Charging a quantum battery with linear feedback control

Mark T. Mitchison; John Goold; Javier Prior

doi:10.22331/q-2021-07-13-500

Charging a quantum battery with linear feedback control

Mark T. Mitchison¹, John Goold¹, and Javier Prior^2,3

¹School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
²Departamento de Física Aplicada, Universidad Politécnica de Cartagena, Cartagena E-30202, Spain
³Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada E-18071, Spain

Published:	2021-07-13, volume 5, page 500
Eprint:	arXiv:2012.00350v2
Doi:	https://doi.org/10.22331/q-2021-07-13-500
Citation:	Quantum 5, 500 (2021).

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

Updated version: The authors have uploaded version v3 of this work to the arXiv which may contain updates or corrections not contained in the published version v2. The authors left the following comment on the arXiv:

v1: 10 pages, 8 figures. Comments welcome! v2: Final version; v3: Fixed some broken hyperlinks in bibliography

Abstract

Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.

Featured image: Illustration of a quantum feedback loop that pumps energy into a qubit charger, $C$, connected to a battery, $B$. The central inset shows two different feedback strategies on the qubit's Bloch sphere, which are based on stabilising populations (blue arrows) or coherences (red arrows).

Talk at International Workshop “Open Quantum Dynamics and Thermodynamics”, hosted by the Center for Theoretical Physics of Complex Systems, Institute for Basic Science, South Korea.

Popular summary

Quantum batteries are useful models to explore the fundamental limits of energy transduction using controlled quantum systems. Recent research has focused on the effect of noise from the battery's environment on the charging process. Here, we introduce and explore a charging protocol based on quantum feedback control. Focussing our attention on a minimal model, we show that information gained through weak measurements on the environment can be exploited to reliably suppress noise and enhance the battery's charging performance. Such control can be implemented in various platforms including electronic and optical systems, opening up interesting possibilities for the experimental manipulation of energetic quantities with continuous quantum feedback.

► BibTeX data

@article{Mitchison2021chargingquantum,
  doi = {10.22331/q-2021-07-13-500},
  url = {https://doi.org/10.22331/q-2021-07-13-500},
  title = {Charging a quantum battery with linear feedback control},
  author = {Mitchison, Mark T. and Goold, John and Prior, Javier},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {500},
  month = jul,
  year = {2021}
}

► References

[1] H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, 2009).
https://doi.org/10.1017/cbo9780511813948

[2] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010).
https://www.ebook.de/de/product/13055864/michael_a_nielsen_isaac_l_chuang_quantum_computation_and_quantum_information.html

[3] A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011).
https://doi.org/10.1103/RevModPhys.83.863

[4] F. Campaioli, F. A. Pollock, and S. Vinjanampathy, in Thermodynamics in the Quantum Regime, edited by F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer Nature, 2018) 1805.05507.
https://doi.org/10.1007/978-3-319-99046-0
arXiv:1805.05507

[5] S. Bhattacharjee and A. Dutta, arXiv:2008.07889 [quant-ph] (2020).
arXiv:2008.07889

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

[7] M. Esposito and C. van den Broeck, Europhys. Lett. 95, 40004 (2011).
https://doi.org/10.1209/0295-5075/95/40004

[8] F. Brandão, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, Proc. Nat. Acad. Sci. 112, 3275 (2015).
https://doi.org/10.1073/pnas.1411728112

[9] E. G. Brown, N. Friis, and M. Huber, New J. Phys. 18, 113028 (2016).
https://doi.org/10.1088/1367-2630/18/11/113028

[10] G. T. Landi and M. Paternostro, arXiv:2009.07668 [quant-ph] (2020).
arXiv:2009.07668

[11] R. Alicki and M. Fannes, Phys. Rev. E 87, 042123 (2013).
https://doi.org/10.1103/PhysRevE.87.042123

[12] K. V. Hovhannisyan, M. Perarnau-Llobet, M. Huber, and A. Acín, Phys. Rev. Lett. 111, 240401 (2013).
https://doi.org/10.1103/PhysRevLett.111.240401

[13] M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, and A. Acín, Phys. Rev. X 5, 041011 (2015).
https://doi.org/10.1103/PhysRevX.5.041011

[14] G. L. Giorgi and S. Campbell, J. Phys. B: Atom. Mol. Opt. Phys. 48, 035501 (2015).
https://doi.org/10.1088/0953-4075/48/3/035501

[15] K. Korzekwa, M. Lostaglio, J. Oppenheim, and D. Jennings, New J. Phys. 18, 023045 (2016).
https://doi.org/10.1088/1367-2630/18/2/023045

[16] G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Phys. Rev. Lett. 125, 180603 (2020).
https://doi.org/10.1103/PhysRevLett.125.180603

[17] F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, New J. Phys. 17, 075015 (2015a).
https://doi.org/10.1088/1367-2630/17/7/075015

[18] F. Campaioli, F. A. Pollock, F. C. Binder, L. Céleri, J. Goold, S. Vinjanampathy, and K. Modi, Phys. Rev. Lett. 118, 150601 (2017).
https://doi.org/10.1103/PhysRevLett.118.150601

[19] T. P. Le, J. Levinsen, K. Modi, M. M. Parish, and F. A. Pollock, Phys. Rev. A 97, 022106 (2018).
https://doi.org/10.1103/PhysRevA.97.022106

[20] G. M. Andolina, M. Keck, A. Mari, M. Campisi, V. Giovannetti, and M. Polini, Phys. Rev. Lett. 122, 047702 (2019a).
https://doi.org/10.1103/PhysRevLett.122.047702

[21] G. M. Andolina, M. Keck, A. Mari, V. Giovannetti, and M. Polini, Phys. Rev. B 99, 205437 (2019b).
https://doi.org/10.1103/PhysRevB.99.205437

[22] D. Ferraro, G. M. Andolina, M. Campisi, V. Pellegrini, and M. Polini, Phys. Rev. B 100, 075433 (2019).
https://doi.org/10.1103/PhysRevB.100.075433

[23] D. Rosa, D. Rossini, G. M. Andolina, M. Polini, and M. Carrega, J. High Energy Phys. 2020, 67 (2020).
https://doi.org/10.1007/jhep11(2020)067

[24] Y.-Y. Zhang, T.-R. Yang, L. Fu, and X. Wang, Phys. Rev. E 99, 052106 (2019).
https://doi.org/10.1103/PhysRevE.99.052106

[25] F. Caravelli, G. Coulter-De Wit, L. P. García-Pintos, and A. Hamma, Phys. Rev. Research 2, 023095 (2020).
https://doi.org/10.1103/PhysRevResearch.2.023095

[26] S. Ghosh, T. Chanda, and A. Sen(De), Phys. Rev. A 101, 032115 (2020).
https://doi.org/10.1103/PhysRevA.101.032115

[27] D. Rossini, G. M. Andolina, D. Rosa, M. Carrega, and M. Polini, Phys. Rev. Lett. 125, 236402 (2020).
https://doi.org/10.1103/PhysRevLett.125.236402

[28] F. H. Kamin, F. T. Tabesh, S. Salimi, and A. C. Santos, Phys. Rev. E 102, 052109 (2020a).
https://doi.org/10.1103/PhysRevE.102.052109

[29] S. Julià-Farré, T. Salamon, A. Riera, M. N. Bera, and M. Lewenstein, Phys. Rev. Research 2, 023113 (2020).
https://doi.org/10.1103/PhysRevResearch.2.023113

[30] D. Rossini, G. M. Andolina, and M. Polini, Phys. Rev. B 100, 115142 (2019).
https://doi.org/10.1103/PhysRevB.100.115142

[31] F. Pirmoradian and K. Mølmer, Phys. Rev. A 100, 043833 (2019).
https://doi.org/10.1103/PhysRevA.100.043833

[32] F. H. Kamin, F. T. Tabesh, S. Salimi, F. Kheirandish, and A. C. Santos, New J. Phys. 22, 083007 (2020b).
https://doi.org/10.1088/1367-2630/ab9ee2

[33] M. Carrega, A. Crescente, D. Ferraro, and M. Sassetti, New J. Phys. 22, 083085 (2020).
https://doi.org/10.1088/1367-2630/abaa01

[34] G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giovannetti, and M. Polini, Phys. Rev. B 98, 205423 (2018).
https://doi.org/10.1103/PhysRevB.98.205423

[35] D. Ferraro, M. Campisi, G. M. Andolina, V. Pellegrini, and M. Polini, Phys. Rev. Lett. 120, 117702 (2018).
https://doi.org/10.1103/PhysRevLett.120.117702

[36] D. Farina, G. M. Andolina, A. Mari, M. Polini, and V. Giovannetti, Phys. Rev. B 99, 035421 (2019).
https://doi.org/10.1103/PhysRevB.99.035421

[37] S. Gherardini, F. Campaioli, F. Caruso, and F. C. Binder, Phys. Rev. Research 2, 013095 (2020).
https://doi.org/10.1103/PhysRevResearch.2.013095

[38] A. C. Santos, B. Çakmak, S. Campbell, and N. T. Zinner, Phys. Rev. E 100, 032107 (2019).
https://doi.org/10.1103/PhysRevE.100.032107

[39] J. Q. Quach and W. J. Munro, Phys. Rev. Applied 14, 024092 (2020).
https://doi.org/10.1103/PhysRevApplied.14.024092

[40] F. Barra, Phys. Rev. Lett. 122, 210601 (2019).
https://doi.org/10.1103/PhysRevLett.122.210601

[41] C. L. Latune, I. Sinayskiy, and F. Petruccione, Phys. Rev. A 99, 052105 (2019).
https://doi.org/10.1103/PhysRevA.99.052105

[42] K. V. Hovhannisyan, F. Barra, and A. Imparato, Phys. Rev. Research 2, 033413 (2020).
https://doi.org/10.1103/PhysRevResearch.2.033413

[43] B. Çakmak, Phys. Rev. E 102, 042111 (2020).
https://doi.org/10.1103/PhysRevE.102.042111

[44] F. T. Tabesh, F. H. Kamin, and S. Salimi, Phys. Rev. A 102, 052223 (2020).
https://doi.org/10.1103/PhysRevA.102.052223

[45] F. Tacchino, T. F. F. Santos, D. Gerace, M. Campisi, and M. F. Santos, Phys. Rev. E 102, 062133 (2020).
https://doi.org/10.1103/PhysRevE.102.062133

[46] A. C. Santos, A. Saguia, and M. S. Sarandy, Phys. Rev. E 101, 062114 (2020).
https://doi.org/10.1103/PhysRevE.101.062114

[47] H. F. Hofmann, G. Mahler, and O. Hess, Phys. Rev. A 57, 4877 (1998).
https://doi.org/10.1103/PhysRevA.57.4877

[48] J. Wang and H. M. Wiseman, Phys. Rev. A 64, 063810 (2001).
https://doi.org/10.1103/PhysRevA.64.063810

[49] R. Ruskov and A. N. Korotkov, Phys. Rev. B 66, 041401 (2002).
https://doi.org/10.1103/PhysRevB.66.041401

[50] T. L. Patti, A. Chantasri, L. P. García-Pintos, A. N. Jordan, and J. Dressel, Phys. Rev. A 96, 022311 (2017).
https://doi.org/10.1103/PhysRevA.96.022311

[51] V. Belavkin, in Information Complexity and Control in Quantum Physics (Springer Vienna, 1987) pp. 311–329.
https://doi.org/10.1007/978-3-7091-2971-5_19

[52] H. M. Wiseman and G. J. Milburn, Phys. Rev. Lett. 70, 548 (1993).
https://doi.org/10.1103/PhysRevLett.70.548

[53] A. N. Korotkov, Phys. Rev. B 60, 5737 (1999).
https://doi.org/10.1103/PhysRevB.60.5737

[54] A. Serafini, ISRN Optics 2012, 1 (2012).
https://doi.org/10.5402/2012/275016

[55] J. Zhang, Y.-x. Liu, R.-B. Wu, K. Jacobs, and F. Nori, Phys. Rep. 679, 1 (2017).
https://doi.org/10.1016/j.physrep.2017.02.003

[56] J. M. Horowitz and K. Jacobs, Phys. Rev. Lett. 115, 130501 (2015).
https://doi.org/10.1103/PhysRevLett.115.130501

[57] J. J. Alonso, E. Lutz, and A. Romito, Phys. Rev. Lett. 116, 080403 (2016).
https://doi.org/10.1103/PhysRevLett.116.080403

[58] C. Elouard, D. A. Herrera-Martí, M. Clusel, and A. Auffèves, npj Quantum Inf. 3, 9 (2017).
https://doi.org/10.1038/s41534-017-0008-4

[59] M. Naghiloo, D. Tan, P. M. Harrington, J. J. Alonso, E. Lutz, A. Romito, and K. W. Murch, Phys. Rev. Lett. 124, 110604 (2020).
https://doi.org/10.1103/PhysRevLett.124.110604

[60] M. Debiossac, D. Grass, J. J. Alonso, E. Lutz, and N. Kiesel, Nature Commun. 11, 1360 (2020).
https://doi.org/10.1038/s41467-020-15148-5

[61] 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

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

[63] S. Nimmrichter, J. Dai, A. Roulet, and V. Scarani, Quantum 1, 37 (2017).
https://doi.org/10.22331/q-2017-12-11-37

[64] G. Maslennikov, S. Ding, R. Hablützel, J. Gan, A. Roulet, S. Nimmrichter, J. Dai, V. Scarani, and D. Matsukevich, Nature Commun. 10, 202 (2019).
https://doi.org/10.1038/s41467-018-08090-0

[65] H. Carmichael, An Open Systems Approach to Quantum Optics (Springer Berlin Heidelberg, 1993).
https://doi.org/10.1007/978-3-540-47620-7

[66] H. M. Wiseman, Phys. Rev. A 49, 2133 (1994).
https://doi.org/10.1103/PhysRevA.49.2133

[67] P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, Phys. Rev. Lett. 96, 043003 (2006).
https://doi.org/10.1103/PhysRevLett.96.043003

[68] F. Tebbenjohanns, M. Frimmer, A. Militaru, V. Jain, and L. Novotny, Phys. Rev. Lett. 122, 223601 (2019).
https://doi.org/10.1103/PhysRevLett.122.223601

[69] G. P. Conangla, F. Ricci, M. T. Cuairan, A. W. Schell, N. Meyer, and R. Quidant, Phys. Rev. Lett. 122, 223602 (2019).
https://doi.org/10.1103/PhysRevLett.122.223602

[70] R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Nature 490, 77 (2012).
https://doi.org/10.1038/nature11505

[71] E. Buks, R. Schuster, M. Heiblum, D. Mahalu, and V. Umansky, Nature 391, 871 (1998).
https://doi.org/10.1038/36057

[72] H.-S. Goan, G. J. Milburn, H. M. Wiseman, and H. Bi Sun, Phys. Rev. B 63, 125326 (2001).
https://doi.org/10.1103/PhysRevB.63.125326

[73] W. Pusz and S. L. Woronowicz, Commun. Math. Phys. 58, 273 (1978).
https://doi.org/10.1007/bf01614224

[74] F. Binder, S. Vinjanampathy, K. Modi, and J. Goold, Phys. Rev. E 91, 032119 (2015b).
https://doi.org/10.1103/PhysRevE.91.032119

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

[76] P. Skrzypczyk, R. Silva, and N. Brunner, Phys. Rev. E 91, 052133 (2015).
https://doi.org/10.1103/PhysRevE.91.052133

[77] P. Rouchon and J. F. Ralph, Phys. Rev. A 91, 012118 (2015).
https://doi.org/10.1103/PhysRevA.91.012118

[78] A. C. Doherty and K. Jacobs, Phys. Rev. A 60, 2700 (1999).
https://doi.org/10.1103/PhysRevA.60.2700

[79] H. M. Wiseman, S. Mancini, and J. Wang, Phys. Rev. A 66, 013807 (2002).
https://doi.org/10.1103/PhysRevA.66.013807

[80] N. Friis and M. Huber, Quantum 2, 61 (2018).
https://doi.org/10.22331/q-2018-04-23-61

[81] L. P. García-Pintos, A. Hamma, and A. del Campo, Phys. Rev. Lett. 125, 040601 (2020).
https://doi.org/10.1103/PhysRevLett.125.040601

[82] A. Crescente, M. Carrega, M. Sassetti, and D. Ferraro, New J. Phys. 22, 063057 (2020).
https://doi.org/10.1088/1367-2630/ab91fc

[83] A. Rignon-Bret, G. Guarnieri, J. Goold, and M. T. Mitchison, Phys. Rev. E 103, 012133 (2021).
https://doi.org/10.1103/PhysRevE.103.012133

[84] J. Åberg, Nature Commun. 4, 1925 (2013).
https://doi.org/10.1038/ncomms2712

[85] D. Egloff, O. C. O. Dahlsten, R. Renner, and V. Vedral, New J. Phys. 17, 073001 (2015).
https://doi.org/10.1088/1367-2630/17/7/073001

[86] K. Abdelkhalek, Y. Nakata, and D. Reeb, arXiv:1609.06981 [quant-ph] (2016).
arXiv:1609.06981

[87] P. Kammerlander and J. Anders, Sci. Rep. 6, 22174 (2016).
https://doi.org/10.1038/srep22174

[88] C. Elouard and A. N. Jordan, Phys. Rev. Lett. 120, 260601 (2018).
https://doi.org/10.1103/PhysRevLett.120.260601

[89] T. Debarba, G. Manzano, Y. Guryanova, M. Huber, and N. Friis, New J. Phys. 21, 113002 (2019).
https://doi.org/10.1088/1367-2630/ab4d9d

[90] Y. Guryanova, N. Friis, and M. Huber, Quantum 4, 222 (2020).
https://doi.org/10.22331/q-2020-01-13-222

[91] G. Schaller, C. Emary, G. Kiesslich, and T. Brandes, Phys. Rev. B 84, 085418 (2011).
https://doi.org/10.1103/PhysRevB.84.085418

[92] M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V. Vedral, and I. A. Walmsley, Phys. Rev. Lett. 116, 050401 (2016).
https://doi.org/10.1103/PhysRevLett.116.050401

[93] N. Cottet, S. Jezouin, L. Bretheau, P. Campagne-Ibarcq, Q. Ficheux, J. Anders, A. Auffèves, R. Azouit, P. Rouchon, and B. Huard, Proc. Nat. Acad. Sci. 114, 7561 (2017).
https://doi.org/10.1073/pnas.1704827114

[94] T. Sagawa and M. Ueda, Phys. Rev. Lett. 100, 080403 (2008).
https://doi.org/10.1103/PhysRevLett.100.080403

[95] K. Jacobs, Phys. Rev. A 80, 012322 (2009).
https://doi.org/10.1103/PhysRevA.80.012322

[96] T. Sagawa and M. Ueda, Phys. Rev. Lett. 104, 090602 (2010).
https://doi.org/10.1103/PhysRevLett.104.090602

[97] K. Jacobs, Phys. Rev. E 86, 040106 (2012).
https://doi.org/10.1103/PhysRevE.86.040106

[98] Z. Gong, Y. Ashida, and M. Ueda, Phys. Rev. A 94, 012107 (2016).
https://doi.org/10.1103/PhysRevA.94.012107

[99] M. Esposito and G. Schaller, Europhys. Lett. 99, 30003 (2012).
https://doi.org/10.1209/0295-5075/99/30003

[100] P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Phys. Rev. Lett. 110, 040601 (2013a).
https://doi.org/10.1103/PhysRevLett.110.040601

[101] P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Phys. Rev. E 88, 062107 (2013b).
https://doi.org/10.1103/PhysRevE.88.062107

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

[103] J. Dressel, A. Chantasri, A. N. Jordan, and A. N. Korotkov, Phys. Rev. Lett. 119, 220507 (2017).
https://doi.org/10.1103/PhysRevLett.119.220507

[104] P. Strasberg, Phys. Rev. E 100, 022127 (2019).
https://doi.org/10.1103/PhysRevE.100.022127

[105] A. Belenchia, L. Mancino, G. T. Landi, and M. Paternostro, npj Quantum Inf. 6, 97 (2020).
https://doi.org/10.1038/s41534-020-00334-6

[106] J. Monsel, M. Fellous-Asiani, B. Huard, and A. Auffèves, Phys. Rev. Lett. 124, 130601 (2020).
https://doi.org/10.1103/PhysRevLett.124.130601

[107] M. T. Mitchison, Contemp. Physics 60, 164 (2019).
https://doi.org/10.1080/00107514.2019.1631555

[108] S. Lloyd, Phys. Rev. A 62, 022108 (2000).
https://doi.org/10.1103/PhysRevA.62.022108

Cited by

[1] Gabriel T. Landi, "Battery Charging in Collision Models with Bayesian Risk Strategies", Entropy 23 12, 1627 (2021).

[2] Y. Yao and X. Q. Shao, "Optimal charging of open spin-chain quantum batteries via homodyne-based feedback control", Physical Review E 106 1, 014138 (2022).

[3] Daniele Morrone, Matteo A C Rossi, Andrea Smirne, and Marco G Genoni, "Charging a quantum battery in a non-Markovian environment: a collisional model approach", Quantum Science and Technology 8 3, 035007 (2023).

[4] Francesco Mazzoncini, Vasco Cavina, Gian Marcello Andolina, Paolo Andrea Erdman, and Vittorio Giovannetti, "Optimal control methods for quantum batteries", Physical Review A 107 3, 032218 (2023).

[5] Alba Crescente, Dario Ferraro, Matteo Carrega, and Maura Sassetti, "Analytically Solvable Model for Qubit-Mediated Energy Transfer between Quantum Batteries", Entropy 25 5, 758 (2023).

[6] Fu-Quan Dou, Hang Zhou, and Jian-An Sun, "Cavity Heisenberg-spin-chain quantum battery", Physical Review A 106 3, 032212 (2022).

[7] Oisín Culhane, Mark T. Mitchison, and John Goold, "Extractable work in quantum electromechanics", Physical Review E 106 3, L032104 (2022).

[8] Kai Xu, Han-Jie Zhu, Guo-Feng Zhang, and Wu-Ming Liu, "Enhancing the performance of an open quantum battery via environment engineering", Physical Review E 104 6, 064143 (2021).

[9] Fu-Quan Dou, You-Qi Lu, Yuan-Jin Wang, and Jian-An Sun, "Extended Dicke quantum battery with interatomic interactions and driving field", Physical Review B 105 11, 115405 (2022).

[10] Hai-Long Shi, Shu Ding, Qing-Kun Wan, Xiao-Hui Wang, and Wen-Li Yang, "Entanglement, Coherence, and Extractable Work in Quantum Batteries", Physical Review Letters 129 13, 130602 (2022).

[11] Jeongrak Son, Peter Talkner, and Juzar Thingna, "Charging quantum batteries via Otto machines: Influence of monitoring", Physical Review A 106 5, 052202 (2022).

[12] Srijon Ghosh, Titas Chanda, Shiladitya Mal, and Aditi Sen(De), "Fast charging of a quantum battery assisted by noise", Physical Review A 104 3, 032207 (2021).

[13] Y. Yao and X. Q. Shao, "Stable charging of a Rydberg quantum battery in an open system", Physical Review E 104 4, 044116 (2021).

[14] Salvatore Tirone, Raffaele Salvia, and Vittorio Giovannetti, "Quantum Energy Lines and the Optimal Output Ergotropy Problem", Physical Review Letters 127 21, 210601 (2021).

[15] Michael J. Kewming, Mark T. Mitchison, and Gabriel T. Landi, "Diverging current fluctuations in critical Kerr resonators", Physical Review A 106 3, 033707 (2022).

[16] Kai Xu, Han-Jie Zhu, Hao Zhu, Guo-Feng Zhang, and Wu-Ming Liu, "Charging and self-discharging process of a quantum battery in composite environments", Frontiers of Physics 18 3, 31301 (2023).

[17] Archak Purkayastha, Giacomo Guarnieri, Steve Campbell, Javier Prior, and John Goold, "Periodically refreshed quantum thermal machines", Quantum 6, 801 (2022).

[18] 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).

[19] Michael J. Kewming and Sally Shrapnel, "Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature", Quantum 6, 685 (2022).

[20] P. Chen, T. S. Yin, Z. Q. Jiang, and G. R. Jin, "Quantum enhancement of a single quantum battery by repeated interactions with large spins", Physical Review E 106 5, 054119 (2022).

[21] Maria Maffei, Patrice A. Camati, and Alexia Auffèves, "Probing nonclassical light fields with energetic witnesses in waveguide quantum electrodynamics", Physical Review Research 3 3, L032073 (2021).

[22] Sourav Bhattacharjee and Amit Dutta, "Quantum thermal machines and batteries", The European Physical Journal B 94 12, 239 (2021).

[23] N Behzadi and H Kasani, "Mechanism of controlling robust and stable charging of open quantum batteries", Journal of Physics A: Mathematical and Theoretical 55 42, 425303 (2022).

[24] Kai Xu, Hong-Guo Li, Zong-Guo Li, Han-Jie Zhu, Guo-Feng Zhang, and Wu-Ming Liu, "Charging performance of quantum batteries in a double-layer environment", Physical Review A 106 1, 012425 (2022).

[25] Alba Crescente, Dario Ferraro, Matteo Carrega, and Maura Sassetti, "Enhancing coherent energy transfer between quantum devices via a mediator", Physical Review Research 4 3, 033216 (2022).

[26] Dominik Šafránek, Dario Rosa, and Felix C. Binder, "Work Extraction from Unknown Quantum Sources", Physical Review Letters 130 21, 210401 (2023).

[27] Anna Delmonte, Alba Crescente, Matteo Carrega, Dario Ferraro, and Maura Sassetti, "Characterization of a Two-Photon Quantum Battery: Initial Conditions, Stability and Work Extraction", Entropy 23 5, 612 (2021).

[28] Daniele Morrone, Matteo A. C. Rossi, and Marco G. Genoni, "Daemonic ergotropy in continuously-monitored open quantum batteries", arXiv:2302.12279, (2023).

[29] Liliana Arrachea, "Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines", Reports on Progress in Physics 86 3, 036501 (2023).

[30] Tathagata Karmakar, Philippe Lewalle, and Andrew N. Jordan, "Stochastic Path-Integral Analysis of the Continuously Monitored Quantum Harmonic Oscillator", PRX Quantum 3 1, 010327 (2022).

[31] Marius de Leeuw and Chiara Paletta, "The Bethe ansatz for a new integrable open quantum system", arXiv:2207.14193, (2022).

[32] Junjie Liu and Dvira Segal, "Boosting quantum battery performance by structure engineering", arXiv:2104.06522, (2021).

[33] Faraj Bakhshinezhad, Beniamin R. Jablonski, Felix C. Binder, and Nicolai Friis, "Trade-offs between precision and fluctuations in charging finite-dimensional quantum systems", arXiv:2303.16676, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2023-06-05 12:47:39) and SAO/NASA ADS (last updated successfully 2023-06-05 12:47:40). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.