Quantum and classical dynamics of a three-mode absorption refrigerator

Stefan Nimmrichter; Jibo Dai; Alexandre Roulet; Valerio Scarani

doi:10.22331/q-2017-12-11-37

Quantum and classical dynamics of a three-mode absorption refrigerator

Stefan Nimmrichter¹, Jibo Dai^1,2, Alexandre Roulet^1,3, and Valerio Scarani^1,4

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

Published:	2017-12-11, volume 1, page 37
Eprint:	arXiv:1709.08353v2
Doi:	https://doi.org/10.22331/q-2017-12-11-37
Citation:	Quantum 1, 37 (2017).

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Abstract

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

@article{Nimmrichter2017quantumclassical,
  doi = {10.22331/q-2017-12-11-37},
  url = {https://doi.org/10.22331/q-2017-12-11-37},
  title = {Quantum and classical dynamics of a three-mode absorption refrigerator},
  author = {Nimmrichter, Stefan and Dai, Jibo and Roulet, Alexandre and Scarani, Valerio},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {1},
  pages = {37},
  month = dec,
  year = {2017}
}

► References

[1] M. Horodecki and J. Oppenheim, Nat. Commun. 4, 2059 (2013).
https://doi.org/10.1038/ncomms3059

[2] P. Skrzypczyk, A. J. Short, and S. Popescu, Nat. Commun. 5, 4185 (2014).
https://doi.org/10.1038/ncomms5185

[3] M. O. Scully, M. S. Zubairy, G. S. Agarwal, and H. Walther, Science 299, 862 (2003).
https://doi.org/10.1126/science.1078955

[4] R. Dillenschneider and E. Lutz, Europhys. Lett. 88, 50003 (2009).
https://doi.org/10.1209/0295-5075/88/50003

[5] J. Roßnagel, O. Abah, F. Schmidt-Kaler, K. Singer, and E. Lutz, Phys. Rev. Lett. 112, 030602 (2014).
https://doi.org/10.1103/PhysRevLett.112.030602

[6] L. A. Correa, J. P. Palao, D. Alonso, and G. Adesso, Sci. Rep. 4, 3949 (2014).
https://doi.org/10.1038/srep03949

[7] P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Phys. Rev. X 7, 021003 (2017).
https://doi.org/10.1103/PhysRevX.7.021003

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

[9] A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Europhys. Lett. 67, 565 (2004).
https://doi.org/10.1209/epl/i2004-10101-2

[10] P. Talkner, E. Lutz, and P. Hänggi, Phys. Rev. E 75, 050102 (2007).
https://doi.org/10.1103/PhysRevE.75.050102

[11] M. Campisi, P. Hänggi, and P. Talkner, Rev. Mod. Phys. 83, 771 (2011).
https://doi.org/10.1103/RevModPhys.83.771

[12] A. J. Roncaglia, F. Cerisola, and J. P. Paz, Phys. Rev. Lett. 113, 250601 (2014).
https://doi.org/10.1103/PhysRevLett.113.250601

[13] P. Talkner and P. Hänggi, Phys. Rev. E 93, 022131 (2016).
https://doi.org/10.1103/PhysRevE.93.022131

[14] E. Geva and R. Kosloff, J. Chem. Phys. 104, 7681 (1996).
https://doi.org/10.1063/1.471453

[15] D. Venturelli, R. Fazio, and V. Giovannetti, Phys. Rev. Lett. 110, 256801 (2013).
https://doi.org/10.1103/PhysRevLett.110.256801

[16] R. Kosloff and A. Levy, Annu. Rev. Phys. Chem. 65, 365 (2014).
https://doi.org/10.1146/annurev-physchem-040513-103724

[17] A. Mari, A. Farace, and V. Giovannetti, J. Phys. B 48, 175501 (2015).
https://doi.org/10.1088/0953-4075/48/17/175501

[18] P. P. Hofer, J.-R. Souquet, and A. A. Clerk, Phys. Rev. B 93, 041418 (2016a).
https://doi.org/10.1103/PhysRevB.93.041418

[19] K. Joulain, J. Drevillon, Y. Ezzahri, and J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016).
https://doi.org/10.1103/PhysRevLett.116.200601

[20] M. T. Mitchison, M. Huber, J. Prior, M. P. Woods, and M. B. Plenio, Quantum Sci. Technol. 1, 015001 (2016).
https://doi.org/10.1088/2058-9565/1/1/015001

[21] P. P. Hofer, M. Perarnau-Llobet, J. B. Brask, R. Silva, M. Huber, and N. Brunner, Phys. Rev. B 94, 235420 (2016b).
https://doi.org/10.1103/PhysRevB.94.235420

[22] B. Karimi and J. P. Pekola, Phys. Rev. B 94, 184503 (2016).
https://doi.org/10.1103/PhysRevB.94.184503

[23] A. Roulet, S. Nimmrichter, J. Arrazola, S. Seah, and V. Scarani, Phys. Rev. E 95, 062131 (2017).
https://doi.org/10.1103/PhysRevE.95.062131

[24] U. Bissbort, C. Teo, C. Guo, G. Casati, G. Benenti, and D. Poletti, Phys. Rev. E 95, 062143 (2017).
https://doi.org/10.1103/PhysRevE.95.062143

[25] K. Zhang and W. Zhang, Phys. Rev. A 95, 053870 (2017).
https://doi.org/10.1103/PhysRevA.95.053870

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

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

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

[29] J. P. Palao, R. Kosloff, and J. M. Gordon, Phys. Rev. E 64, 056130 (2001).
https://doi.org/10.1103/PhysRevE.64.056130

[30] N. Linden, S. Popescu, and P. Skrzypczyk, Phys. Rev. Lett. 105, 130401 (2010).
https://doi.org/10.1103/PhysRevLett.105.130401

[31] A. Levy and R. Kosloff, Phys. Rev. Lett. 108, 070604 (2012).
https://doi.org/10.1103/PhysRevLett.108.070604

[32] J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, J. Phys. A Math. Theor. 49, 143001 (2016).
https://doi.org/10.1088/1751-8113/49/14/143001

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

[34] D. F. Walls and R. Barakat, Phys. Rev. A 1, 446 (1970).
https://doi.org/10.1103/PhysRevA.1.446

[35] G. P. Agrawal and C. L. Mehta, J. Phys. A , 607.
https://doi.org/10.1088/0305-4470/7/5/011

[36] R. Gambini, Phys. Rev. A 15, 1157 (1977).
https://doi.org/10.1103/PhysRevA.15.1157

[37] A. Levy and R. Kosloff, Europhys. Lett. 107, 20004 (2014).
https://doi.org/10.1209/0295-5075/107/20004

[38] J. O. González, L. A. Correa, G. Nocerino, J. P. Palao, D. Alonso, and G. Adesso, (2017), arXiv:1707.09228.
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.
arXiv:1707.09211

[40] R. Bonifacio and G. Preparata, Phys. Rev. A 2, 336 (1970).
https://doi.org/10.1103/PhysRevA.2.336

[41] C. Gogolin and J. Eisert, Rep. Prog. Phys. 79, 56001 (2016).
https://doi.org/10.1088/0034-4885/79/5/056001

[42] N. Brunner, N. Linden, S. Popescu, and P. Skrzypczyk, Phys. Rev. E 85, 051117 (2012).
https://doi.org/10.1103/PhysRevE.85.051117

[43] J. B. Brask and N. Brunner, Phys. Rev. E 92, 062101 (2015).
https://doi.org/10.1103/PhysRevE.92.062101

[44] M. T. Mitchison, M. P. Woods, J. Prior, and M. Huber, New J. Phys. 17, 115013 (2015).
https://doi.org/10.1088/1367-2630/17/11/115013

[45] M. Kulkarni, K. L. Tiwari, and D. Segal, Phys. Rev. B 86, 155424 (2012).
https://doi.org/10.1103/PhysRevB.86.155424

[46] T. Farrelly, F. G. S. L. Brandão, and M. Cramer, Phys. Rev. Lett. 118, 140601 (2017).
https://doi.org/10.1103/PhysRevLett.118.140601

[47] N. Erez, G. Gordon, M. Nest, and G. Kurizki, Nature 452, 724 (2008).
https://doi.org/10.1038/nature06873

[48] R. J. Glauber, Quantum Theory of Optical Coherence (Wiley-VCH, 2007).
https://doi.org/10.1002/9783527610075

[49] R. V. Jensen and R. Shankar, Phys. Rev. Lett. 54, 1879 (1985).
https://doi.org/10.1103/PhysRevLett.54.1879

[50] H. Tasaki, Phys. Rev. Lett. 80, 1373 (1998).
https://doi.org/10.1103/PhysRevLett.80.1373

[51] P. Reimann, Phys. Rev. Lett. 101, 190403 (2008).
https://doi.org/10.1103/PhysRevLett.101.190403

[52] M. Rigol, V. Dunjko, and M. Olshanii, Nature 452, 854 (2008).
https://doi.org/10.1038/nature06838

[53] A. J. Short, New J. Phys. 13, 53009 (2011).
https://doi.org/10.1088/1367-2630/13/5/053009

[54] A. V. Ponomarev, S. Denisov, and P. Hänggi, Phys. Rev. Lett. 106, 010405 (2011).
https://doi.org/10.1103/PhysRevLett.106.010405

[55] A. J. Short and T. C. Farrelly, New J. Phys. 14, 13063 (2012).
https://doi.org/10.1088/1367-2630/14/1/013063

[56] P. Reimann, Phys. Scr. 86, 58512 (2012).
https://doi.org/10.1088/0031-8949/86/05/058512

[57] A. S. L. Malabarba, L. P. García-Pintos, N. Linden, T. C. Farrelly, and A. J. Short, Phys. Rev. E 90, 012121 (2014).
https://doi.org/10.1103/PhysRevE.90.012121

[58] A. S. L. Malabarba, N. Linden, and A. J. Short, Phys. Rev. E 92, 062128 (2015).
https://doi.org/10.1103/PhysRevE.92.062128

[59] S. Goldstein, T. Hara, and H. Tasaki, New J. Phys. 17, 45002 (2015).
https://doi.org/10.1088/1367-2630/17/4/045002

[60] A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, Science 353, 794 (2016).
https://doi.org/10.1126/science.aaf6725

[61] L. P. García-Pintos, N. Linden, A. S. L. Malabarba, A. J. Short, and A. Winter, Phys. Rev. X 7, 031027 (2017).
https://doi.org/10.1103/PhysRevX.7.031027

[62] N. Linden, S. Popescu, A. J. Short, and A. Winter, Phys. Rev. E 79, 061103 (2009).
https://doi.org/10.1103/PhysRevE.79.061103

[63] P. Reimann and M. Kastner, New J. Phys. 14, 43020 (2012).
https://doi.org/10.1088/1367-2630/14/4/043020

[64] D. Shaffer, C. Chamon, A. Hamma, and E. R. Mucciolo, J. Stat. Mech. 2014, P12007 (2014).
https://doi.org/10.1088/1742-5468/2014/12/P12007

[65] K. Sengupta, S. Powell, and S. Sachdev, Phys. Rev. A 69, 053616 (2004).
https://doi.org/10.1103/PhysRevA.69.053616

[66] S. R. Manmana, S. Wessel, R. M. Noack, and A. Muramatsu, Phys. Rev. Lett. 98, 210405 (2007).
https://doi.org/10.1103/PhysRevLett.98.210405

[67] D. J. Luitz, N. Laflorencie, and F. Alet, Phys. Rev. B 91, 081103 (2015).
https://doi.org/10.1103/PhysRevB.91.081103

[68] C. Kollath, A. M. Läuchli, and E. Altman, Phys. Rev. Lett. 98, 180601 (2007).
https://doi.org/10.1103/PhysRevLett.98.180601

[69] M. Rigol, Phys. Rev. Lett. 103, 100403 (2009).
https://doi.org/10.1103/PhysRevLett.103.100403

[70] M. C. Bañuls, J. I. Cirac, and M. B. Hastings, Phys. Rev. Lett. 106, 050405 (2011).
https://doi.org/10.1103/PhysRevLett.106.050405

[71] J. Bajer and A. Miranowicz, J. Opt. B Quantum Semiclass. Opt. 3, 251 (2001).
https://doi.org/10.1088/1464-4266/3/4/309

[72] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1965).
https://www.worldcat.org/title/handbook-of-mathematical-functions-with-formulas-graphs-and-mathematical-tables/oclc/18003605

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