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Probabilistic motional averaging

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Abstract

In a continuous measurement scheme a spin-1/2 particle can be measured and simultaneously driven by an external resonant signal. When the driving is weak, it does not prevent the particle wave-function from collapsing and a detector randomly outputs two responses corresponding to the states of the particle. In contrast, when driving is strong, the detector returns a single response corresponding to the mean of the two single-state responses. This situation is similar to a motional averaging, observed in nuclear magnetic resonance spectroscopy. We study such quantum system, being periodically driven and probed, which consists of a qubit coupled to a quantum resonator. It is demonstrated that the transmission through the resonator is defined by the interplay between driving strength, qubit dissipation, and resonator linewidth. We demonstrate that our experimental results are in good agreement with numerical and analytical calculations.

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References

  1. O. Astafiev, K. Inomata, A.O. Niskanen, T. Yamamoto, Y.A. Pashkin, Y. Nakamura, J.S. Tsai, Nature 449, 588 (2007)

    Article  ADS  Google Scholar 

  2. S. Ashhab, J.R. Johansson, A.M. Zagoskin, F. Nori, New J. Phys. 11, 023030 (2009)

    Article  ADS  Google Scholar 

  3. M. Grajcar, S.H.W. van der Ploeg, A. Izmalkov, E. Il’ichev, H.G. Meyer, A. Fedorov, A. Shnirman, G. Schön, Nature Phys. 4, 612 (2008)

    Article  Google Scholar 

  4. F. Nori, Nature Phys. 4, 589 (2008)

    Article  ADS  Google Scholar 

  5. J. Hauss, A. Fedorov, S. André, V. Brosco, C. Hutter, R. Kothari, S. Yeshwanth, A. Shnirman, G. Schön, New J. Phys. 10, 095018 (2008)

    Article  ADS  Google Scholar 

  6. J.Q. You, Y.x. Liu, F. Nori, Phys. Rev. Lett. 100, 047001 (2008)

    Article  ADS  Google Scholar 

  7. L. Zhou, Z.R. Gong, Y.x. Liu, C.P. Sun, F. Nori, Phys. Rev. Lett. 101, 100501 (2008)

    Article  ADS  Google Scholar 

  8. O. Astafiev, A.M. Zagoskin, A.A. Abdumalikov, Y.A. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, J.S. Tsai, Science 327, 840 (2010)

    Article  ADS  Google Scholar 

  9. Y.S. Greenberg, A.N. Sultanov, Phys. Rev. A 95, 053840 (2017)

    Article  ADS  Google Scholar 

  10. A.A. Abdumalikov, O.V. Astafiev, Y.A. Pashkin, Y. Nakamura, J.S. Tsai, Phys. Rev. Lett. 107, 043604 (2011)

    Article  ADS  Google Scholar 

  11. A. Abragam,Principles of Nuclear Magnetism (Oxford, Oxford University Press, 1986)

  12. J. Li, M.P. Silveri, K.S. Kumar, J.M. Pirkkalainen, A. Vepsäläinen, W.C. Chien, J. Tuorila, M.A. Sillanpää, P.J. Hakonen, E.V. Thuneberg et al., Nat. Commun. 4, 1420 (2013)

    Article  ADS  Google Scholar 

  13. O.V. Ivakhnenko, S.N. Shevchenko, F. Nori, Sci. Rep. 8, 12218 (2018)

    Article  ADS  Google Scholar 

  14. K. Ono, S.N. Shevchenko, T. Mori, S. Moriyama, F. Nori, Phys. Rev. Lett. 122, 207703 (2019)

    Article  ADS  Google Scholar 

  15. S. Kono, Y. Masuyama, T. Ishikawa, Y. Tabuchi, R. Yamazaki, K. Usami, K. Koshino, Y. Nakamura, Phys. Rev. Lett. 119, 023602 (2017)

    Article  ADS  Google Scholar 

  16. J. Pan, Y. Fan, Y. Li, X. Dai, X. Wei, Y. Lu, C. Cao, L. Kang, W. Xu, J. Chen et al., Phys. Rev. B 96, 024502 (2017)

    Article  ADS  Google Scholar 

  17. D. Szombati, A.G. Frieiro, C. Müller, T. Jones, M. Jerger, A. Fedorov, Phys. Rev. Lett. 124, 070401 (2020)

    Article  ADS  Google Scholar 

  18. S. Ashhab, J.Q. You, F. Nori, New J. Phys. 11, 083017 (2009)

    Article  ADS  Google Scholar 

  19. S. Ashhab, J.Q. You, F. Nori, Phys. Scr. T137, 014005 (2009)

    Article  ADS  Google Scholar 

  20. W.P. Schleich,Quantum Optics in Phase Space (Wiley-, Berlin, 2001)

  21. M.O. Scully, M.S. Zubairy,Quantum Optics (Cambridge, Cambridge University Press, 1997)

  22. X. Gu, A.F. Kockum, A. Miranowicz, Y. Xi Liu, F. Nori, Phys. Rep. 718–719, 1 (2017)

    Article  ADS  Google Scholar 

  23. A.F. Kockum, F. Nori, inQuantum Bits with Josephson Junctions (Springer International Publishing, 2019), p. 703

  24. J.M. Pirkkalainen, S.U. Cho, F. Massel, J. Tuorila, T.T. Heikkila, P.J. Hakonen, M.A. Sillanpää, Nat. Commun. 6, 6981 (2014)

    Article  ADS  Google Scholar 

  25. M. Silveri, J. Tuorila, M. Kemppainen, E. Thuneberg, Phys. Rev. B 87, 134505 (2013)

    Article  ADS  Google Scholar 

  26. A.P. Saiko, R. Fedaruk, A. Kolasa, S.A. Markevich, Phys. Scr. 85, 045301 (2012)

    Article  ADS  Google Scholar 

  27. A.M. Zagoskin,Quantum Engineering: Theory and Design of Quantum Coherent Structures (Cambridge University Press, 2011)

  28. G. Wendin, Rep. Prog. Phys. 80, 106001 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  29. S.N. Shevchenko,Mesoscopic Physics meets Quantum Engineering (World Scientific, Singapore, 2019)

  30. A.P. Saiko, R. Fedaruk, S.A. Markevich, J. Phys. B: At. Mol.Opt. Phys. 47, 9 (2014)

    Article  Google Scholar 

  31. J.Q. You, Y.X. Liu, C.P. Sun, F. Nori, Phys. Rev. B 75, 104516 (2007)

    Article  ADS  Google Scholar 

  32. P. Scarlino, D.J. van Woerkom, U.C. Mendes, J.V. Koski, A.J. Landig, C.K. Andersen, S. Gasparinetti, C. Reichl, W. Wegscheider, K. Ensslin et al., Nat. Commun. 10, 3011 (2018)

    Article  ADS  Google Scholar 

  33. M. Silveri, K. Kumar, J. Tuorila, J. Li, A. Vepsäläinen, E. Thuneberg, G. Paraoanu, New J. Phys. 17, 043058 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  34. H. Ian, Y.x. Liu, F. Nori, Phys. Rev. A 81, 063823 (2010)

    Article  ADS  Google Scholar 

  35. G. Oelsner, P. Macha, O.V. Astafiev, E. Il’ichev, M. Grajcar, U. Hübner, B.I. Ivanov, P. Neilinger, H.G. Meyer, Phys. Rev. Lett. 110, 053602 (2013)

    Article  ADS  Google Scholar 

  36. S.N. Shevchenko, G. Oelsner, Y.S. Greenberg, P. Macha, D.S. Karpov, M. Grajcar, U. Hübner, A.N. Omelyanchouk, E. Il’ichev, Phys. Rev. B 89, 184504 (2014)

    Article  ADS  Google Scholar 

  37. D.S. Karpov, G. Oelsner, S.N. Shevchenko, Y.S. Greenberg, E. Ilichev, Low Temp. Phys. 42, 189 (2016)

    Article  ADS  Google Scholar 

  38. G. Oelsner, E. Il’ichev, U. Hübner, Phys. Rev. B 101, 054511 (2020)

    Article  ADS  Google Scholar 

  39. Y.H. Chang, D. Dubyna, W.C. Chien, C.H. Chen, C.S. Wu, W. Kuo, https://arXiv:1906.06730 (2019)

  40. R. Bianchetti, S. Filipp, M. Baur, J.M. Fink, M. Göppl, P.J. Leek, L. Steffen, A. Blais, A. Wallraff, Phys. Rev. A 80, 043840 (2009)

    Article  ADS  Google Scholar 

  41. S. André, V. Brosco, M. Marthaler, A. Shnirman, G. Schön, Phys. Scr. 137, 014016 (2009)

    Article  Google Scholar 

  42. S.N. Shevchenko, D.S. Karpov, Phys. Rev. Appl. 10, 014013 (2018)

    Article  ADS  Google Scholar 

  43. A.P. Saiko, S.A. Markevich, R. Fedaruk, Phys. Rev. A 93, 063834 (2016)

    Article  ADS  Google Scholar 

  44. S. Kohler, Phys. Rev. A 98, 023849 (2018)

    Article  ADS  Google Scholar 

  45. I. Pietikäinen, S. Danilin, K.S. Kumar, J. Tuorila, G.S. Paraoanu, J. Low Temp. Phys. 191, 354 (2018)

    Article  ADS  Google Scholar 

  46. I. Pietikäinen, S. Danilin, K.S. Kumar, A. Vepsäläinen, D.S. Golubev, J. Tuorila, G.S. Paraoanu, Phys. Rev. B 96, 020501 (2017)

    Article  ADS  Google Scholar 

  47. I. Pietikäinen, J. Tuorila, D.S. Golubev, G.S. Paraoanu, Phys. Rev. A 99, 063828 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  48. J.Q. You, X. Hu, S. Ashhab, F. Nori, Phys. Rev. B 75, 140515 (2007)

    Article  ADS  Google Scholar 

  49. J. Koch, T.M. Yu, J. Gambetta, A.A. Houck, D.I. Schuster, J. Majer, A. Blais, M.H. Devoret, S.M. Girvin, R.J. Schoelkopf, Phys. Rev. A 76, 042319 (2007)

    Article  ADS  Google Scholar 

  50. L.S. Bishop, J.M. Chow, J. Koch, A.A. Houck, M.H. Devoret, E. Thuneberg, S.M. Girvin, R.J. Schoelkopf, Nat. Phys. 5, 105 (2009)

    Article  Google Scholar 

  51. P. Macha, G. Oelsner, J.M. Reiner, M. Marthaler, S. André, G. Schön, U. Hübner, H.G. Meyer, E. Il’ichev, A.V. Ustinov, Nat. Commun. 5, 5146 (2014)

    Article  ADS  Google Scholar 

  52. A.L. Rakhmanov, A.M. Zagoskin, S. Savel’ev, F. Nori, Phys. Rev. B 77, 144507 (2008)

    Article  ADS  Google Scholar 

  53. G. Oelsner, S.H.W. van der Ploeg, P. Macha, U. Hübner, D. Born, S. Anders, E. Il’ichev, H.G. Meyer, M. Grajcar, S. Wünsch et al., Phys. Rev. B 81, 172505 (2010)

    Article  ADS  Google Scholar 

  54. M. Reagor, W. Pfaff, C. Axline, R.W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou et al., Phys. Rev. B 94, 014506 (2016)

    Article  ADS  Google Scholar 

  55. J.M. Fink, L. Steffen, P. Studer, L.S. Bishop, M. Baur, R. Bianchetti, D. Bozyigit, C. Lang, S. Filipp, P.J. Leek et al., Phys. Rev. Lett. 105, 163601 (2010)

    Article  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. B. Verkin Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine

    Denys S. Karpov & Aleksander N. Omelyanchouk

  2. Leibniz Institute of Photonic Technology, Jena, Germany

    Denys S. Karpov & Evgeni Il’ichev

  3. ARC Centre of Excellence for Engineered Quantum Systems, St. Lucia, Queensland, 4072, Australia

    Vladimir Y. Monarkha, Daniel Szombati, Alejandro G. Frieiro & Arkady Fedorov

  4. Okinawa Institute of Science and Technology Graduate University, Onna, 904-0495, Okinawa, Japan

    Vladimir Y. Monarkha

  5. School of Mathematics and Physics, University of Queensland, St Lucia, Queensland, 4072, Australia

    Alejandro G. Frieiro

  6. Novosibirsk State Technical University, Novosibirsk, Russia

    Evgeni Il’ichev

  7. V. N. Karazin Kharkov National University, Kharkov, Ukraine

    Sergey N. Shevchenko

Authors
  1. Denys S. Karpov
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  2. Vladimir Y. Monarkha
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  5. Aleksander N. Omelyanchouk
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  6. Evgeni Il’ichev
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  7. Arkady Fedorov
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  8. Sergey N. Shevchenko
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Corresponding author

Correspondence to Denys S. Karpov.

Additional information

Contribution to the Topical Issue “Advances in Quasi-Periodic and Non-Commensurate Systems”, edited by Tobias Stauber and Sigmund Kohler.

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Karpov, D.S., Monarkha, V.Y., Szombati, D. et al. Probabilistic motional averaging. Eur. Phys. J. B 93, 49 (2020). https://doi.org/10.1140/epjb/e2019-100514-8

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