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The Leggett–Garg inequalities and the relative entropy of coherence in the Bixon–Jortner model

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Abstract

We investigate the Leggett–Garg inequalities and the relative entropy of coherence in the Bixon–Jortner model. First, we analytically derive the general solution of the Bixon–Jortner model by a technique of the Laplace transform. So far, only a special solution has been known for this model. The model has a single state coupled to equally spaced quasi-continuum states. These couplings cause discontinuities in the time evolution of the occupation probability of each state. Second, using the analytical solution, we show that the probability distribution of the quasi-continuum states approaches the Lorentzian function in a period of time between the initial time and the first discontinuity. Third, we examine violation of the Leggett–Garg inequalities and temporal variation of the relative entropy of coherence in the model. We prove that both the inequalities and the relative entropy are invariant under transformations of the energy-level detuning of the single state.

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References

  1. M. Bixon, J. Jortner, J. Chem. Phys. 48, 715 (1968)

    Article  ADS  Google Scholar 

  2. R. Englman, J. Jortner, Mol. Phys. 18, 145 (1970)

    Article  ADS  Google Scholar 

  3. J. Jortner, J. Chem. Phys. 64, 4860 (1976)

    Article  ADS  Google Scholar 

  4. G.C. Stey, R.W. Gibberd, Physica 60, 1 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  5. R. Lefebvre, J. Savolainen, J. Chem. Phys. 60, 2509 (1974)

    Article  ADS  Google Scholar 

  6. J.J. Yeh, C.M. Bowden, J.H. Eberly, J. Chem. Phys. 76, 5936 (1982)

    Article  ADS  Google Scholar 

  7. P.W. Milonni, J.R. Ackerhalt, H.W. Galbraith, M.-L. Shih, Phys. Rev. A 28, 32 (1983)

    Article  ADS  Google Scholar 

  8. J.L. Skinner, H.C. Andersen, M.D. Fayer, Phys. Rev. A 24, 1994 (1981)

    Google Scholar 

  9. S. Bar-Ad, P. Kner, M.V. Marquezini, S. Mukamel, D.S. Chemla, Phys. Rev. Lett. 78, 1363 (1997)

    Article  ADS  Google Scholar 

  10. S. Santra, B. Cruikshank, R. Balu, K. Jacobs, J. Phys. A: Math. Theor. 50, 415302 (2017)

    Article  Google Scholar 

  11. P.M. Radmore, S. Tarzi, P.L. Knight, J. Mod. Opt. 34, 587 (1987)

    Article  ADS  Google Scholar 

  12. S. Tarzi, P.M. Radmore, Phys. Rev. A 37, 4734 (1988)

    Article  ADS  Google Scholar 

  13. S. Tarzi, P.M. Radmore, S.M. Barnett, J. Phys. B: At. Mol. Opt. Phys. 22, 2935 (1989)

    Article  ADS  Google Scholar 

  14. P.M. Radmore, J. Mod. Opt. 42, 579 (1995)

    Article  ADS  Google Scholar 

  15. S.M. Barnett, P.M. Radmore,Methods in Theoretical Quantum Optics (Oxford University Press, Oxford, 1997)

  16. A.J. Leggett, A. Garg, Phys. Rev. Lett. 54, 857 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  17. C. Emary, N. Lambert, F. Nori, Rep. Prog. Phys. 77, 016001 (2014)

    Article  ADS  Google Scholar 

  18. A. Palacios-Laloy, F. Mallet, F. Nguyen, P. Bertet, D. Vion, D. Esteve, A.N. Korotkov, Nat. Phys. 6, 442 (2010)

    Article  Google Scholar 

  19. M.E. Goggin, M.P. Almeida, M. Barbieri, B.P. Lanyon, J.L. O’Brien, A.G. White, G.J. Pryde, Proc. Natl. Acad. Sci. U.S.A. 108, 1256 (2011)

    Article  ADS  Google Scholar 

  20. G.C. Knee, S. Simmons, E.M. Gauger, J.J.L. Morton, H. Riemann, N.V. Abrosimov, P. Becker, H.-J. Pohl, K.M. Itoh, M.L.W. Thewalt, G.A.D. Briggs, S.C. Benjamin, Nat. Commun. 3, 606 (2012)

    Article  ADS  Google Scholar 

  21. T. Baumgratz, M. Cramer, M.B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)

    Article  ADS  Google Scholar 

  22. Y.-R. Zhang, L.-H. Shao, Y. Li, H. Fan, Phys. Rev. A 93, 012334 (2016)

    Article  ADS  Google Scholar 

  23. A. Friedenberger, E. Lutz, Phys. Rev. A 95, 022101 (2017)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Advanced Algorithm and Systems Co., Ltd., 7F Ebisu-IS Building, 1-13-6 Ebisu, Shibuya-ku, Tokyo, 150-0013, Japan

    Hiroo Azuma

  2. Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo, 112-8610, Japan

    Masashi Ban

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  1. Hiroo Azuma
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  2. Masashi Ban
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Correspondence to Hiroo Azuma.

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Azuma, H., Ban, M. The Leggett–Garg inequalities and the relative entropy of coherence in the Bixon–Jortner model. Eur. Phys. J. D 72, 187 (2018). https://doi.org/10.1140/epjd/e2018-90275-7

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  • DOI: https://doi.org/10.1140/epjd/e2018-90275-7

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