Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Quantum Information Processing
Published in: Quantum Information Processing 7/2015

01-07-2015

Analytical solution and entanglement swapping of a double Jaynes–Cummings model in non-Markovian environments

Authors: Hong-Mei Zou, Mao-Fa Fang

Published in: Quantum Information Processing | Issue 7/2015

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Analytical solution and entanglement swapping of a double Jaynes–Cummings model in non-Markovian environments are investigated by the time convolution less master equation method. We obtain the analytical solution of this model and discuss in detail the influence of atom–cavity coupling, non-Markovian effect and initial state purity on entanglement dynamics. The results show that in the non-Markovian environments, the entanglement between two cavities can be swapped to other bipartite subsystems by interaction between an atom and its own cavity. Due to the dissipation of environment, the entanglements of all bipartite subsystems will eventually decay to zero when the atom couples weakly to its cavity and the non-Markovian effect is also weak. All bipartite subsystems can tend to steady entanglement states if and only if there is the strong atom–cavity coupling or the strong non-Markovian effect. The steady state of the subsystem composed of an atom and its own cavity is independent on the purity, but the steady states of other bipartite subsystems are dependent on the purity.
previous article Witnessing the boundary between Markovian and non-Markovian quantum dynamics: a Green’s function approach

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now
Literature
1.
Schrödinger, E.: The present status of quantum mechanics. Naturwissenschaften 23, 807 (1935)ADSCrossRef
2.
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH
3.
4.
Julsgaard, B., Kozhekin, A., Polzik, E.S.: Experimental long-lived entanglement of two macroscopic objects. Nature 413, 400 (2001)ADSCrossRef
5.
Blinov, B.B., et al.: Observation of entanglement between a single trapped atom and a single photon. Nature 428, 153 (2004)ADSCrossRef
6.
Haroche, S., Raimond, J.M.: Exploring the Quantum: Atoms, Cavities, and Photons. Oxford University Press, Oxford (2006)CrossRef
7.
Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)ADSCrossRef
8.
Bellomo, B., et al.: Entanglement trapping in structured environments. Phys. Rev. A 78, 060302(R) (2008)ADSCrossRef
9.
Breuer, H.P., Piilo, J.: Stochastic jump processes for non-Markovian quantum dynamics. Europhys. Lett. 85, 50004 (2009)ADSCrossRef
10.
Li, Y., Zhou, J., Guo, H.: Effect of the dipole–dipole interaction for two atoms with different couplings in a non-Markovian environment. Phys. Rev. A 79, 012309 (2009)ADSCrossRef
11.
An, J.H., Zhang, W.M.: Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels. Phys. Rev. A 76, 042127 (2007)ADSCrossRef
12.
Tong, Q.J., et al.: Mechanism of entanglement preservation. Phys. Rev. A 81, 052330 (2010)ADSCrossRef
13.
Xiao, X., Fang, M.-F., Li, Y.-L.: Non-Markovian dynamics of two qubits driven by classical fields: population trapping and entanglement preservation. J. Phys. B At. Mol. Opt. Phys. 43, 185505 (2010)ADSCrossRef
14.
Cai, J., Popescu, S., Briegel, H.-J.: Dynamic entanglement in oscillating molecules and potential biological implications. Phys. Rev. E 82, 021921 (2010)ADSCrossRef
15.
Mazzola, L., et al.: Sudden death and sudden birth of entanglement in common structured reservoirs. Phys. Rev. A 79, 042302 (2009)ADSCrossRef
16.
Cao, X.F., Zheng, H.: Non-Markovian disentanglement dynamics of a two-qubit system. Phys. Rev. A 77, 022320 (2008)ADSCrossRef
17.
Xu, Z.Y., Feng, M.: Sudden death and birth of entanglement beyond the Markovian approximation. Phys. Lett. A 373, 1906 (2009)MATHADSCrossRef
18.
Wolf, A., et al.: Entangling two distant oscillators with a quantum reservoir. Europhys. Lett. 95, 60008 (2011)ADSCrossRef
19.
Altintas, F., Eryigit, R.: Dissipative dynamics of quantum correlations in the strong-coupling regime. Phys. Rev. A 87, 022124 (2013)ADSCrossRef
20.
Memarzadeh, L., Mancini, S.: Entanglement dynamics for qubits dissipating into a common environment. Phys. Rev. A 87, 032303 (2013)ADSCrossRef
21.
Fanchini, F.F., et al.: Non-Markovianity through accessible information. Phys. Rev. Lett. 112, 210402 (2014)ADSCrossRef
22.
Haseli, S., et al.: Non-Markovianity through flow of information between a system and an environment. Phys. Rev. A 90, 052118 (2014)ADSCrossRef
23.
Reina, J.H., Susa, C.E., Fanchini, F.F.: Extracting information from qubit-environment correlations. Sci. Rep. 4, 7443 (2014)ADSCrossRef
24.
Fanchini, F.F., Cornelio, M.F., de Oliveira, M.C., Caldeira, A.O.: Conservation law for distributed entanglement of formation and quantum discord. Phys. Rev. A 84, 012313 (2011)ADSCrossRef
25.
26.
Jaynes, E.T., Cummings, F.W.: Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89 (1963)CrossRef
27.
Law, C.K., Eberly, J.H.: Arbitrary control of a quantum electromagnetic field. Phys. Rev. Lett. 76, 1055 (1996)ADSCrossRef
28.
Strauch, F.W., Jacobs, K., Simmonds, R.W.: Arbitrary control of entanglement between two superconducting resonators. Phys. Rev. Lett. 105, 050501 (2010)ADSCrossRef
29.
Childs, A.M., Chuang, I.L.: Universal quantum computation with two-level trapped ions. Phys. Rev. A 63, 012306 (2000)ADSCrossRef
30.
Ben-Kish, A., et al.: Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-\(\frac{1}{2}\) particle. Phys. Rev. Lett. 90, 037902 (2003)ADSCrossRef
31.
Strauch, F.W., et al.: Entangled-state synthesis for superconducting resonators. Phys. Rev. A 85, 022335 (2012)ADSCrossRef
32.
Brion, E., Moølmer, K., Saffman, M.: Quantum computing with collective ensembles of multilevel systems. Phys. Rev. Lett. 99, 260501 (2007)ADSCrossRef
33.
Yönaç, M., Yu, T., Eberly, J.H.: Sudden death of entanglement of two Jaynes–Cummings atoms. J. Phys. B 39, S621 (2006)ADSCrossRef
34.
Yönaç, M., Yu, T., Eberly, J.H.: Pairwise concurrence dynamics: a four-qubit model. J. Phys. B 40, S45 (2007)ADSCrossRef
35.
Sainz, I., Björk, G.: Entanglement invariant for the double Jaynes–Cummings model. Phys. Rev. A 76, 042313 (2007)ADSCrossRef
36.
Vieira, A.R., de Oliveira Junior, J.G.G., Peixoto de Faria, J.G., Nemes, M.C.: Geometry in the entanglement dynamics of the double Jaynes–Cummings model. Braz. J. Phys. 44, 19 (2014)CrossRef
37.
Veitia, A., et al.: Mutual preservation of entanglement. Phys. Lett. A 376, 2755 (2012)ADSCrossRef
38.
Breuer, H.-P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)MATH
39.
Bellomo, B., Lo Franco, R., Compagno, G.: Non-Markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99, 160502 (2007)ADSCrossRef
40.
Wei, T.C., et al.: Maximal entanglement versus entropy for mixed quantum states. Phys. Rev. A 67, 022110 (2003)ADSCrossRef
41.
Żukowski, M., et al.: “Event-readydetectors” Bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287 (1993)ADSCrossRef
42.
43.
Bose, S., Vedral, V., Knight, P.L.: Multiparticle generalization of entanglement swapping. Phys. Rev. A 57, 822 (1998)ADSCrossRef
44.
45.
Wang, L., Li, S., Zheng, H.: Conditions for the local manipulation of tripartite Gaussian states. Phys. Rev. A 67, 062317 (2003)ADSCrossRef
46.
Pirandola, S., et al.: Macroscopic entanglement by entanglement swapping. Phys. Rev. Lett. 97, 150403 (2006)ADSCrossRef
47.
Megidish, E., et al.: Entanglement swapping between photons that have never coexisted. Phys. Rev. Lett. 110, 210403 (2013)ADSCrossRef
48.
Scala, M., et al.: Population trapping due to cavity losses. Phys. Rev. A 77, 043827 (2008)ADSCrossRef
49.
Scala, M., et al.: Microscopic derivation of the Jaynes–Cummings model with cavity losses. Phys. Rev. A 75, 013811 (2007)ADSCrossRef
50.
Bellomo, B., Franco, R.L., Compagno, G.: Entanglement dynamics of two independent qubits in environments with and without memory. Phys. Rev. A 77, 032342 (2008)ADSCrossRef
51.
Wootter, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRef
52.
Hagley, E., et al.: Generation of Einstein–Podolsky–Rosen pairs of atoms. Phys. Rev. Lett. 79, 1 (1997)ADSCrossRef
53.
Kuhr, S., et al.: Ultrahigh finesse Fabry–Pérot superconducting resonator. Appl. Phys. Lett. 90, 164101 (2007)ADSCrossRef
Metadata
Title
Analytical solution and entanglement swapping of a double Jaynes–Cummings model in non-Markovian environments
Authors
Hong-Mei Zou
Mao-Fa Fang
Publication date
01-07-2015
Publisher
Springer US
Published in
Quantum Information Processing / Issue 7/2015
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-015-1006-0

Other articles of this Issue 7/2015

Quantum Information Processing 7/2015 Go to the issue

OriginalPaper

A quantum algorithm for Viterbi decoding of classical convolutional codes

OriginalPaper

Perfect discrimination of projective measurements with the rank of all projectors being one

OriginalPaper

Effect of local filtering on freezing phenomena of quantum correlation

OriginalPaper

Quantum circuits for -multiplication with subquadratic gate count

OriginalPaper

Criticality, factorization and Wigner–Yanase skew information in quantum spin chains

OriginalPaper

Construction of mutually unbiased bases in