Quantum Stirling heat engine with squeezed thermal reservoir

doi:10.1088/1674-1056/acc7f8

摘要/Abstract

摘要： We analyze the performance of a quantum Stirling heat engine (QSHE), using a two-level system and a harmonic oscillator as the working medium, that is in contact with a squeezed thermal reservoir and a cold reservoir. First, we derive closed-form expressions for the produced work and efficiency, which strongly depend on the squeezing parameter $r_{\rm h}$. Then, we prove that the effect of squeezing heats the working medium to a higher effective temperature, which leads to better overall performance. In particular, the efficiency increases with the degree of squeezing, surpassing the standard Carnot limit when the ratio of the temperatures of the hot and cold reservoirs is small. Furthermore, we derive the analytical expressions for the efficiency at maximum work and the maximum produced work in the high and low temperature regimes, and we find that at extreme temperatures the squeezing parameter $r_{\rm h}$ does not affect the performance of the QSHE. Finally, the performance of the QSHE depends on the nature of the working medium.

关键词: quantum heat engine, open systems, thermodynamics, performance characteristics

Abstract: We analyze the performance of a quantum Stirling heat engine (QSHE), using a two-level system and a harmonic oscillator as the working medium, that is in contact with a squeezed thermal reservoir and a cold reservoir. First, we derive closed-form expressions for the produced work and efficiency, which strongly depend on the squeezing parameter $r_{\rm h}$. Then, we prove that the effect of squeezing heats the working medium to a higher effective temperature, which leads to better overall performance. In particular, the efficiency increases with the degree of squeezing, surpassing the standard Carnot limit when the ratio of the temperatures of the hot and cold reservoirs is small. Furthermore, we derive the analytical expressions for the efficiency at maximum work and the maximum produced work in the high and low temperature regimes, and we find that at extreme temperatures the squeezing parameter $r_{\rm h}$ does not affect the performance of the QSHE. Finally, the performance of the QSHE depends on the nature of the working medium.

Key words: quantum heat engine, open systems, thermodynamics, performance characteristics

中图分类号: (Heat engines; heat pumps; heat pipes)

07.20.Pe

03.65.Yz (Decoherence; open systems; quantum statistical methods) 05.70.-a (Thermodynamics)

Nikolaos Papadatos. Quantum Stirling heat engine with squeezed thermal reservoir[J]. 中国物理B, 2023, 32(10): 100702-100702.

Nikolaos Papadatos. Quantum Stirling heat engine with squeezed thermal reservoir[J]. Chin. Phys. B, 2023, 32(10): 100702-100702.

参考文献

[1] Vinjanampathy S and Anders J 2016 Contemporary Physics 57 545
[2] Bimalendu N Roy 2002 Fundamentals of Classical and Statistical Thermodynamics, (John Wiley and Sons)
[3] Alicki R and Kosloff R 2018 Introduction to Quantum Thermodynamics: History and Prospects. In: Binder F., Correa L., Gogolin C., Anders J., Adesso G. (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol. 195, Springer
[4] Callen H B 1985 Thermodynamics and an Introduction to Thermostatistics Wiley: New York
[5] Yuen C K 1970 American Journal of Physics 38 246
[6] Callen H and Horwitz G 1971 American Journal of Physics 39 938
[7] Farias C, Pinto V A and Moya P S 2017 Sci. Rep. 7 17657
[8] Mosengeil K von 1907 Ann. Phys. (Leipzig) 327 867
[9] Planck M 1908 Ann. Phys. 331 1
[10] Einstein A 1907 Jahrbuch der Radioaktivität und Elektronik 4 411
[11] Ott H 1963 Zeitschrift für Physik 175 70
[12] Arzeliés H 1965 Il Nuovo Cimento B Series 10 40 333
[13] Landsberg P T 1966 Nature 212 571
[14] Cai H 2021 Eur. Phys. J. C 81 673
[15] Papadatos N and Anastopoulos C 2020 Phys. Rev. D 102 085005
[16] Cavalleri G and Salgarelli G 1969 Nuovo Cimento A 62 722
[17] Costa S S and Matsas G E A 1995 Phys. Lett. A 209 155
[18] Landsberg P T and Matsas G E A 1966 Phys. Lett. A 223 401
[19] Landsberg P T and Matsas G E A 2004 Physica A 340 92
[20] Chattopadhyay P and Paul G 2019 Sci. Rep. 9 16967
[21] Bruschi D E, Morris B and Fuentes I 2020 Phys. Lett. A 384 126601
[22] Papadatos N 2021 Int. J. Theor. Phys. 60 4210
[23] Xu H and Yung M H 2020 Phys. Lett. B 801 135201
[24] Gray F and Mann R B 2018 J. High Energ. Phys. 2018 174
[25] Nakamura T K 2009 Europhys. Lett. 88 20004
[26] Scovil H E D and Schulz-DuBois E O 1959 Phys. Rev. Lett. 2 262
[27] Gelbwaser-Klimovsky D, Alicki R and Kurizki G 2013 Phys. Rev. E 87 012140
[28] Alicki R 1979 J. Phys. A: Math. Gen. 12 L103
[29] Geva E and Kosloff R 1992 J. Chem. Phys. 96 3054
[30] Scully M O, Zubairy M S, Agarwal G S and Walther H 2003 Science 299 862
[31] Scully M O, Chapin K R, Dorfman K E, Kim M B and Svidzinsky A 2011 Proc. Natl. Acad. Sci. 108 15097
[32] Uzdin R 2016 Phys. Rev. Appl. 6 024004
[33] Watanabe G, Venkatesh B P, Talkner P and del Campo 2017 Phys. Rev. Lett. 118 050601
[34] Dann R, R and Kosloff R 2020 New J. Phys. 22 013055
[35] Feldmann T and Kosloff R 2012 Phys. Rev. E 85 051114
[36] Hammam K, Hassouni Y, Fazio R and Manzano G 2021 New J. Phys. 23 043024
[37] Zhang T, Liu W T, Chen P X and Li C Z 2007 Phys. Rev. A 75 062102
[38] Wang H, Liu S and He J 2009 Phys. Rev. E 79 041113
[39] Dillenschneider R and Lutz E 2009 Europhys. Lett. 88 50003
[40] He J Z, He X and Zheng J 2012 Chin. Phys. B 21 050303
[41] Beau M, Jaramillo J and Del Campo A 2016 Entropy 18 168
[42] Li J, Fogarty T, Campbell S, Chen X and Busch T 2018 New J. Phys. 20 015005
[43] Chen, YY, Watanabe G, Yu, YC and et al 2019 npj Quantum Inf. 5 88
[44] Watanabe G, Venkatesh B P, Talkner P, Hwang M J and del Campo A 2020 Phys. Rev. Lett. 124 210603
[45] Jussiau E, Bresque L, Aufféves A, Murch K W and Jordan A N 2022 arXiv: 2208.07225 [quant-ph]
[46] Mehta V and Johal R S 2017 Phys. Rev. E 96 032110
[47] Peña F J, González A, Nunez A S, Orellana P A, Rojas R G and Vargas P 2017 Entropy 19 639
[48] Alvarado Barrios G, Peña FJ, Albarrán-Arriagada F, Vargas P and Retamal J C 2018 Entropy 20 767
[49] Erdman P A, Cavina V, Fazio R, Taddei F and Giovannetti V 2019 New J. Phys. 21 103049
[50] Deffner S 2018 Entropy 20 875
[51] Smith Z, Pal P S and Deffner S 2020 Journal of Non-Equilibrium Thermodynamics 45 305
[52] Myers N M and Deffner S 2021 PRX Quantum 2 040312
[53] Halpern N Y, White C D, Gopalakrishnan S and Refael G 2019 Phys. Rev. B 99 024203
[54] Scully M O 2002 Phys. Rev. Lett. 88 050602
[55] Abah O and Lutz E 2017 Europhys. Lett. 118 40005
[56] Erdman P A and Noé F 2022 npj Quantum Inf. 8 1
[57] Abah O and Lutz E 2014 Europhys. Lett. 106 20001
[58] Quan H T, Zhang P and Sun C P 2006 Phys. Rev. E 73 036122
[59] Li H, Zou J, Yu W L, Xu B M, Li J G and Shao B 2014 Phys. Rev. E 89 052132
[60] Hardal A and Müstecaplhoǧlu Ö 2015 Sci. Rep. 5 12953
[61] Dillenschneider R and Lutz E 2009 EPL 88 50003
[62] Huang X L, Wang T and Yi X X 2012 Phys. Rev. E 86 051105
[63] Roßnagel J, Abah O, Schmidt-Kaler F, Singer K and Lutz E 2014 Phys. Rev. Lett. 112 030602
[64] Correa L A, Palao J P, Alonso D and Adesso G 2014 Sci. Rep. 4 3949
[65] Long R and Liu W 2015 Phys. Rev. E 91 062137
[66] Klaers J, Faelt S, Imamoglu A and Togan E 2017 Phys. Rev. X 7 031044
[67] Zhang Y, Guo J and Chen J 2020 Quantum Inf. Process 19 268
[68] Zhang Y 2020 Physica A 559 125083
[69] Manzano G, Galve F, Zambrini R and Parrondo J M R 2016 Phys. Rev. E 93 052120
[70] Leff H S 1987 Am. J. Phys. 55 602
[71] Curzon F L and Ahlborn B 1975 Am. J. Phys. 43 22
[72] Quan H T, Liu Y X, Sun C P and Nori F 2007 Phys. Rev. E 76 031105
[73] Çakmak S 2022 J. Opt. Soc. Am. B 39 1209
[74] Scully M O and Zubairy M S 1997 Quantum Opt. (Cambridge University Press)
[75] Dung H T and Khanh N Q 1997 J. Mod. Opt. 44 1497
[76] Dung H T, Joshi A and Knöll L 2009 J. Mod. Opt. 45 1067
[77] Chen J and Yan Z 1996 J. Phys. D: Appl. Phys. 29 987
[78] Wu F, Chen L, Sun F, Wu C and Zhu Y 1998 Energy Conversion and Management 39 733
[79] Kaushik S C and Kumar S 2000 Energy 25 989
[80] Sisman A and Saygin H 2001 Phys. Scr. 63 263
[81] Saygin H and Sisman A 2001 J. Appl. Phys. 90 3086
[82] Huang Z, Wu F, Chen L, Wu C and Guo F 2002 J. Therm. Sci. 11 193
[83] Ahmadi M H, Sayyaadi H and Hosseinzadeh H 2014 Heat Trans. Asian Res. 44 347
[84] Ahmadi M H, Ahmadi M A and Pourfayaz F 2015 Eur. Phys. J. Plus 130 190
[85] Rao R V, More K C, Taler J and Ocloń P 2016 Sadhana 41 1321
[86] Zakine R, Solon A, Gingrich T and Van Wijland F 2017 Entropy 19 193
[87] Yong Y, Lingen C and Feng W 2017 Eur. Phys. J. Plus 132 45
[88] Yin Y, Chen L and Wu F 2018 Physica A 503 58
[89] Enock O, Emmanuel U and Oghenetega A 2020 arXiv: 2010.01581 [quant-ph]
[90] Raja S H, Maniscalco S, Paraoanu G S, Pekola J P and Gullo N L 2021 New J. Phys. 23 033034
[91] Cruz C, Rastegar-Sedehi H, Anka M F, Oliveira, T R and Reis M 2023 Quantum Sci. Technol. 8 035010
[92] Purkait C and Biswas A 2022 Phys. Lett. A 442 128180
[93] Xiao Y, Liu D, He J, Liu W and Wang J 2022 arXiv: 2205.13290 [quant-ph]
[94] Alicki R and Gelbwaser-Klimovsky D 2015 New J. Phys. 17 115012
[95] Huang X L, Wang T and Yi X X 2012 Phys. Rev. E 86 051105
[96] Agarwalla B K, Jiang J H and Segal D 2017 Phys. Rev. B 96 104304
[97] Galve F and Lutz E 2009 Phys. Rev. A 79 055804
[98] Zagoskin A M, Il'ichev E and Nori F 2012 Phys. Rev. A 85 063811
[99] Singh V and Müstecaplhoǧlu O E 2020 Phys. Rev. E 102 062123
[100] Breuer H P and Petruccione F P 2007 The Theory of Open Quantum Systems (Oxford University Press)
[101] Banerjee S and Srikanth R 2008 Eur. Phys. J. D 46 335
[102] Ren J, Hänggi P and Li B 2010 Phys. Rev. Lett. 104 170601
[103] Chen T, Wang X B and Ren J 2013 Phys. Rev. B 87 144303
[104] Wang C, Ren J and Cao J 2017 Phys. Rev. A 95 023610
[105] Wang Z, Wang L, Chen J, Chen W and Ren J 2022 Front. Phys. 17 13201
[106] Kieu T D 2004 Phys. Rev. Lett. 93 140403
[107] Van den Broeck C 2005 Phys. Rev. Lett. 95 190602
[108] Abah O, Roßnagel J, Jacob G, Deffner S, Schmidt-Kaler F, Singer K and Lutz E 2012 Phys. Rev. Lett. 109 203006
[109] Assis R J, Sales J S, Cunha J A R and Almeida N G 2020 Phys. Rev. E 102 052131
[110] Assis R J, Sales J S, Mendes U C and Almeida N G 2021 J. Phys. B: At. Mol. Opt. Phys. 54 095501
[111] Arisoy O, Hsiang J T and Hu B L 2022 Phys. Rev. E 105 014108
[112] Rezek Y and Kosloff R 2006 New J. Phys. 8 83
[113] Marian P and Marian T A 1993 Phys. Rev. A 47 4487
[114] Asboth J K, Calsamiglia J and Ritsch H 2005 Phys. Rev. Lett. 94 173602
[115] Lin B and Chen J 2005 J. Phys. A: Math. Gen. 38 69
[116] Huang X L and Wang L C and Yi X X 2013 Phys. Rev. E 87 012144
[117] Thomas G and Johal R S 2011 Phys. Rev. E 83 031135