Quantum and classical dynamics of a three-mode absorption refrigerator

Stefan Nimmrichter1, Jibo Dai1,2, Alexandre Roulet1,3, and Valerio Scarani1,4

1Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
2Data Storage Institute, A*STAR, Singapore
3Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
4Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


We study the quantum and classical evolution of a system of three harmonic modes interacting via a trilinear Hamiltonian. With the modes prepared in thermal states of different temperatures, this model describes the working principle of an absorption refrigerator that transfers energy from a cold to a hot environment at the expense of free energy provided by a high-temperature work reservoir. Inspired by a recent experimental realization with trapped ions, we elucidate key features of the coupling Hamiltonian that are relevant for the refrigerator performance. The coherent system dynamics exhibits rapid effective equilibration of the mode energies and correlations, as well as a transient enhancement of the cooling performance at short times. We find that these features can be fully reproduced in a classical framework.

► BibTeX data

► References

[1] M. Horodecki and J. Oppenheim, Nat. Commun. 4, 2059 (2013).

[2] P. Skrzypczyk, A. J. Short, and S. Popescu, Nat. Commun. 5, 4185 (2014).

[3] M. O. Scully, M. S. Zubairy, G. S. Agarwal, and H. Walther, Science 299, 862 (2003).

[4] R. Dillenschneider and E. Lutz, Europhys. Lett. 88, 50003 (2009).

[5] J. Roßnagel, O. Abah, F. Schmidt-Kaler, K. Singer, and E. Lutz, Phys. Rev. Lett. 112, 030602 (2014).

[6] L. A. Correa, J. P. Palao, D. Alonso, and G. Adesso, Sci. Rep. 4, 3949 (2014).

[7] P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Phys. Rev. X 7, 021003 (2017).

[8] W. Niedenzu, V. Mukherjee, A. Ghosh, A. G. Kofman, and G. Kurizki, (2017), arXiv:1703.02911.

[9] A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Europhys. Lett. 67, 565 (2004).

[10] P. Talkner, E. Lutz, and P. Hänggi, Phys. Rev. E 75, 050102 (2007).

[11] M. Campisi, P. Hänggi, and P. Talkner, Rev. Mod. Phys. 83, 771 (2011).

[12] A. J. Roncaglia, F. Cerisola, and J. P. Paz, Phys. Rev. Lett. 113, 250601 (2014).

[13] P. Talkner and P. Hänggi, Phys. Rev. E 93, 022131 (2016).

[14] E. Geva and R. Kosloff, J. Chem. Phys. 104, 7681 (1996).

[15] D. Venturelli, R. Fazio, and V. Giovannetti, Phys. Rev. Lett. 110, 256801 (2013).

[16] R. Kosloff and A. Levy, Annu. Rev. Phys. Chem. 65, 365 (2014).

[17] A. Mari, A. Farace, and V. Giovannetti, J. Phys. B 48, 175501 (2015).

[18] P. P. Hofer, J.-R. Souquet, and A. A. Clerk, Phys. Rev. B 93, 041418 (2016a).

[19] K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016).

[20] M. T. Mitchison, M. Huber, J. Prior, M. P. Woods, and M. B. Plenio, Quantum Sci. Technol. 1, 015001 (2016).

[21] P. P. Hofer, M. Perarnau-Llobet, J. B. Brask, R. Silva, M. Huber, and N. Brunner, Phys. Rev. B 94, 235420 (2016b).

[22] B. Karimi and J. P. Pekola, Phys. Rev. B 94, 184503 (2016).

[23] A. Roulet, S. Nimmrichter, J. Arrazola, S. Seah, and V. Scarani, Phys. Rev. E 95, 062131 (2017).

[24] U. Bissbort, C. Teo, C. Guo, G. Casati, G. Benenti, and D. Poletti, Phys. Rev. E 95, 062143 (2017).

[25] K. Zhang and W. Zhang, Phys. Rev. A 95, 053870 (2017).

[26] B. Reid, S. Pigeon, M. Antezza, and G. De Chiara, (2017), arXiv:1708.07435.

[27] A. Ü. C. Hardal, N. Aslan, C. M. Wilson, and Ö. E. Müstecaplıoğlu, (2017), arXiv:1708.01182.

[28] A. Mu, B. K. Agarwalla, G. Schaller, and D. Segal, (2017), arXiv:1709.02835.

[29] J. P. Palao, R. Kosloff, and J. M. Gordon, Phys. Rev. E 64, 056130 (2001).

[30] N. Linden, S. Popescu, and P. Skrzypczyk, Phys. Rev. Lett. 105, 130401 (2010).

[31] A. Levy and R. Kosloff, Phys. Rev. Lett. 108, 070604 (2012).

[32] J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, J. Phys. A Math. Theor. 49, 143001 (2016).

[33] G. Maslennikov, S. Ding, R. Hablutzel, J. Gan, A. Roulet, S. Nimmrichter, J. Dai, V. Scarani, and D. Matsukevich, (2017), arXiv:1702.08672.

[34] D. F. Walls and R. Barakat, Phys. Rev. A 1, 446 (1970).

[35] G. P. Agrawal and C. L. Mehta, J. Phys. A , 607.

[36] R. Gambini, Phys. Rev. A 15, 1157 (1977).

[37] A. Levy and R. Kosloff, Europhys. Lett. 107, 20004 (2014).

[38] J. O. González, L. A. Correa, G. Nocerino, J. P. Palao, D. Alonso, and G. Adesso, (2017), arXiv:1707.09228.

[39] P. P. Hofer, M. Perarnau-Llobet, L. D. M. Miranda, G. Haack, R. Silva, J. B. Brask, and N. Brunner, (2017), arXiv:1707.09211.

[40] R. Bonifacio and G. Preparata, Phys. Rev. A 2, 336 (1970).

[41] C. Gogolin and J. Eisert, Rep. Prog. Phys. 79, 56001 (2016).

[42] N. Brunner, N. Linden, S. Popescu, and P. Skrzypczyk, Phys. Rev. E 85, 051117 (2012).

[43] J. B. Brask and N. Brunner, Phys. Rev. E 92, 062101 (2015).

[44] M. T. Mitchison, M. P. Woods, J. Prior, and M. Huber, New J. Phys. 17, 115013 (2015).

[45] M. Kulkarni, K. L. Tiwari, and D. Segal, Phys. Rev. B 86, 155424 (2012).

[46] T. Farrelly, F. G. S. L. Brandão, and M. Cramer, Phys. Rev. Lett. 118, 140601 (2017).

[47] N. Erez, G. Gordon, M. Nest, and G. Kurizki, Nature 452, 724 (2008).

[48] R. J. Glauber, Quantum Theory of Optical Coherence (Wiley-VCH, 2007).

[49] R. V. Jensen and R. Shankar, Phys. Rev. Lett. 54, 1879 (1985).

[50] H. Tasaki, Phys. Rev. Lett. 80, 1373 (1998).

[51] P. Reimann, Phys. Rev. Lett. 101, 190403 (2008).

[52] M. Rigol, V. Dunjko, and M. Olshanii, Nature 452, 854 (2008).

[53] A. J. Short, New J. Phys. 13, 53009 (2011).

[54] A. V. Ponomarev, S. Denisov, and P. Hänggi, Phys. Rev. Lett. 106, 010405 (2011).

[55] A. J. Short and T. C. Farrelly, New J. Phys. 14, 13063 (2012).

[56] P. Reimann, Phys. Scr. 86, 58512 (2012).

[57] A. S. L. Malabarba, L. P. García-Pintos, N. Linden, T. C. Farrelly, and A. J. Short, Phys. Rev. E 90, 012121 (2014).

[58] A. S. L. Malabarba, N. Linden, and A. J. Short, Phys. Rev. E 92, 062128 (2015).

[59] S. Goldstein, T. Hara, and H. Tasaki, New J. Phys. 17, 45002 (2015).

[60] A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, Science 353, 794 (2016).

[61] L. P. García-Pintos, N. Linden, A. S. L. Malabarba, A. J. Short, and A. Winter, Phys. Rev. X 7, 031027 (2017).

[62] N. Linden, S. Popescu, A. J. Short, and A. Winter, Phys. Rev. E 79, 061103 (2009).

[63] P. Reimann and M. Kastner, New J. Phys. 14, 43020 (2012).

[64] D. Shaffer, C. Chamon, A. Hamma, and E. R. Mucciolo, J. Stat. Mech. 2014, P12007 (2014).

[65] K. Sengupta, S. Powell, and S. Sachdev, Phys. Rev. A 69, 053616 (2004).

[66] S. R. Manmana, S. Wessel, R. M. Noack, and A. Muramatsu, Phys. Rev. Lett. 98, 210405 (2007).

[67] D. J. Luitz, N. Laflorencie, and F. Alet, Phys. Rev. B 91, 081103 (2015).

[68] C. Kollath, A. M. Läuchli, and E. Altman, Phys. Rev. Lett. 98, 180601 (2007).

[69] M. Rigol, Phys. Rev. Lett. 103, 100403 (2009).

[70] M. C. Bañuls, J. I. Cirac, and M. B. Hastings, Phys. Rev. Lett. 106, 050405 (2011).

[71] J. Bajer and A. Miranowicz, J. Opt. B Quantum Semiclass. Opt. 3, 251 (2001).

[72] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1965).

Cited by

[1] Viktor Holubec and Tomáš Novotný, "Effects of Noise-Induced Coherence on the Performance of Quantum Absorption Refrigerators", Journal of Low Temperature Physics 192 3-4, 147 (2018).

[2] Mark T. Mitchison, "Quantum thermal absorption machines: refrigerators, engines and clocks", Contemporary Physics 60 2, 164 (2019).

[3] Varinder Singh and Ramandeep S. Johal, "Three-level laser heat engine at optimal performance with ecological function", Physical Review E 100 1, 012138 (2019).

[4] Adam Hewgill, J. Onam González, José P. Palao, Daniel Alonso, Alessandro Ferraro, and Gabriele De Chiara, "Three-qubit refrigerator with two-body interactions", Physical Review E 101 1, 012109 (2020).

[5] Sandipan Mohanta, Sushant Saryal, and Bijay Kumar Agarwalla, "Universal bounds on cooling power and cooling efficiency for autonomous absorption refrigerators", Physical Review E 105 3, 034127 (2022).

[6] Yuxia Zhang, Jian Zou, and Bin Shao, "Comparing Leggett–Garg inequality for work moments with Leggett–Garg inequality and NSIT", The European Physical Journal Plus 135 2, 154 (2020).

[7] Sreetama Das, Avijit Misra, Amit Kumar Pal, Aditi Sen(De), and Ujjwal Sen, "Necessarily transient quantum refrigerator", EPL (Europhysics Letters) 125 2, 20007 (2019).

[8] Mark T. Mitchison and Patrick P. Potts, "Physical Implementations of Quantum Absorption Refrigerators", Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions Fundamental Theories of Physics 195, 149 (2018) ISBN:978-3-319-99045-3.

[9] Raffaele Salvia, Martí Perarnau-Llobet, Géraldine Haack, Nicolas Brunner, and Stefan Nimmrichter, "Quantum advantage in charging cavity and spin batteries by repeated interactions", Physical Review Research 5 1, 013155 (2023).

[10] Ravi T. Wijesekara, Sarath D. Gunapala, and Malin Premaratne, "Towards quantum thermal multi-transistor systems: Energy divider formalism", Physical Review B 105 23, 235412 (2022).

[11] J. Onam González, José P. Palao, Daniel Alonso, and Luis A. Correa, "Classical emulation of quantum-coherent thermal machines", Physical Review E 99 6, 062102 (2019).

[12] Ravi T. Wijesekara, Sarath D. Gunapala, and Malin Premaratne, "Darlington pair of quantum thermal transistors", Physical Review B 104 4, 045405 (2021).

[13] Stella Seah, Stefan Nimmrichter, and Valerio Scarani, "Refrigeration beyond weak internal coupling", Physical Review E 98 1, 012131 (2018).

[14] Mark T. Mitchison, John Goold, and Javier Prior, "Charging a quantum battery with linear feedback control", Quantum 5, 500 (2021).

[15] Hava Meira Friedman and Dvira Segal, "Cooling condition for multilevel quantum absorption refrigerators", Physical Review E 100 6, 062112 (2019).

[16] Matteo Lostaglio, "Certifying Quantum Signatures in Thermodynamics and Metrology via Contextuality of Quantum Linear Response", Physical Review Letters 125 23, 230603 (2020).

[17] Gleb Maslennikov, Shiqian Ding, Roland Hablützel, Jaren Gan, Alexandre Roulet, Stefan Nimmrichter, Jibo Dai, Valerio Scarani, and Dzmitry Matsukevich, "Quantum absorption refrigerator with trapped ions", Nature Communications 10 1, 202 (2019).

[18] Elisa Bäumer, Matteo Lostaglio, Martí Perarnau-Llobet, and Rui Sampaio, Fundamental Theories of Physics 195, 275 (2018) ISBN:978-3-319-99045-3.

[19] Camille L. Latune, Ilya Sinayskiy, and Francesco Petruccione, "Roles of quantum coherences in thermal machines", The European Physical Journal Special Topics 230 4, 841 (2021).

[20] Stella Seah, Stefan Nimmrichter, Alexandre Roulet, and Valerio Scarani, Fundamental Theories of Physics 195, 227 (2018) ISBN:978-3-319-99045-3.

[21] Loris Maria Cangemi, Chitrak Bhadra, and Amikam Levy, "Quantum Engines and Refrigerators", arXiv:2302.00726, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2023-06-05 21:10:32) and SAO/NASA ADS (last updated successfully 2023-06-05 21:10:33). The list may be incomplete as not all publishers provide suitable and complete citation data.