Multi-spin counter-diabatic driving in many-body quantum Otto refrigerators

Andreas Hartmann1, Victor Mukherjee2, Glen Bigan Mbeng1, Wolfgang Niedenzu1, and Wolfgang Lechner1

1Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria
2Department of Physical Sciences, IISER Berhampur, Berhampur 760010, India

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Quantum refrigerators pump heat from a cold to a hot reservoir. In the few-particle regime, counter-diabatic (CD) driving of, originally adiabatic, work-exchange strokes is a promising candidate to overcome the bottleneck of vanishing cooling power. Here, we present a finite-time many-body quantum refrigerator that yields finite cooling power at high coefficient of performance, that considerably outperforms its non-adiabatic counterpart. We employ multi-spin CD driving and numerically investigate the scaling behavior of the refrigeration performance with system size. We further prove that optimal refrigeration via the exact CD protocol is a catalytic process.

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[1] Y. A. Çengel and M. A. Boles, Thermodynamics: An Engineering Approach, eighth ed. (McGraw-Hill Education, New York, 2015).

[2] R. Alicki, The quantum open system as a model of the heat engine, J. Phys. A 12, L103 (1979).

[3] R. Kosloff, A quantum mechanical open system as a model of a heat engine, J. Chem. Phys. 80, 1625 (1984).

[4] R. Kosloff, Quantum Thermodynamics: A Dynamical Viewpoint, Entropy 15, 2100 (2013).

[5] D. Gelbwaser-Klimovsky, W. Niedenzu, and G. Kurizki, Thermodynamics of Quantum Systems Under Dynamical Control, Adv. At. Mol. Opt. Phys. 64, 329 (2015).

[6] S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemp. Phys. 57, 1 (2016).

[7] B. Karimi and J. P. Pekola, Otto refrigerator based on a superconducting qubit: Classical and quantum performance, Phys. Rev. B 94, 184503 (2016).

[8] R. Kosloff and Y. Rezek, The Quantum Harmonic Otto Cycle, Entropy 19 (2017), 10.3390/​e19040136.

[9] F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, eds., Thermodynamics in the Quantum Regime (Springer, Cham, 2019).

[10] S. Bhattacharjee and A. Dutta, Quantum thermal machines and batteries, (2020), arXiv:2008.07889 [quant-ph].

[11] H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017).

[12] J.-y. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio-Abadal, T. Yefsah, V. Khemani, D. A. Huse, I. Bloch, and C. Gross, Exploring the many-body localization transition in two dimensions, Science 352, 1547 (2016).

[13] P. Bordia, H. Lüschen, S. Scherg, S. Gopalakrishnan, M. Knap, U. Schneider, and I. Bloch, Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasiperiodic Systems, Phys. Rev. X 7, 041047 (2017).

[14] J. V. Koski, V. F. Maisi, J. P. Pekola, and D. V. Averin, Experimental realization of a Szilard engine with a single electron, Proc. Natl. Acad. Sci. USA 111, 13786 (2014).

[15] J. Roßnagel, S. T. Dawkins, K. N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, and K. Singer, A single-atom heat engine, Science 352, 325 (2016).

[16] J. Klaers, S. Faelt, A. Imamoglu, and E. Togan, Squeezed Thermal Reservoirs as a Resource for a Nanomechanical Engine beyond the Carnot Limit, Phys. Rev. X 7, 031044 (2017).

[17] J. P. S. Peterson, T. B. Batalhão, M. Herrera, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Experimental Characterization of a Spin Quantum Heat Engine, Phys. Rev. Lett. 123, 240601 (2019).

[18] D. von Lindenfels, O. Gräb, C. T. Schmiegelow, V. Kaushal, J. Schulz, M. T. Mitchison, J. Goold, F. Schmidt-Kaler, and U. G. Poschinger, Spin Heat Engine Coupled to a Harmonic-Oscillator Flywheel, Phys. Rev. Lett. 123, 080602 (2019).

[19] J. Klatzow, J. N. Becker, P. M. Ledingham, C. Weinzetl, K. T. Kaczmarek, D. J. Saunders, J. Nunn, I. A. Walmsley, R. Uzdin, and E. Poem, Experimental Demonstration of Quantum Effects in the Operation of Microscopic Heat Engines, Phys. Rev. Lett. 122, 110601 (2019).

[20] Y. Rezek, P. Salamon, K. H. Hoffmann, and R. Kosloff, The quantum refrigerator: The quest for absolute zero, EPL 85, 30008 (2009).

[21] A. Levy and R. Kosloff, Quantum Absorption Refrigerator, Phys. Rev. Lett. 108, 070604 (2012).

[22] Y. Yuan, R. Wang, J. He, Y. Ma, and J. Wang, Coefficient of performance under maximum ${\chi}$ criterion in a two-level atomic system as a refrigerator, Phys. Rev. E 90, 052151 (2014).

[23] R. Long and W. Liu, Performance of quantum Otto refrigerators with squeezing, Phys. Rev. E 91, 062137 (2015).

[24] O. Abah and E. Lutz, Optimal performance of a quantum Otto refrigerator, EPL 113, 60002 (2016).

[25] W. Niedenzu, I. Mazets, G. Kurizki, and F. Jendrzejewski, Quantized refrigerator for an atomic cloud, Quantum 3, 155 (2019).

[26] H. B. Callen, Thermodynamics and an introduction to thermostatistics (Wiley, New York, 1985).

[27] E. Arimondo, P. R. Berman, and C. C. Lin, eds., Advances in Atomic, Molecular, and Optical Physics, Adv. At. Mol. Opt. Phys., Vol. 62 (Academic Press, 2013) pp. 117 – 169.

[28] A. del Campo and K. Sengupta, Controlling quantum critical dynamics of isolated systems, Eur Phys J Spec Top 224, 189 (2015).

[29] A. del Campo and K. Kim, Focus on Shortcuts to Adiabaticity, New J. Phys. 21, 050201 (2019).

[30] D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019).

[31] R. Kosloff and T. Feldmann, Discrete four-stroke quantum heat engine exploring the origin of friction, Phys. Rev. E 65, 055102 (2002).

[32] T. Feldmann and R. Kosloff, Quantum four-stroke heat engine: Thermodynamic observables in a model with intrinsic friction, Phys. Rev. E 68, 016101 (2003).

[33] T. Feldmann and R. Kosloff, Quantum lubrication: Suppression of friction in a first-principles four-stroke heat engine, Phys. Rev. E 73, 025107 (2006).

[34] M. Demirplak and S. A. Rice, Adiabatic Population Transfer with Control Fields, J. Phys. Chem. A, J. Phys. Chem. A 107, 9937 (2003).

[35] K. Takahashi, Transitionless quantum driving for spin systems, Phys. Rev. E 87, 062117 (2013a).

[36] X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Fast Optimal Frictionless Atom Cooling in Harmonic Traps: Shortcut to Adiabaticity, Phys. Rev. Lett. 104, 063002 (2010).

[37] X. Chen, E. Torrontegui, and J. G. Muga, Lewis-Riesenfeld invariants and transitionless quantum driving, Phys. Rev. A 83, 062116 (2011).

[38] K. Takahashi, Transitionless quantum driving for spin systems, Phys. Rev. E 87, 062117 (2013b).

[39] C. Jarzynski, Generating shortcuts to adiabaticity in quantum and classical dynamics, Phys. Rev. A 88, 040101 (2013).

[40] A. del Campo, Shortcuts to Adiabaticity by Counterdiabatic Driving, Phys. Rev. Lett. 111, 100502 (2013).

[41] B. Damski, Counterdiabatic driving of the quantum Ising model, J. Stat. Mech. Theory Exp. 2014, P12019 (2014).

[42] D. Sels and A. Polkovnikov, Minimizing irreversible losses in quantum systems by local counterdiabatic driving, Proc. Natl. Acad. Sci. USA 114, E3909 (2017).

[43] P. W. Claeys, M. Pandey, D. Sels, and A. Polkovnikov, Floquet-Engineering Counterdiabatic Protocols in Quantum Many-Body Systems, Phys. Rev. Lett. 123, 090602 (2019).

[44] A. Hartmann and W. Lechner, Rapid counter-diabatic sweeps in lattice gauge adiabatic quantum computing, New J. Phys. 21, 043025 (2019).

[45] A. d. Campo, J. Goold, and M. Paternostro, More bang for your buck: Super-adiabatic quantum engines, Sci. Rep. 4, 6208 EP (2014).

[46] O. Abah and E. Lutz, Performance of shortcut-to-adiabaticity quantum engines, Phys. Rev. E 98, 032121 (2018).

[47] O. Abah and M. Paternostro, Shortcut-to-adiabaticity Otto engine: A twist to finite-time thermodynamics, Phys. Rev. E 99, 022110 (2019).

[48] L. Dupays, I. L. Egusquiza, A. del Campo, and A. Chenu, Superadiabatic thermalization of a quantum oscillator by engineered dephasing, Phys. Rev. Research 2, 033178 (2020).

[49] B. Çakmak and Ö. E. Müstecaplıoğlu, Spin quantum heat engines with shortcuts to adiabaticity, Phys. Rev. E 99, 032108 (2019).

[50] K. Funo, N. Lambert, B. Karimi, J. P. Pekola, Y. Masuyama, and F. Nori, Speeding up a quantum refrigerator via counterdiabatic driving, Phys. Rev. B 100, 035407 (2019).

[51] O. Abah, M. Paternostro, and E. Lutz, Shortcut-to-adiabaticity quantum Otto refrigerator, Phys. Rev. Research 2, 023120 (2020).

[52] A. Hartmann, V. Mukherjee, W. Niedenzu, and W. Lechner, Many-body quantum heat engines with shortcuts to adiabaticity, Phys. Rev. Research 2, 023145 (2020).

[53] J. I. Cirac and P. Zoller, Goals and opportunities in quantum simulation, Nat. Phys. 8, 264 (2012).

[54] I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).

[55] A. Lucas, Ising formulations of many NP problems, Front. Phys. 2, 5 (2014).

[56] T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys. 90, 015002 (2018).

[57] M. Kolodrubetz, D. Sels, P. Mehta, and A. Polkovnikov, Geometry and non-adiabatic response in quantum and classical systems, Phys. Rep. 697, 1 (2017).

[58] A. del Campo, M. M. Rams, and W. H. Zurek, Assisted Finite-Rate Adiabatic Passage Across a Quantum Critical Point: Exact Solution for the Quantum Ising Model, Phys. Rev. Lett. 109, 115703 (2012).

[59] S. Alipour, A. Chenu, A. T. Rezakhani, and A. del Campo, Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution, Quantum 4, 336 (2020).

[60] R. Dann, A. Tobalina, and R. Kosloff, Fast route to equilibration, Phys. Rev. A 101, 052102 (2020).

[61] R. Dann, A. Tobalina, and R. Kosloff, Shortcut to Equilibration of an Open Quantum System, Phys. Rev. Lett. 122, 250402 (2019).

[62] A. Das and V. Mukherjee, Quantum-enhanced finite-time Otto cycle, Phys. Rev. Research 2, 033083 (2020).

[63] J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184, 1234 (2013).

[64] O. Abah and E. Lutz, Energy efficient quantum machines, EPL 118, 40005 (2017).

[65] S. Campbell and S. Deffner, Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity, Phys. Rev. Lett. 118, 100601 (2017).

[66] Y. Zheng, S. Campbell, G. De Chiara, and D. Poletti, Cost of counterdiabatic driving and work output, Phys. Rev. A 94, 042132 (2016).

[67] A. Tobalina, I. Lizuain, and J. G. Muga, Vanishing efficiency of a speeded-up ion-in-Paul-trap Otto engine, EPL 127, 20005 (2019).

[68] A. Manatuly, W. Niedenzu, R. Román-Ancheyta, B. Çakmak, Ö. E. Müstecaplıoğlu, and G. Kurizki, Collectively enhanced thermalization via multiqubit collisions, Phys. Rev. E 99, 042145 (2019).

[69] K. Funo, J.-N. Zhang, C. Chatou, K. Kim, M. Ueda, and A. del Campo, Universal Work Fluctuations During Shortcuts to Adiabaticity by Counterdiabatic Driving, Phys. Rev. Lett. 118, 100602 (2017).

Cited by

[1] Sourav Bhattacharjee and Amit Dutta, "Quantum thermal machines and batteries", arXiv:2008.07889.

[2] Tamiro Villazon, Pieter W. Claeys, Anatoli Polkovnikov, and Anushya Chandran, "Shortcuts to Dynamic Polarization", arXiv:2011.05349.

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