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Non-Markovian Dynamics for a Two-Atom-Coupled System Interacting with Local Reservoir at Finite Temperature

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Abstract

By using the effective non-Markovian measure (Breuer et al., Phys. Rev. Lett. 103, 210401 2009) we investigate non-Markovian dynamics of a pair of two-level atoms (TLAs) system, each of which interacting with a local reservoir. We show that subsystem dynamics can be controlled by manipulating the coupling between TLAs, temperature and relaxation rate of the atoms. Moreover, the correlation between non-Markovianity of subsystem and entanglement between the subsystem and the structured bath is investigated, the results show that the emergence of non-Markovianity has a negative effect on the entanglement.

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References

  1. Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of n-level systems. J. Math. Phys. (N.Y.) 17, 821 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  2. Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Breuer, H.P., Petruccione, F.: The theory of open quantum systems, Oxford University Press. Oxford (2007)

  4. Chru´sci´nski, D., Kossakowski, A.: Non-Markovian quantum dynamics: local versus nonlocal. Phys. Rev. Lett. 104, 070406 (2010)

    Article  ADS  Google Scholar 

  5. Jing, J., Yu, T.: Non-Markovian relaxation of a three-level system: quantum trajectory approach. Phys. Rev. Lett. 105, 240403 (2010)

    Article  ADS  Google Scholar 

  6. Madsen, K.H., Ates, S., Lund-Hansen, T., Löffler, A., Reitzenstein, S., Forchel, A., Lodahl, P.: Observation of non-Markovian dynamics of a single quantum dot in a micropillar cavity. Phys. Rev. Lett. 106, 233601 (2011)

    Article  ADS  Google Scholar 

  7. Liu, B.H., Li, L., Huang, Y.F., Li, C.F., Guo, G.C., Laine, E.M., Breuer, H.P., Piilo, J.: Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems. Nat. Phys. 7, 931 (2011)

    Article  Google Scholar 

  8. Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum metrology in non-Markovian environments. Phys. Rev. Lett. 109, 233601 (2012)

    Article  ADS  Google Scholar 

  9. Huelga, S.F., Rivas, Á., Plenio, M.B.: Non-Markovianity-assisted steady state entanglement. Phys. Rev. Lett. 108, 160402 (2012)

    Article  ADS  Google Scholar 

  10. Deffner, S., Lutz, E.: Quantum speed limit for non-Markovian dynamics. Phys. Rev. Lett. 111, 010402 (2013)

    Article  ADS  Google Scholar 

  11. Kennes, D. M., Kashuba, O., Pletyukhov, M., Schoeller, H., Meden, V.: Oscillatory dynamics and non-Markovian memory in dissipative quantum systems. Phys. Rev. Lett. 110, 100405 (2013)

    Article  ADS  Google Scholar 

  12. Tahara, H., Ogawa, Y., Minami, F., Akahane, K., Sasaki, M.: Long-time correlation in non-Markovian dephasing of an exciton-phonon System in InAs quantum dots. Phys. Rev. Lett. 112, 147404 (2014)

    Article  ADS  Google Scholar 

  13. Cerrillo, J., Cao, J.: Non-Markovian dynamical maps: numerical processing of open quantum trajectories. Phys. Rev. Lett. 112, 110401 (2014)

    Article  ADS  Google Scholar 

  14. McCutcheon, D.P.S., Lindner, N.H., Rudolph, T.: Error distributions on large entangled states with non-Markovian dynamics. Phys. Rev. Lett. 113, 260503 (2014)

    Article  ADS  Google Scholar 

  15. Fischer, R., Vidal, I., Gilboa, D., Correia, R.R.B., Ribeiro-Teixeira, A.C., Prado, S.D., Hickman, J., Silberberg, Y.: Light with tunable non-Markovian phase imprint. Phys. Phys. Rev. Lett. 115, 073901 (2015)

    Article  ADS  Google Scholar 

  16. Nagy, D., Domokos, P.: Nonequilibrium quantum criticality and non-Markovian environment: critical exponent of a quantum phase transition. Phys. Rev. Lett. 115, 043601 (2015)

    Article  ADS  Google Scholar 

  17. Wolf, M.M., Eisert, J., Cubitt, T.S., Cirac, J. I.: Assessing non-Markovian quantum dynamics. Phys. Rev. Lett. 101, 150402 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Breuer, H.P., Laine, E.M., Piilo, J.: Measure for the degree of non-Markovian behavior of quantum processes in open systems. Phys. Rev. Lett. 103, 210401 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  19. Laine, E.-M., Piilo, J., Breuer, H.-P.: Measure for the non-Markovianity of quantum processes. Phys. Rev. A 81, 062115 (2010)

    Article  ADS  Google Scholar 

  20. Vasile, R., Maniscalco, S., Paris, M.G.A., Breuer, H.P., Piilo, J.: Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps. Phys. Rev. A 84, 052118 (2011)

    Article  ADS  Google Scholar 

  21. Liu, J., Lu, X.-M., Wang, X.: Nonunital non-Markovianity of quantum dynamics. Phys. Rev. A 87, 042103 (2013)

    Article  ADS  Google Scholar 

  22. Rivas, Á., Huelga, S.F., Plenio, M.B.: Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105, 050403 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  23. Hou, S.C., Liang, S.L., Yi, X.X.: Non-Markovianity and memory effects in quantum open systems. Phys. Rev. A 91, 012109 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  24. Lu, X.-M., Wang, X., Sun, C.P.: Quantum fisher information flow and non-Markovian processes of open systems. Phys. Rev. A 82, 042103 (2010)

    Article  ADS  Google Scholar 

  25. Luo, S., Fu, S., Song, H.: Quantifying non-Markovianity via correlations. Phys. Rev. A 86, 044101 (2012)

    Article  ADS  Google Scholar 

  26. Lorenzo, S., Plastina, F., Paternostro, M.: Geometrical characterization of non-Markovianity. Phys. Rev. A 88, 020102 (2013)

    Article  ADS  Google Scholar 

  27. Bylicka, B., Chru´sci´nski, D., Maniscalco, S: Non-Markovianity as a resource for quantum technologies. arXiv:1301.2585

  28. Hou, S.C., Yi, X.X., Yu, S.X., Oh, C.H.: An alternative non-Markovianity measure by divisibility of dynamical map. Phys. Rev. A 83, 062115 (2011)

    Article  ADS  Google Scholar 

  29. Hou, S.C., Yi, X.X., Yu, S.X., Oh, C.H.: Singularity of dynamical maps. Phys. Rev. A 86, 012101 (2012)

    Article  ADS  Google Scholar 

  30. Rajagopal, A.K., Usha Devi, A.R., Rendell, R.W.: Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras. Phys. Rev. A 82, 042107 (2010)

    Article  ADS  Google Scholar 

  31. Alipour, S., Mani, A., Rezakhani, A.T.: Quantum discord and non-Markovianity of quantum dynamics. Phys. Rev. A 85, 052108 (2012)

    Article  ADS  Google Scholar 

  32. Hall, M.J.W., Cresser, J.D., Li, L., Andersson, E.: Canonical form of master equations and characterization of non-Markovianity. Phys. Rev. A 89, 042120 (2014)

    Article  ADS  Google Scholar 

  33. Chruscinski, D., Maniscalco, S.: Degree of non-Markovianity of quantum evolution. Phys. Rev. Lett. 112, 120404 (2014)

    Article  ADS  Google Scholar 

  34. Liu, B.H., Li, L., Huang, Y.F., Li, C.F., Guo, G.C., Laine, E.M., Breuer, H.P., Piilo, J.: Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems. Nat. Phys. 7, 931 (2011)

    Article  Google Scholar 

  35. Yu, T., Eberly, J.H.: Evolution and control of decoherence of “standard” mixed states. Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  36. Carmichael, H.J.: Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Plank Equations, pp 6–32. Springer, Berlin (1999)

    Book  Google Scholar 

  37. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 11574022 and 11174024) and the Open Project Program of State Key Laboratory of Low-Dimensional Quantum Physics (Tsinghua University) grants Nos. KF201407.

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Correspondence to Guo-Feng Zhang.

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Jiang, L., Zhang, GF. Non-Markovian Dynamics for a Two-Atom-Coupled System Interacting with Local Reservoir at Finite Temperature. Int J Theor Phys 56, 906–915 (2017). https://doi.org/10.1007/s10773-016-3233-2

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  • DOI: https://doi.org/10.1007/s10773-016-3233-2

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