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Chin. Phys. B, 2020, Vol. 29(8): 080504    DOI: 10.1088/1674-1056/ab973b
Special Issue: SPECIAL TOPIC — Phononics and phonon engineering
SPECIAL TOPIC—Phononics and phonon engineering Prev   Next  

A polaron theory of quantum thermal transistor in nonequilibrium three-level systems

Chen Wang(王晨)1, Da-Zhi Xu(徐大智)2
1 Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
2 School of Physics and Center for Quantum Technology Research, Beijing Institute of Technology, Beijing 100081, China

We investigate the quantum thermal transistor effect in nonequilibrium three-level systems by applying the polaron-transformed Redfield equation combined with full counting statistics. The steady state heat currents are obtained via this unified approach over a wide region of system-bath coupling, and can be analytically reduced to the Redfield and nonequilibrium noninteracting blip approximation results in the weak and strong coupling limits, respectively. A giant heat amplification phenomenon emerges in the strong system-bath coupling limit, where transitions mediated by the middle thermal bath are found to be crucial to unravel the underlying mechanism. Moreover, the heat amplification is also exhibited with moderate coupling strength, which can be properly explained within the polaron framework.

Keywords:  quantum transport      open systems      nonequilibrium and irreversible thermodynamics      phonons or vibrational states in low-dimensional structures and nanoscale materials  
Received:  26 March 2020      Revised:  26 May 2020      Accepted manuscript online: 
PACS:  05.60.Gg (Quantum transport)  
  03.65.Yz (Decoherence; open systems; quantum statistical methods)  
  05.70.Ln (Nonequilibrium and irreversible thermodynamics)  
  63.22.-m (Phonons or vibrational states in low-dimensional structures and nanoscale materials)  

Project supported by the National Natural Science Foundation of China (Grant Nos. 11704093 and 11705008) and Beijing Institute of Technology Research Fund Program for Young Scholars, China.

Corresponding Authors:  Chen Wang, Da-Zhi Xu     E-mail:;

Cite this article: 

Chen Wang(王晨), Da-Zhi Xu(徐大智) A polaron theory of quantum thermal transistor in nonequilibrium three-level systems 2020 Chin. Phys. B 29 080504

[1] Clausius R 1879 The Mechanical Theory of Heat (London:MacMillan)
[2] Esposito M, Ochoa M A and Galperin M 2015 Phys. Rev. Lett. 114 080602
[3] Katz G and Kosloff R 2016 Entropy 18 186
[4] Chen X B and Duan W H 2015 Acta Phys. Sin. 64 186302(in Chinese)
[5] Benenti G, Casati G, Saito K and Whitney R S 2017 Phys. Rep. 694 1
[6] Segal D 2008 Phys. Rev. Lett. 101 260601
[7] Ren J, Hanggi P and Li B 2010 Phys. Rev. Lett. 104 170601
[8] Micadei K, Peterson J P S, Souza A M, Sarthour R S, Oliveira I S, Landi G T, Batalhao T B, Serra R M and Lutz E 2019 Nat. Comm. 10 2456
[9] Wang L and Li B 2007 Phys. Rev. Lett. 99 177208
[10] Cui L, Jeong W H, Hur S H, Matt M, Klockner J C, Pauly F, Nielaba P, Cuevas J C, Meyhofer E and Reddy P 2017 Science 355 1192
[11] Segal D 2017 Science 355 1125
[12] Li B 2006 Appl. Phys. Lett. 88 143501
[13] Li N B, Ren J, Wang L, Zhang G, Hanggi P and Li B 2012 Rev. Mod. Phys. 84 1045
[14] He D H, Buyukdagli S and Hu B 2009 Phys. Rev. B 80 104302
[15] He D H, Ai B Q, Chan H K and Hu B 2010 Phys. Rev. E 81 041131
[16] Chan H K, He D H and Hu B 2014 Phys. Rev. E 89 052126
[17] Joulain K, Drevillon K, Ezzahri Y and Ordonez-Miranda J 2016 Phys. Rev. Lett. 116 200601
[18] Guo B Q, Liu T and Yu C S 2018 Phys. Rev. E 98 022118
[19] Guo B Q, Liu T and Yu C S 2019 Phys. Rev. E 99 032112
[20] Du J Y, Sheng W, Su S H and Chen J C 2019 Phys. Rev. E 99 062123
[21] Wang C, Chen X M, Sun K W and Ren J 2018 Phys. Rev. A 97 052112
[22] Liu H, Wang C, Wang L Q and Ren J 2019 Phys. Rev. E 99 032114
[23] Jiang J H, Kulkarni M, Segal D and Imary Y 2015 Phys. Rev. B 92 045309
[24] Su S H, Zhang Y C, Andresen B and Chen J C arXiv:1811.02400
[25] Scovil H E D and Schulz-DuBois E O 1959 Phys. Rev. Lett. 2 262
[26] Quan H T, Liu Y X, Sun C P and Nori F 2007 Phys. Rev. E 76 031105
[27] Boukobza E and Tannor D J 2007 Phys. Rev. Lett. 98 240601
[28] Krause T, Brandes T, Esposito M and Shaller G 2015 J. Chem. Phys. 142 134106
[29] Xu D Z, Wang C, Zhao Y and Cao J 2016 New J. Phys. 18 023003
[30] Li S W, Kim M B, Agarwal G S and Scully M O 2017 Phys. Rev. A 96 063806
[31] Segal D 2018 Phys. Rev. E 97 052145
[32] Kilgour M and Segal D 2018 Phys. Rev. E 98 012117
[33] Friedman H M and Segal D 2019 Phys. Rev. E 100 062112
[34] Wang C, Ren J and Cao J 2015 Sci. Rep. 5 11787
[35] Wang C, Ren J and Cao J 2017 Phys. Rev. A 95 023610
[36] Segal D and Nitzan A 2005 Phys. Rev. Lett. 94 034301
[37] Segal D 2006 Phys. Rev. B 73 205415
[38] Nicolin L and Segal D 2011 J. Chem. Phys. 135 164106
[39] Nicolin L and Segal D 2011 Phys. Rev. B 84 161414
[40] Scully M O and Zubairy M S 1997 Quantum Optics (Cambridge:Cambridge University Press)
[41] Tscherbul T V and Brumer P 2014 Phys. Rev. Lett. 113 113601
[42] Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A and Zwerger W 1987 Rev. Mod. Phys. 59 1
[43] Jang Seogjoo, Berkelbach T C and Reichman D 2013 New J. Phys. 15 105020
[44] Nazir A 2009 Phys. Rev. Lett. 103 146404
[45] Xu D Z and Cao J 2016 Frontiers of Physics 11 110308
[46] Qin M, Wang C Y, Cui H T and Yi X X 2019 Phys. Rev. A 99 032111
[47] The component frequencies are given by ω={0,±Λ}, Λ=2√(δε)2 +(η△)2. For α=x, the projecting operators are Px(0)=sin θ(|+>< +|-|-><-|), Px(Λ)=cos θ|->< +|, and Px(-Λ)=[Px(Λ)]†. While for α=y, the operators become Py(0)=0, Py(Λ)=i, and Py(-Λ)=-i.
[48] The component frequencies are given by ω={E+, E-} with E+=ε+√(δε)2 +(η△)2 and E-=ε -√(δε)2 +(η△)2. For u=l, the projecting operators are Ŝl(E+)=cos θ/2|0>< +|and Ŝl(E-)=-sin θ/2|0><-|. While for u=r, the operators are Ŝr(E+)=sin θ/2|0><+|and Ŝr(E-)=cos θ/2|0><-|.
[49] Friedman H M, Agarwalla B K and Segal D 2018 New J. Phys. 20 083026
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