$ changing with the temperature ratio at different transition coefficient ${\varGamma _{n{\rm{r}}}}$

    图 8  在不同温度${T_{\rm{S}}}$下, 两个优化性能参数${\dot Q}_{\rm{R}}^{\max }$${\eta ^{{Q_{\rm{R}}}}}$随温比的变化

    Fig. 8.  The curves of two optimalperformance parameters ${\dot Q}_{\rm{R}}^{\max }$ and ${\eta ^{{Q_{\rm{R}}}}}$ changing with the temperature ratio at different temperature ${T_{\rm{S}}}$.

    图 10  在不同温度${T_{\rm{S}}}$下, 两个优化性能参数${\eta ^{\max }}$${\dot Q}_{\rm{R}}^\eta $随温比的变化

    Fig. 10.  The curves of two optimal performance parameters ${\eta ^{\max }}$ and ${\dot Q}_{\rm{R}}^\eta $ changing with the temperature ratio at different temperature ${T_{\rm{S}}}$.

    图 9  在不同跃迁系数${\varGamma _{n{\rm{r}}}}$下, 两个优化性能参数${\dot Q}_{\rm{R}}^{\max }$${\eta ^{{Q_{\rm{R}}}}}$随着温比的变化

    Fig. 9.  The curves of two optimal performance parameters ${\dot Q}_{\rm{R}}^{\max }$ and ${\eta ^{{Q_{\rm{R}}}}}$ changing with the temperature ratio at different transition coefficient ${\varGamma _{n{\rm{r}}}}$.

  • [1]

    Giazotto F, Heikkila T T, Luukanen A, Savin A M, Pekola J P 2006 Rev. Mod. Phys. 78 217Google Scholar

    [2]

    Koumoto K, Mori T 2013 Thermoelectric Nanomaterials: Materials Design and Applications (Vol. 182) (Berlin: Springer Press) pp255-285

    [3]

    Maciá E 2015 Thermoelectric Materials: Advances and Applications (Jenny: Stanford Publishing)

    [4]

    Pichanusakorn P, Bandaru P 2010 Mater. Sci. Eng. R 67 19Google Scholar

    [5]

    Benenti G, Casati G, Saito K, Whitney R S 2017 Phys. Reports 694 1Google Scholar

    [6]

    Sothmann B, Sánchez R, Jordan A N 2014 Nanotechnology 26 032001Google Scholar

    [7]

    Sánchez R, Büttiker M 2011 Phys. Rev. B 83 085428Google Scholar

    [8]

    Dare A M, Lombardo P 2017 Phys. Rev. B 96 115414Google Scholar

    [9]

    Zhang Y C, Gin G X, Chen J C 2015 Phys. Rev. E 91 052118Google Scholar

    [10]

    Sothmann B, Sánchez R, Jordan A N, Büttiker M 2012 Phys. Rev. B 85 205301Google Scholar

    [11]

    Zhang Y C, Zhang X, Ye Z L, Gin G X, Chen J C 2017 Appl. Phys. Lett. 110 153501Google Scholar

    [12]

    Jordan A N, Sothmann B, Sánchez R, Buttiker M 2013 Phys. Rev. B 87 075312Google Scholar

    [13]

    Prance J R, Smith C G, Griffiths J P, Chorley S J, Anderson D, Jones G A C, Farrer I, Ritchie D A 2009 Phys. Rev. Lett. 102 146602Google Scholar

    [14]

    Sothmann B, Sánchez R, Jordan A N, Büttiker M 2013 N. J. Phys. 15 095021Google Scholar

    [15]

    Choi Y J, Jordan A N 2015 Physica E 74 465Google Scholar

    [16]

    Su S H, Zhang Y C, Chen J C, Shih T M 2016 Sci. Rep. 6 21425Google Scholar

    [17]

    Wohlman O E, Imry Y, Aharony A 2015 Phys. Rev. B 91 054302Google Scholar

    [18]

    Szukiewicz B, Eckern U, Wysokinski K I 2016 New J. Phys. 18 023050Google Scholar

    [19]

    Whitney R S, Sánchez R, Haupt F, Splettstoesser J 2016 Physica E 75 257Google Scholar

    [20]

    Lim J S, Sanchez D, Lopez R 2018 New J. Phys. 20 023038Google Scholar

    [21]

    Walldorf N, Jauho A P, Kaasbjerg K 2017 Phys. Rev. B 96 115415

    [22]

    Jiang J H, Entin-Wohlman O, Imry Y 2013 New J. Phys. 15 075021Google Scholar

    [23]

    Su H, Shi Z C, He J Z 2015 Chin. Phys. Lett. 32 100501Google Scholar

    [24]

    Lin Z B, Li W, Fu J, Yang Y Y, He J Z 2019 Chin. Phys. Lett. 36 060501Google Scholar

    [25]

    Josefsson M, Svilans A, Burke A M, Hoffmann E A, Fahlvik S, Thelander C, Leijnse M, Linke H 2018 Nature Nanotechnol. 13 920Google Scholar

    [26]

    Thierschmann H, Sanchez R, Sothmann B, Arnold F, Heyn C, Hansen W, Buhmann H, Molenkamp L W 2015 Nature Nanotechnol. 10 854Google Scholar

    [27]

    Roche B, Roulleau P, Ulien T J, Jompol Y, Farrer I, Ritchie D A, Glattli D C 2015 Nature Commun. 6 6738Google Scholar

    [28]

    Hartmann F, Pfeffer P, Hofling S, Kamp M, Worschech L 2015 Phys. Rev. Lett. 114 146805Google Scholar

    [29]

    Cleuren B, Rutten B, van den Broeck C 2012 Phys. Rev. Lett. 108 120603Google Scholar

    [30]

    Levy A, Alicki R, Kosloff R 2012 Phys. Rev. Lett. 109 248901Google Scholar

    [31]

    Wang J H, Lai Y M, Ye Z L, He J Z, Ma Y L, Liao Q H 2015 Phys. Rev. E 91 050102Google Scholar

    [32]

    van den Broeck C 2005 Phys. Rev. Lett. 95 190602Google Scholar

    [33]

    Yuan Y, Wang R, He J Z, Ma Y L, Wang J H 2014 Phys. Rev. E 90 052151Google Scholar

    [34]

    Sheng S Q, Tu Z C 2014 Phys. Rev. E 89 012129Google Scholar

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出版历程
  • 收稿日期:  2019-07-16
  • 修回日期:  2019-08-29
  • 上网日期:  2019-11-01
  • 刊出日期:  2019-11-20

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