Non-Markovian dynamics and quantum interference in open three-level quantum systems

  • Hao-Sheng ZengEmail author
  • Yu-Kun Ren
  • Xiao-Lan Wang
  • Zhi He


The exact analytical solutions for the dynamics of the dissipative three-level V-type and \(\varLambda \)-type atomic systems in the vacuum Lorentzian environments are presented. Quantum interference between the spontaneous emissions of different decaying channels for the V-type atomic system is observed. For the dissipative \(\varLambda \)-type atomic system, however, similar phenomenon of quantum interference does not exist. We demonstrate that quantum interference can be used to protect effectively the quantum entanglement and quantum coherence. The control of the transition from Markovian to non-Markovian processes is discussed.


Non-Markovian dynamics Quantum interference Quantum entanglement Quantum coherence 



This work is supported by the National Natural Science Foundation of China (Grant No. 11275064), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20124306110003) and the Construct Program of the National Key Discipline.


  1. 1.
    Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119–130 (1976)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821–825 (1976)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    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(1–4), 210401 (2009)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Laine, E.M., Piilo, J., Breuer, H.P.: Measure for the non-Markovianity of quantum processes. Phys. Rev. A 81(1–8), 062115 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    Rivas, Á., Huelga, S.F., Plenio, M.B.: Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105(1–4), 050403 (2010)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Lu, X.M., Wang, X.G., Sun, C.P.: Quantum Fisher information flow and non-Markovian processes of open systems. Phys. Rev. A 82(1–4), 042103 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    Luo, S., Fu, S., Song, H.: Quantifying non-Markovianity via correlations. Phys. Rev. A 86(1–4), 044101 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Chruscinski, D., Maniscalco, S.: Degree of non-Markovianity of quantum evolution. Phys. Rev. Lett. 112(1–5), 120404 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    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(1–11), 042120 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    Fanchini, F.F., Karpat, G., Cakmak, B., Castelano, L.K., Aguilar, G.H., Farias, O.J., Walborn, S.P., Souto Ribeiro, P.H., de Oliveira, M.C.: Non-Markovianity through accessible information. Phys. Rev. Lett. 112(1–5), 210402 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    Chruscinski, D., Macchiavello, C., Maniscalco, S.: Detecting non-Markovianity of quantum evolution via spectra of dynamical maps. Phys. Rev. Lett. 118(1–5), 080404 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    Song, H., Luo, S., Hong, Y.: Quantum non-Markovianity based on the Fisher-information matrix. Phys. Rev. A 91(1–6), 042110 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    Chen, S.L., Lambert, N., Li, C.M., Miranowicz, A., Chen, Y.N., Nori, F.: Quantifying non-markovianity with temporal steering. Phys. Rev. Lett. 116(1–6), 020503 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    Dhar, H.S., Bera, M.N., Adesso, G.: Characterizing non-Markovianity via quantum interferometric power. Phys. Rev. A 91(1–9), 032115 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    Paula, F.M., Obando, P.C., Sarandy, M.S.: Non-Markovianity through multipartite correlation measures. Phys. Rev. A 93(1–6), 042337 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    He, Z., Zeng, H.S., Li, Y., Wang, Q., Yao, C.M.: Non-Markovianity measure based on the relative entropy of coherence in an extended space. Phys. Rev. A 96(1–7), 022106 (2017)ADSCrossRefGoogle Scholar
  17. 17.
    Breuer, H.P., Vacchini, B.: Quantum semi-Markov processes. Phys. Rev. Lett. 101(1–4), 140402 (2008)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Shabani, A., Lidar, D.A.: Vanishing quantum discord is necessary and sufficient for completely positive maps. Phys. Rev. Lett. 102(1–4), 100402 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    Breuer, H.P., Vacchini, B.: Structure of completely positive quantum master equations with memory kernel. Phys. Rev. E 79(1–12), 041147 (2009)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Haikka, P., Johnson, T.H., Maniscalco, S.: Non-Markovianity of local dephasing channels and time-invariant discord. Phys. Rev. A 87(R1–5), 010103 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    Addis, C., Brebner, G., Haikka, P., Maniscalco, S.: Coherence trapping and information backflow in dephasing qubits. Phys. Rev. A 89(1–4), 024101 (2014)ADSCrossRefGoogle Scholar
  22. 22.
    Zeng, H.S., Zheng, Y.P., Tang, N., Wang, G.Y.: Correlation quantum beats induced by non-Markovian effect. Quantum Inf. Process 12, 1637–1650 (2013)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Chruściński, D., Kossakowski, A., Pascazio, S.: Long-time memory in non-Markovian evolutions. Phys. Rev. A 81(1–6), 032101 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    Haikka, P., Cresser, J.D., Maniscalco, S.: Comparing different non-Markovianity measures in a driven qubit system. Phys. Rev. A 83(1–5), 012112 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    Zeng, H.S., Tang, N., Zheng, Y.P., Wang, G.Y.: Equivalence of the measure of non-Markovianity for open two-level systems. Phys. Rev. A 84(1–6), 032118 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    Wissmann, S., Breuer, H.P., Vacchini, B.: Generalized trace-distance measure connecting quantum and classical non-Markovianity. Phys. Rev. A 92(1–10), 042108 (2015)ADSCrossRefGoogle Scholar
  27. 27.
    Bae, J., Chruscinski, D.: Operational characterization of divisibility of dynamical maps. Phys. Rev. Lett. 117(1–6), 050403 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    Bylicka, B., Johansson, M., Acin, A.: Constructive method for detecting the information backflow of non-Markovian dynamics. Phys. Rev. Lett. 118(1–5), 120501 (2017)ADSCrossRefGoogle Scholar
  29. 29.
    Liu, Y., Cheng, W., Gao, Z.Y., Zeng, H.S.: Environmental coherence and excitation effects in non-Markovian dynamics. Opt. Express 23, 023021–023034 (2015)CrossRefGoogle Scholar
  30. 30.
    Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum metrology in non-Markovian environments. Phys. Rev. Lett. 109(1–5), 233601 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    Ren, Y.K., Tang, L.M., Zeng, H.S.: Protection of quantum Fisher information in entangled states via classical driving. Quantum Inf. Process 15, 5011–5021 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Ren, Y.K., Wang, X.L., Zeng, H.S.: Protection of quantum Fisher information for multiple phases in open quantum systems. Quantum Inf. Process 17(1–16), 5 (2018)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Vasile, R., Olivares, S., Paris, M.G.A., Maniscalco, S.: Continuous-variable quantum key distribution in non-Markovian channels. Phys. Rev. A 83(1–6), 042321 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    Laine, E.M., Breuer, H.P., Piilo, J.: Nonlocal memory effects allow perfect teleportation with mixed states. Sci. Rep. 4(1–5), 4620 (2014)Google Scholar
  35. 35.
    Bylicka, B., Chruściński, D., Maniscalco, S.: Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective. Sci. Rep. 4(1–7), 5720 (2014)ADSGoogle Scholar
  36. 36.
    Tang, N., Fan, Z.L., Zeng, H.S.: Improving the quality of noisy spatial quantum channels. Quantum Inf. Comput. 15, 0568–0581 (2015)MathSciNetGoogle Scholar
  37. 37.
    Schmidt, R., Negretti, A., Ankerhold, J., Calarco, T., Stockburger, J.T.: Optimal control of open quantum systems: cooperative effects of driving and dissipation. Phys. Rev. Lett. 107(1–5), 130404 (2011)ADSCrossRefGoogle Scholar
  38. 38.
    Dalton, B.J., Barnett, S.M., Garraway, B.M.: Theory of pseudomodes in quantum optical processes. Phys. Rev. A 64(1–21), 053813 (2001)ADSzbMATHCrossRefGoogle Scholar
  39. 39.
    Gu, W.J., Li, G.X.: Non-Markovian behavior for spontaneous decay of a V-type three-level atom with quantum interference. Phys. Rev. A 85(1–4), 014101 (2012)ADSCrossRefGoogle Scholar
  40. 40.
    Bruß, D., Macchiavello, C.: Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88(1–4), 127901 (2002)ADSCrossRefGoogle Scholar
  41. 41.
    Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88(1–4), 127902 (2002)ADSCrossRefGoogle Scholar
  42. 42.
    Knill, E.: Fault-tolerant postselected quantum computation: schemes (2004). arXiv:quant-ph/0402171
  43. 43.
    Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)CrossRefGoogle Scholar
  44. 44.
    Zhou, P., Swain, S.: Ultranarrow spectral lines via quantum interference. Phys. Rev. Lett. 77, 3995–3998 (1996)ADSCrossRefGoogle Scholar
  45. 45.
    Zhu, S.Y., Scully, M.O.: Spectral line elimination and spontaneous emission cancellation via quantum interference. Phys. Rev. Lett. 76, 388–391 (1996)ADSCrossRefGoogle Scholar
  46. 46.
    Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413–1415 (1996)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Horodečki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232, 333–339 (1997)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)ADSzbMATHCrossRefGoogle Scholar
  49. 49.
    Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett 113(1–5), 140401 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, and Department of PhysicsHunan Normal UniversityChangshaChina

Personalised recommendations