Skip to main content
Erschienen in: Quantum Information Processing 12/2019

01.12.2019

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

verfasst von: Hao-Sheng Zeng, Yu-Kun Ren, Xiao-Lan Wang, Zhi He

Erschienen in: Quantum Information Processing | Ausgabe 12/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
2.
Zurück zum Zitat Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821–825 (1976)ADSMathSciNetCrossRef Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821–825 (1976)ADSMathSciNetCrossRef
3.
Zurück zum Zitat 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)ADSMathSciNetCrossRef 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)ADSMathSciNetCrossRef
4.
Zurück zum Zitat Laine, E.M., Piilo, J., Breuer, H.P.: Measure for the non-Markovianity of quantum processes. Phys. Rev. A 81(1–8), 062115 (2010)ADSCrossRef Laine, E.M., Piilo, J., Breuer, H.P.: Measure for the non-Markovianity of quantum processes. Phys. Rev. A 81(1–8), 062115 (2010)ADSCrossRef
5.
Zurück zum Zitat Rivas, Á., Huelga, S.F., Plenio, M.B.: Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105(1–4), 050403 (2010)ADSMathSciNetCrossRef Rivas, Á., Huelga, S.F., Plenio, M.B.: Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105(1–4), 050403 (2010)ADSMathSciNetCrossRef
6.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
7.
Zurück zum Zitat Luo, S., Fu, S., Song, H.: Quantifying non-Markovianity via correlations. Phys. Rev. A 86(1–4), 044101 (2012)ADSCrossRef Luo, S., Fu, S., Song, H.: Quantifying non-Markovianity via correlations. Phys. Rev. A 86(1–4), 044101 (2012)ADSCrossRef
8.
Zurück zum Zitat Chruscinski, D., Maniscalco, S.: Degree of non-Markovianity of quantum evolution. Phys. Rev. Lett. 112(1–5), 120404 (2014)ADSCrossRef Chruscinski, D., Maniscalco, S.: Degree of non-Markovianity of quantum evolution. Phys. Rev. Lett. 112(1–5), 120404 (2014)ADSCrossRef
9.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
10.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
11.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
12.
Zurück zum Zitat Song, H., Luo, S., Hong, Y.: Quantum non-Markovianity based on the Fisher-information matrix. Phys. Rev. A 91(1–6), 042110 (2015)ADSCrossRef Song, H., Luo, S., Hong, Y.: Quantum non-Markovianity based on the Fisher-information matrix. Phys. Rev. A 91(1–6), 042110 (2015)ADSCrossRef
13.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
14.
Zurück zum Zitat Dhar, H.S., Bera, M.N., Adesso, G.: Characterizing non-Markovianity via quantum interferometric power. Phys. Rev. A 91(1–9), 032115 (2015)ADSCrossRef Dhar, H.S., Bera, M.N., Adesso, G.: Characterizing non-Markovianity via quantum interferometric power. Phys. Rev. A 91(1–9), 032115 (2015)ADSCrossRef
15.
Zurück zum Zitat Paula, F.M., Obando, P.C., Sarandy, M.S.: Non-Markovianity through multipartite correlation measures. Phys. Rev. A 93(1–6), 042337 (2016)ADSCrossRef Paula, F.M., Obando, P.C., Sarandy, M.S.: Non-Markovianity through multipartite correlation measures. Phys. Rev. A 93(1–6), 042337 (2016)ADSCrossRef
16.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
18.
Zurück zum Zitat Shabani, A., Lidar, D.A.: Vanishing quantum discord is necessary and sufficient for completely positive maps. Phys. Rev. Lett. 102(1–4), 100402 (2009)ADSCrossRef Shabani, A., Lidar, D.A.: Vanishing quantum discord is necessary and sufficient for completely positive maps. Phys. Rev. Lett. 102(1–4), 100402 (2009)ADSCrossRef
19.
Zurück zum Zitat Breuer, H.P., Vacchini, B.: Structure of completely positive quantum master equations with memory kernel. Phys. Rev. E 79(1–12), 041147 (2009)ADSMathSciNetCrossRef Breuer, H.P., Vacchini, B.: Structure of completely positive quantum master equations with memory kernel. Phys. Rev. E 79(1–12), 041147 (2009)ADSMathSciNetCrossRef
20.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
21.
Zurück zum Zitat Addis, C., Brebner, G., Haikka, P., Maniscalco, S.: Coherence trapping and information backflow in dephasing qubits. Phys. Rev. A 89(1–4), 024101 (2014)ADSCrossRef Addis, C., Brebner, G., Haikka, P., Maniscalco, S.: Coherence trapping and information backflow in dephasing qubits. Phys. Rev. A 89(1–4), 024101 (2014)ADSCrossRef
22.
Zurück zum Zitat 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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
23.
Zurück zum Zitat Chruściński, D., Kossakowski, A., Pascazio, S.: Long-time memory in non-Markovian evolutions. Phys. Rev. A 81(1–6), 032101 (2010)ADSCrossRef Chruściński, D., Kossakowski, A., Pascazio, S.: Long-time memory in non-Markovian evolutions. Phys. Rev. A 81(1–6), 032101 (2010)ADSCrossRef
24.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
25.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
26.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
27.
Zurück zum Zitat Bae, J., Chruscinski, D.: Operational characterization of divisibility of dynamical maps. Phys. Rev. Lett. 117(1–6), 050403 (2016)ADSCrossRef Bae, J., Chruscinski, D.: Operational characterization of divisibility of dynamical maps. Phys. Rev. Lett. 117(1–6), 050403 (2016)ADSCrossRef
28.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
29.
Zurück zum Zitat 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)CrossRef 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)CrossRef
30.
Zurück zum Zitat Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum metrology in non-Markovian environments. Phys. Rev. Lett. 109(1–5), 233601 (2012)ADSCrossRef Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum metrology in non-Markovian environments. Phys. Rev. Lett. 109(1–5), 233601 (2012)ADSCrossRef
31.
Zurück zum Zitat 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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
32.
Zurück zum Zitat 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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
33.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
34.
Zurück zum Zitat Laine, E.M., Breuer, H.P., Piilo, J.: Nonlocal memory effects allow perfect teleportation with mixed states. Sci. Rep. 4(1–5), 4620 (2014) Laine, E.M., Breuer, H.P., Piilo, J.: Nonlocal memory effects allow perfect teleportation with mixed states. Sci. Rep. 4(1–5), 4620 (2014)
35.
Zurück zum Zitat 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)ADS 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)ADS
36.
Zurück zum Zitat Tang, N., Fan, Z.L., Zeng, H.S.: Improving the quality of noisy spatial quantum channels. Quantum Inf. Comput. 15, 0568–0581 (2015)MathSciNet Tang, N., Fan, Z.L., Zeng, H.S.: Improving the quality of noisy spatial quantum channels. Quantum Inf. Comput. 15, 0568–0581 (2015)MathSciNet
37.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
38.
Zurück zum Zitat Dalton, B.J., Barnett, S.M., Garraway, B.M.: Theory of pseudomodes in quantum optical processes. Phys. Rev. A 64(1–21), 053813 (2001)ADSMATHCrossRef Dalton, B.J., Barnett, S.M., Garraway, B.M.: Theory of pseudomodes in quantum optical processes. Phys. Rev. A 64(1–21), 053813 (2001)ADSMATHCrossRef
39.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
40.
Zurück zum Zitat Bruß, D., Macchiavello, C.: Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88(1–4), 127901 (2002)ADSCrossRef Bruß, D., Macchiavello, C.: Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88(1–4), 127901 (2002)ADSCrossRef
41.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
43.
Zurück zum Zitat Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)CrossRef Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)CrossRef
44.
Zurück zum Zitat Zhou, P., Swain, S.: Ultranarrow spectral lines via quantum interference. Phys. Rev. Lett. 77, 3995–3998 (1996)ADSCrossRef Zhou, P., Swain, S.: Ultranarrow spectral lines via quantum interference. Phys. Rev. Lett. 77, 3995–3998 (1996)ADSCrossRef
45.
Zurück zum Zitat Zhu, S.Y., Scully, M.O.: Spectral line elimination and spontaneous emission cancellation via quantum interference. Phys. Rev. Lett. 76, 388–391 (1996)ADSCrossRef Zhu, S.Y., Scully, M.O.: Spectral line elimination and spontaneous emission cancellation via quantum interference. Phys. Rev. Lett. 76, 388–391 (1996)ADSCrossRef
47.
Zurück zum Zitat Horodečki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232, 333–339 (1997)ADSMathSciNetMATHCrossRef Horodečki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232, 333–339 (1997)ADSMathSciNetMATHCrossRef
48.
Zurück zum Zitat Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)ADSMATHCrossRef Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)ADSMATHCrossRef
49.
Zurück zum Zitat Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett 113(1–5), 140401 (2014)ADSCrossRef Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett 113(1–5), 140401 (2014)ADSCrossRef
Metadaten
Titel
Non-Markovian dynamics and quantum interference in open three-level quantum systems
verfasst von
Hao-Sheng Zeng
Yu-Kun Ren
Xiao-Lan Wang
Zhi He
Publikationsdatum
01.12.2019
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 12/2019
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-019-2493-1

Weitere Artikel der Ausgabe 12/2019

Quantum Information Processing 12/2019 Zur Ausgabe

Neuer Inhalt