Abstract

In this work, we study the effects of different forms of correlations of environments on the dynamics of open systems’ entanglement and discord. We consider two two-level atoms A and B interacting, respectively with two spatially separated modes a and b, each of which is in turn surrounded by a dissipative reservoir. The two modes may initially be in an entangled or classically correlated or product state with their marginal state being the same in all the cases. We compare the power of different environmental correlation forms in the revival of the atoms’ entanglement and discord in the strong atom–mode coupling regime. We also show how the dynamical behavior of the atoms’ entanglement and discord nontrivially change by the presence of initial environmental correlation in the weak atom–mode coupling regime. Finally, we reveal that initial entanglement between the modes can induce correlations between initially uncorrelated atoms.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  48. B.-H. Liu, D.-Y. Cao, Y.-F. Huang, C.-F. Li, G.-C. Guo, E.-M. Laine, H.-P. Breuer, and J. Piilo, “Photonic realization of nonlocal memory effects and non-Markovian quantum probes,” arXiv 1208.1358v1 (2012).
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    [CrossRef]
  51. M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo, and K.-A. Suominen, “Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation,” J. Phys. A 40, 14527 (2007).
    [CrossRef]
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    [CrossRef]

2012

O. Jiménez Farías, A. Valdés-Hernández, G. H. Aguilar, P. H. Souto Ribeiro, S. P. Walborn, L. Davidovich, X. F. Qian, and J. H. Eberly, “Experimental investigation of dynamical invariants in bipartite entanglement,” Phys. Rev. A 85, 012314 (2012).
[CrossRef]

Z. X. Man, Y. J. Xia, A. Smirne, and B. Vacchini, “Quantum interference induced by initial system–environment correlations,” Phys. Lett. A 376, 2477–2483 (2012).
[CrossRef]

E.-M. Laine, H.-P. Breuer, J. Piilo, C.-F. Li, and G. C. Guo, “Nonlocal memory effects in the dynamics of open quantum systems,” Phys. Rev. Lett. 108, 210402 (2012).
[CrossRef]

2011

D. Z. Rossatto, T. Werlang, L. K. Castelano, C. J. Villas-Boas, and F. F. Fanchini, “Purity as a witness for initial system–environment correlations in open-system dynamics,” Phys. Rev. A 84, 042113 (2011).
[CrossRef]

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83, 064102 (2011).
[CrossRef]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, “Experimental investigation of initial system–environment correlations via trace-distance evolution,” Phys. Rev. A 84, 032112 (2011).
[CrossRef]

J. Dajka, J. Luczka, and P. Hänggi, “Distance between quantum states in the presence of initial qubit–environment correlations: a comparative study,” Phys. Rev. A 84, 032120 (2011).
[CrossRef]

H. T. Tan and W. M. Zhang, “Non-Markovian dynamics of an open quantum system with initial system-reservoir correlations: a nanocavity coupled to a coupled-resonator optical waveguide,” Phys. Rev. A 83, 032102 (2011).
[CrossRef]

A. R. Usha Devi, A. K. Rajagopal, and Sudha, “Open-system quantum dynamics with correlated initial states, not completely positive maps, and non-Markovianity,” Phys. Rev. A 83, 022109 (2011).
[CrossRef]

N. B. An, J. Kim, and K. Kim, “Entanglement dynamics of three interacting two-level atoms within a common structured environment,” Phys. Rev. A 84, 022329 (2011).
[CrossRef]

Z. X. Man, Y. J. Xia, and N. B. An, “Quantum dissonance induced by a thermal field and its dynamics in dissipative systems,” Eur. Phys. J. D 64, 521–529 (2011).
[CrossRef]

2010

E.-M. Laine, J. Piilo, and H.-P. Breuer, “Measure for the non-Markovianity of quantum processes,” Phys. Rev. A 81, 062115 (2010).
[CrossRef]

Y. J. Zhang, X. B. Zou, Y. J. Xia, and G. C. Guo, “Different entanglement dynamical behaviors due to initial system–environment correlations,” Phys. Rev. A 82, 022108 (2010).
[CrossRef]

A. G. Dijkstra and Y. Tanimura, “Non-Markovian entanglement dynamics in the presence of system–bath coherence,” Phys. Rev. Lett. 104, 250401 (2010).
[CrossRef]

Z. X. Man, Y. J. Xia, and N. B. An, “Entanglement measure and dynamics of multiqubit systems: non-Markovian versus Markovian and generalized monogamy relations,” New J. Phys. 12, 033020 (2010).
[CrossRef]

N. B. An, J. Kim, and K. Kim, “Nonperturbative analysis of entanglement dynamics and control for three qubits in a common lossy cavity,” Phys. Rev. A 82, 032316 (2010).
[CrossRef]

F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).
[CrossRef]

J. Maziero, T. Werlang, F. F. Fanchini, L. C. Céleri, and R. M. Serra, “System–reservoir dynamics of quantum and classical correlations,” Phys. Rev. A 81, 022116 (2010).
[CrossRef]

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
[CrossRef]

J. S. Xu, X. Y. Xu, C. F. Li, C. J. Zhang, X. B. Zou, and G. C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Commun. 1, 7 (2010).
[CrossRef]

C. Viviescas, I. Guevara, A. R. R. Carvalho, M. Busse, and A. Buchleitner, “Entanglement dynamics in open two-qubit systems via diffusive quantum trajectories,” Phys. Rev. Lett. 105, 210502 (2010).
[CrossRef]

Q. H. Chen, Y. Yang, T. Liu, and K. L. Wang, “Entanglement dynamics of two independent Jaynes–Cummings atoms without the rotating-wave approximation,” Phys. Rev. A 82, 052306 (2010).
[CrossRef]

E.-M. Laine, J. Piilo, and H.-P. Breuer, “Witness for initial system–environment correlations in open-system dynamics,” Europhys. Lett. 92, 60010 (2010).
[CrossRef]

J. Dajka and J. Luczka, “Distance growth of quantum states due to initial system–environment correlations,” Phys. Rev. A 82, 012341 (2010).
[CrossRef]

A. Smirne, H. P. Breuer, J. Piilo, and B. Vacchini, “Initial correlations in open-systems dynamics: the Jaynes–Cummings model,” Phys. Rev. A 82, 062114 (2010).
[CrossRef]

2009

M. Ban, “Quantum master equation for dephasing of a two-level system with an initial correlation,” Phys. Rev. A 80, 064103 (2009).
[CrossRef]

L. Mazzola, S. Maniscalco, J. Piilo, K. A. Suominen, and B. M. Garraway, “Sudden death and sudden birth of entanglement in common structured reservoirs,” Phys. Rev. A 79, 042302 (2009).
[CrossRef]

J. S. Xu, C. F. Li, X. Y. Xu, C. H. Shi, X. B. Zou, and G. C. Guo, “Experimental characterization of entanglement dynamics in noisy channels,” Phys. Rev. Lett. 103, 240502 (2009).
[CrossRef]

J. Maziero, L. C. Celeri, R. M. Serra, and V. Vedral, “Classical and quantum correlations under decoherence,” Phys. Rev. A 80, 044102 (2009).
[CrossRef]

T. Werlang, S. Souza, F. F. Fanchini, and C. J. Villas Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
[CrossRef]

J. Piilo, K. Härkönen, S. Maniscalco, and K.-A. Suominen, “Open system dynamics with non-Markovian quantum jumps,” Phys. Rev. A 79, 062112 (2009).
[CrossRef]

N. B. An and J. Kim, “Finite-time and infinite-time disentanglement of multipartite Greenberger–Horne–Zeilinger-type states under the collective action of different types of noise,” Phys. Rev. A 79, 022303 (2009).
[CrossRef]

T. Yu and J. H. Eberly, “Sudden death of entanglement,” Science 323, 598–601 (2009).
[CrossRef]

2008

H. P. Breuer and B. Vacchini, “Quantum semi-Markov processes,” Phys. Rev. Lett. 101, 140402 (2008).
[CrossRef]

J. Piilo, S. Maniscalco, K. Härkönen, and K.-A. Suominen, “Non-Markovian quantum jumps,” Phys. Rev. Lett. 100, 180402 (2008).
[CrossRef]

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[CrossRef]

J. P. Paz and A. J. Roncaglia, “Dynamics of the entanglement between two oscillators in the same environment,” Phys. Rev. Lett. 100, 220401 (2008).
[CrossRef]

B. Bellomo, R. Lo Franco, and G. Compagno, “Entanglement dynamics of two independent qubits in environments with and without memory,” Phys. Rev. A 77, 032342 (2008).
[CrossRef]

2007

B. Bellomo, R. Lo Franco, and G. Compagno, “Non-Markovian effects on the dynamics of entanglement,” Phys. Rev. Lett. 99, 160502 (2007).
[CrossRef]

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef]

J. H. Eberly and T. Yu, “The end of an entanglement,” Science 316, 555–557 (2007).
[CrossRef]

M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo, and K.-A. Suominen, “Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation,” J. Phys. A 40, 14527 (2007).
[CrossRef]

2004

T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef]

2003

V. Vedral, “Classical correlations and entanglement in quantum measurements,” Phys. Rev. Lett 90, 050401 (2003).
[CrossRef]

2001

H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[CrossRef]

1998

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

1997

L. D. Romero and J. P. Paz, “Decoherence and initial correlations in quantum Brownian motion,” Phys. Rev. A 55, 4070–4083 (1997).
[CrossRef]

1996

A. Royer, “Reduced dynamics with initial correlations, and time-dependent environment and Hamiltonians,” Phys. Rev. Lett. 77, 3272–3275 (1996).
[CrossRef]

1976

V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, “Completely positive dynamical semigroups of n-level systems,” J. Math. Phys. 17, 821–825 (1976).
[CrossRef]

G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119–130 (1976).
[CrossRef]

Aguilar, G. H.

O. Jiménez Farías, A. Valdés-Hernández, G. H. Aguilar, P. H. Souto Ribeiro, S. P. Walborn, L. Davidovich, X. F. Qian, and J. H. Eberly, “Experimental investigation of dynamical invariants in bipartite entanglement,” Phys. Rev. A 85, 012314 (2012).
[CrossRef]

Almeida, M. P.

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[CrossRef]

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef]

An, N. B.

N. B. An, J. Kim, and K. Kim, “Entanglement dynamics of three interacting two-level atoms within a common structured environment,” Phys. Rev. A 84, 022329 (2011).
[CrossRef]

Z. X. Man, Y. J. Xia, and N. B. An, “Quantum dissonance induced by a thermal field and its dynamics in dissipative systems,” Eur. Phys. J. D 64, 521–529 (2011).
[CrossRef]

Z. X. Man, Y. J. Xia, and N. B. An, “Entanglement measure and dynamics of multiqubit systems: non-Markovian versus Markovian and generalized monogamy relations,” New J. Phys. 12, 033020 (2010).
[CrossRef]

N. B. An, J. Kim, and K. Kim, “Nonperturbative analysis of entanglement dynamics and control for three qubits in a common lossy cavity,” Phys. Rev. A 82, 032316 (2010).
[CrossRef]

N. B. An and J. Kim, “Finite-time and infinite-time disentanglement of multipartite Greenberger–Horne–Zeilinger-type states under the collective action of different types of noise,” Phys. Rev. A 79, 022303 (2009).
[CrossRef]

Arruda, L. G. E.

F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).
[CrossRef]

Ban, M.

M. Ban, “Quantum master equation for dephasing of a two-level system with an initial correlation,” Phys. Rev. A 80, 064103 (2009).
[CrossRef]

Bellomo, B.

B. Bellomo, R. Lo Franco, and G. Compagno, “Entanglement dynamics of two independent qubits in environments with and without memory,” Phys. Rev. A 77, 032342 (2008).
[CrossRef]

B. Bellomo, R. Lo Franco, and G. Compagno, “Non-Markovian effects on the dynamics of entanglement,” Phys. Rev. Lett. 99, 160502 (2007).
[CrossRef]

Boas, C. J. Villas

T. Werlang, S. Souza, F. F. Fanchini, and C. J. Villas Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
[CrossRef]

Brasil, C. A.

F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).
[CrossRef]

Breuer, H. P.

A. Smirne, H. P. Breuer, J. Piilo, and B. Vacchini, “Initial correlations in open-systems dynamics: the Jaynes–Cummings model,” Phys. Rev. A 82, 062114 (2010).
[CrossRef]

H. P. Breuer and B. Vacchini, “Quantum semi-Markov processes,” Phys. Rev. Lett. 101, 140402 (2008).
[CrossRef]

H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, 2002).

Breuer, H.-P.

E.-M. Laine, H.-P. Breuer, J. Piilo, C.-F. Li, and G. C. Guo, “Nonlocal memory effects in the dynamics of open quantum systems,” Phys. Rev. Lett. 108, 210402 (2012).
[CrossRef]

E.-M. Laine, J. Piilo, and H.-P. Breuer, “Witness for initial system–environment correlations in open-system dynamics,” Europhys. Lett. 92, 60010 (2010).
[CrossRef]

E.-M. Laine, J. Piilo, and H.-P. Breuer, “Measure for the non-Markovianity of quantum processes,” Phys. Rev. A 81, 062115 (2010).
[CrossRef]

B.-H. Liu, D.-Y. Cao, Y.-F. Huang, C.-F. Li, G.-C. Guo, E.-M. Laine, H.-P. Breuer, and J. Piilo, “Photonic realization of nonlocal memory effects and non-Markovian quantum probes,” arXiv 1208.1358v1 (2012).

Brivio, D.

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, “Experimental investigation of initial system–environment correlations via trace-distance evolution,” Phys. Rev. A 84, 032112 (2011).
[CrossRef]

Buchleitner, A.

C. Viviescas, I. Guevara, A. R. R. Carvalho, M. Busse, and A. Buchleitner, “Entanglement dynamics in open two-qubit systems via diffusive quantum trajectories,” Phys. Rev. Lett. 105, 210502 (2010).
[CrossRef]

Busse, M.

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L. Mazzola, S. Maniscalco, J. Piilo, K. A. Suominen, and B. M. Garraway, “Sudden death and sudden birth of entanglement in common structured reservoirs,” Phys. Rev. A 79, 042302 (2009).
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L. Mazzola, S. Maniscalco, J. Piilo, K. A. Suominen, and B. M. Garraway, “Sudden death and sudden birth of entanglement in common structured reservoirs,” Phys. Rev. A 79, 042302 (2009).
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J. Piilo, S. Maniscalco, K. Härkönen, and K.-A. Suominen, “Non-Markovian quantum jumps,” Phys. Rev. Lett. 100, 180402 (2008).
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M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo, and K.-A. Suominen, “Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation,” J. Phys. A 40, 14527 (2007).
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O. Jiménez Farías, A. Valdés-Hernández, G. H. Aguilar, P. H. Souto Ribeiro, S. P. Walborn, L. Davidovich, X. F. Qian, and J. H. Eberly, “Experimental investigation of dynamical invariants in bipartite entanglement,” Phys. Rev. A 85, 012314 (2012).
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M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo, and K.-A. Suominen, “Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation,” J. Phys. A 40, 14527 (2007).
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J. Maziero, T. Werlang, F. F. Fanchini, L. C. Céleri, and R. M. Serra, “System–reservoir dynamics of quantum and classical correlations,” Phys. Rev. A 81, 022116 (2010).
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J. S. Xu, C. F. Li, X. Y. Xu, C. H. Shi, X. B. Zou, and G. C. Guo, “Experimental characterization of entanglement dynamics in noisy channels,” Phys. Rev. Lett. 103, 240502 (2009).
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Sudarshan, E. C. G.

V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, “Completely positive dynamical semigroups of n-level systems,” J. Math. Phys. 17, 821–825 (1976).
[CrossRef]

Sudha,

A. R. Usha Devi, A. K. Rajagopal, and Sudha, “Open-system quantum dynamics with correlated initial states, not completely positive maps, and non-Markovianity,” Phys. Rev. A 83, 022109 (2011).
[CrossRef]

Suominen, K. A.

L. Mazzola, S. Maniscalco, J. Piilo, K. A. Suominen, and B. M. Garraway, “Sudden death and sudden birth of entanglement in common structured reservoirs,” Phys. Rev. A 79, 042302 (2009).
[CrossRef]

Suominen, K.-A.

J. Piilo, K. Härkönen, S. Maniscalco, and K.-A. Suominen, “Open system dynamics with non-Markovian quantum jumps,” Phys. Rev. A 79, 062112 (2009).
[CrossRef]

J. Piilo, S. Maniscalco, K. Härkönen, and K.-A. Suominen, “Non-Markovian quantum jumps,” Phys. Rev. Lett. 100, 180402 (2008).
[CrossRef]

M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo, and K.-A. Suominen, “Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation,” J. Phys. A 40, 14527 (2007).
[CrossRef]

Tan, H. T.

H. T. Tan and W. M. Zhang, “Non-Markovian dynamics of an open quantum system with initial system-reservoir correlations: a nanocavity coupled to a coupled-resonator optical waveguide,” Phys. Rev. A 83, 032102 (2011).
[CrossRef]

Tang, J. S.

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83, 064102 (2011).
[CrossRef]

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A. G. Dijkstra and Y. Tanimura, “Non-Markovian entanglement dynamics in the presence of system–bath coherence,” Phys. Rev. Lett. 104, 250401 (2010).
[CrossRef]

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C. C. Tannoudji, G. Grynberg, and J. Dupont-Roe, Atom-Photon Interactions (Wiley, 1998).

Usha Devi, A. R.

A. R. Usha Devi, A. K. Rajagopal, and Sudha, “Open-system quantum dynamics with correlated initial states, not completely positive maps, and non-Markovianity,” Phys. Rev. A 83, 022109 (2011).
[CrossRef]

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Z. X. Man, Y. J. Xia, A. Smirne, and B. Vacchini, “Quantum interference induced by initial system–environment correlations,” Phys. Lett. A 376, 2477–2483 (2012).
[CrossRef]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, “Experimental investigation of initial system–environment correlations via trace-distance evolution,” Phys. Rev. A 84, 032112 (2011).
[CrossRef]

A. Smirne, H. P. Breuer, J. Piilo, and B. Vacchini, “Initial correlations in open-systems dynamics: the Jaynes–Cummings model,” Phys. Rev. A 82, 062114 (2010).
[CrossRef]

H. P. Breuer and B. Vacchini, “Quantum semi-Markov processes,” Phys. Rev. Lett. 101, 140402 (2008).
[CrossRef]

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O. Jiménez Farías, A. Valdés-Hernández, G. H. Aguilar, P. H. Souto Ribeiro, S. P. Walborn, L. Davidovich, X. F. Qian, and J. H. Eberly, “Experimental investigation of dynamical invariants in bipartite entanglement,” Phys. Rev. A 85, 012314 (2012).
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J. Maziero, L. C. Celeri, R. M. Serra, and V. Vedral, “Classical and quantum correlations under decoherence,” Phys. Rev. A 80, 044102 (2009).
[CrossRef]

V. Vedral, “Classical correlations and entanglement in quantum measurements,” Phys. Rev. Lett 90, 050401 (2003).
[CrossRef]

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D. Z. Rossatto, T. Werlang, L. K. Castelano, C. J. Villas-Boas, and F. F. Fanchini, “Purity as a witness for initial system–environment correlations in open-system dynamics,” Phys. Rev. A 84, 042113 (2011).
[CrossRef]

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C. Viviescas, I. Guevara, A. R. R. Carvalho, M. Busse, and A. Buchleitner, “Entanglement dynamics in open two-qubit systems via diffusive quantum trajectories,” Phys. Rev. Lett. 105, 210502 (2010).
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O. Jiménez Farías, A. Valdés-Hernández, G. H. Aguilar, P. H. Souto Ribeiro, S. P. Walborn, L. Davidovich, X. F. Qian, and J. H. Eberly, “Experimental investigation of dynamical invariants in bipartite entanglement,” Phys. Rev. A 85, 012314 (2012).
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B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
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Q. H. Chen, Y. Yang, T. Liu, and K. L. Wang, “Entanglement dynamics of two independent Jaynes–Cummings atoms without the rotating-wave approximation,” Phys. Rev. A 82, 052306 (2010).
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D. Z. Rossatto, T. Werlang, L. K. Castelano, C. J. Villas-Boas, and F. F. Fanchini, “Purity as a witness for initial system–environment correlations in open-system dynamics,” Phys. Rev. A 84, 042113 (2011).
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[CrossRef]

Z. X. Man, Y. J. Xia, and N. B. An, “Quantum dissonance induced by a thermal field and its dynamics in dissipative systems,” Eur. Phys. J. D 64, 521–529 (2011).
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Z. X. Man, Y. J. Xia, and N. B. An, “Entanglement measure and dynamics of multiqubit systems: non-Markovian versus Markovian and generalized monogamy relations,” New J. Phys. 12, 033020 (2010).
[CrossRef]

Y. J. Zhang, X. B. Zou, Y. J. Xia, and G. C. Guo, “Different entanglement dynamical behaviors due to initial system–environment correlations,” Phys. Rev. A 82, 022108 (2010).
[CrossRef]

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J. S. Xu, X. Y. Xu, C. F. Li, C. J. Zhang, X. B. Zou, and G. C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Commun. 1, 7 (2010).
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J. S. Xu, C. F. Li, X. Y. Xu, C. H. Shi, X. B. Zou, and G. C. Guo, “Experimental characterization of entanglement dynamics in noisy channels,” Phys. Rev. Lett. 103, 240502 (2009).
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J. S. Xu, X. Y. Xu, C. F. Li, C. J. Zhang, X. B. Zou, and G. C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Commun. 1, 7 (2010).
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J. S. Xu, C. F. Li, X. Y. Xu, C. H. Shi, X. B. Zou, and G. C. Guo, “Experimental characterization of entanglement dynamics in noisy channels,” Phys. Rev. Lett. 103, 240502 (2009).
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B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
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Q. H. Chen, Y. Yang, T. Liu, and K. L. Wang, “Entanglement dynamics of two independent Jaynes–Cummings atoms without the rotating-wave approximation,” Phys. Rev. A 82, 052306 (2010).
[CrossRef]

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T. Yu and J. H. Eberly, “Sudden death of entanglement,” Science 323, 598–601 (2009).
[CrossRef]

J. H. Eberly and T. Yu, “The end of an entanglement,” Science 316, 555–557 (2007).
[CrossRef]

T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef]

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J. S. Xu, X. Y. Xu, C. F. Li, C. J. Zhang, X. B. Zou, and G. C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Commun. 1, 7 (2010).
[CrossRef]

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H. T. Tan and W. M. Zhang, “Non-Markovian dynamics of an open quantum system with initial system-reservoir correlations: a nanocavity coupled to a coupled-resonator optical waveguide,” Phys. Rev. A 83, 032102 (2011).
[CrossRef]

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Y. J. Zhang, X. B. Zou, Y. J. Xia, and G. C. Guo, “Different entanglement dynamical behaviors due to initial system–environment correlations,” Phys. Rev. A 82, 022108 (2010).
[CrossRef]

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Y. J. Zhang, X. B. Zou, Y. J. Xia, and G. C. Guo, “Different entanglement dynamical behaviors due to initial system–environment correlations,” Phys. Rev. A 82, 022108 (2010).
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J. S. Xu, X. Y. Xu, C. F. Li, C. J. Zhang, X. B. Zou, and G. C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Commun. 1, 7 (2010).
[CrossRef]

J. S. Xu, C. F. Li, X. Y. Xu, C. H. Shi, X. B. Zou, and G. C. Guo, “Experimental characterization of entanglement dynamics in noisy channels,” Phys. Rev. Lett. 103, 240502 (2009).
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Z. X. Man, Y. J. Xia, and N. B. An, “Quantum dissonance induced by a thermal field and its dynamics in dissipative systems,” Eur. Phys. J. D 64, 521–529 (2011).
[CrossRef]

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[CrossRef]

J. Phys. A

M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo, and K.-A. Suominen, “Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation,” J. Phys. A 40, 14527 (2007).
[CrossRef]

Nat. Commun.

J. S. Xu, X. Y. Xu, C. F. Li, C. J. Zhang, X. B. Zou, and G. C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nat. Commun. 1, 7 (2010).
[CrossRef]

New J. Phys.

Z. X. Man, Y. J. Xia, and N. B. An, “Entanglement measure and dynamics of multiqubit systems: non-Markovian versus Markovian and generalized monogamy relations,” New J. Phys. 12, 033020 (2010).
[CrossRef]

Phys. Lett. A

Z. X. Man, Y. J. Xia, A. Smirne, and B. Vacchini, “Quantum interference induced by initial system–environment correlations,” Phys. Lett. A 376, 2477–2483 (2012).
[CrossRef]

Phys. Rev. A

C. F. Li, J. S. Tang, Y. L. Li, and G. C. Guo, “Experimentally witnessing the initial correlation between an open quantum system and its environment,” Phys. Rev. A 83, 064102 (2011).
[CrossRef]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, “Experimental investigation of initial system–environment correlations via trace-distance evolution,” Phys. Rev. A 84, 032112 (2011).
[CrossRef]

H. T. Tan and W. M. Zhang, “Non-Markovian dynamics of an open quantum system with initial system-reservoir correlations: a nanocavity coupled to a coupled-resonator optical waveguide,” Phys. Rev. A 83, 032102 (2011).
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A. Smirne, H. P. Breuer, J. Piilo, and B. Vacchini, “Initial correlations in open-systems dynamics: the Jaynes–Cummings model,” Phys. Rev. A 82, 062114 (2010).
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Y. J. Zhang, X. B. Zou, Y. J. Xia, and G. C. Guo, “Different entanglement dynamical behaviors due to initial system–environment correlations,” Phys. Rev. A 82, 022108 (2010).
[CrossRef]

L. Mazzola, S. Maniscalco, J. Piilo, K. A. Suominen, and B. M. Garraway, “Sudden death and sudden birth of entanglement in common structured reservoirs,” Phys. Rev. A 79, 042302 (2009).
[CrossRef]

D. Z. Rossatto, T. Werlang, L. K. Castelano, C. J. Villas-Boas, and F. F. Fanchini, “Purity as a witness for initial system–environment correlations in open-system dynamics,” Phys. Rev. A 84, 042113 (2011).
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N. B. An, J. Kim, and K. Kim, “Entanglement dynamics of three interacting two-level atoms within a common structured environment,” Phys. Rev. A 84, 022329 (2011).
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T. Werlang, S. Souza, F. F. Fanchini, and C. J. Villas Boas, “Robustness of quantum discord to sudden death,” Phys. Rev. A 80, 024103 (2009).
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F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).
[CrossRef]

J. Maziero, T. Werlang, F. F. Fanchini, L. C. Céleri, and R. M. Serra, “System–reservoir dynamics of quantum and classical correlations,” Phys. Rev. A 81, 022116 (2010).
[CrossRef]

J. Maziero, L. C. Celeri, R. M. Serra, and V. Vedral, “Classical and quantum correlations under decoherence,” Phys. Rev. A 80, 044102 (2009).
[CrossRef]

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101 (2010).
[CrossRef]

O. Jiménez Farías, A. Valdés-Hernández, G. H. Aguilar, P. H. Souto Ribeiro, S. P. Walborn, L. Davidovich, X. F. Qian, and J. H. Eberly, “Experimental investigation of dynamical invariants in bipartite entanglement,” Phys. Rev. A 85, 012314 (2012).
[CrossRef]

Q. H. Chen, Y. Yang, T. Liu, and K. L. Wang, “Entanglement dynamics of two independent Jaynes–Cummings atoms without the rotating-wave approximation,” Phys. Rev. A 82, 052306 (2010).
[CrossRef]

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
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J. Piilo, K. Härkönen, S. Maniscalco, and K.-A. Suominen, “Open system dynamics with non-Markovian quantum jumps,” Phys. Rev. A 79, 062112 (2009).
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E.-M. Laine, J. Piilo, and H.-P. Breuer, “Measure for the non-Markovianity of quantum processes,” Phys. Rev. A 81, 062115 (2010).
[CrossRef]

Phys. Rev. Lett

V. Vedral, “Classical correlations and entanglement in quantum measurements,” Phys. Rev. Lett 90, 050401 (2003).
[CrossRef]

Phys. Rev. Lett.

J. Piilo, S. Maniscalco, K. Härkönen, and K.-A. Suominen, “Non-Markovian quantum jumps,” Phys. Rev. Lett. 100, 180402 (2008).
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[CrossRef]

H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[CrossRef]

T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef]

B. Bellomo, R. Lo Franco, and G. Compagno, “Non-Markovian effects on the dynamics of entanglement,” Phys. Rev. Lett. 99, 160502 (2007).
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J. P. Paz and A. J. Roncaglia, “Dynamics of the entanglement between two oscillators in the same environment,” Phys. Rev. Lett. 100, 220401 (2008).
[CrossRef]

J. S. Xu, C. F. Li, X. Y. Xu, C. H. Shi, X. B. Zou, and G. C. Guo, “Experimental characterization of entanglement dynamics in noisy channels,” Phys. Rev. Lett. 103, 240502 (2009).
[CrossRef]

C. Viviescas, I. Guevara, A. R. R. Carvalho, M. Busse, and A. Buchleitner, “Entanglement dynamics in open two-qubit systems via diffusive quantum trajectories,” Phys. Rev. Lett. 105, 210502 (2010).
[CrossRef]

A. G. Dijkstra and Y. Tanimura, “Non-Markovian entanglement dynamics in the presence of system–bath coherence,” Phys. Rev. Lett. 104, 250401 (2010).
[CrossRef]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

E.-M. Laine, H.-P. Breuer, J. Piilo, C.-F. Li, and G. C. Guo, “Nonlocal memory effects in the dynamics of open quantum systems,” Phys. Rev. Lett. 108, 210402 (2012).
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Science

J. H. Eberly and T. Yu, “The end of an entanglement,” Science 316, 555–557 (2007).
[CrossRef]

T. Yu and J. H. Eberly, “Sudden death of entanglement,” Science 323, 598–601 (2009).
[CrossRef]

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef]

Other

H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, 2002).

B.-H. Liu, D.-Y. Cao, Y.-F. Huang, C.-F. Li, G.-C. Guo, E.-M. Laine, H.-P. Breuer, and J. Piilo, “Photonic realization of nonlocal memory effects and non-Markovian quantum probes,” arXiv 1208.1358v1 (2012).

C. C. Tannoudji, G. Grynberg, and J. Dupont-Roe, Atom-Photon Interactions (Wiley, 1998).

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Figures (4)

Fig. 1.
Fig. 1.

C1, C2, and C, Eqs. (18) through (20), versus the rescaled time Ωt in the strong atom–mode coupling regime with Γ/R=0.1 for c1=c2=1/2 and (a) α=β=1/2; (b) α=1/10, β=9/10; and (c) α=9/10, β=1/10. The atoms’ concurrences CABJ in terms of C1, C2, or C are determined in the text through Eqs. (15) through (17).

Fig. 2.
Fig. 2.

Atoms’ discord DABJ, Eq. (21), versus the rescaled time Ωt in the strong atom–mode coupling regime with Γ/R=0.1 for c1=c2=1/2 and (a) α=β=1/2; (b) α=1/10, β=9/10; and (c) α=9/10, β=1/10.

Fig. 3.
Fig. 3.

Atoms’ (a) entanglement and (b) discord versus the rescaled time Ωt in the weak atom–mode coupling regime with Γ/R=4 for c1=c2=1/2 and α=29/30 and β=1/30.

Fig. 4.
Fig. 4.

Atoms’ concurrence CABI and discord DABI versus the rescaled time Ωt when initially the modes are entangled [Eq. (6)] with c1=c2=1/2, the atoms are in product state (a), (b) |ggAB or (c), (d) |eeAB, and the local atom–mode coupling is (a), (c) weak with Γ/R=4 or (b), (d) strong with Γ/R=0.1.

Equations (50)

Equations on this page are rendered with MathJax. Learn more.

dρAa(t)dt=i[HAa,ρAa(t)]Γ2[a+aρAa(t)2aρAa(t)a++ρAa(t)a+a]
dρBb(t)dt=i[HBb,ρBb(t)]Γ2[b+bρBb(t)2bρBb(t)b++ρBb(t)b+b],
HAa=ω0σ^+Aσ^A+ωca^+a^+Ω(σ^Aa^++σ^+Aa^)
HBb=ω0σ^+Bσ^B+ωcb^+b^+Ω(σ^Bb^++σ^+Bb^).
|ψ(0)AB=α|ggAB+β|eeAB,
ρabI(0)=|ϕ(0)abϕ(0)|,
|ϕ(0)ab=c1|01ab+c2|10ab
ρabII(0)=|c1|2|01ab01|+|c2|2|10ab10|,
ρabIII(0)=|c1c2|2|00ab00|+|c1|4|01ab01|+|c2|4|10ab10|+|c1c2|2|11ab11|.
ρABabJ(0)=ρAB(0)ρabJ(0)
ρAaBbI(0)=|αc1|2|g0Aag0||g1Bbg1|+|αc2|2|g1Aag1||g0Bbg0|+|α|2c1c2*|g0Aag1||g1Bbg0|+|α|2c2c1*|g1Aag0||g0Bbg1|+|βc1|2|e0Aae0||e1Bbe1|+|βc2|2|e1Aae1||e0Bbe0|+|β|2c1c2*|e0Aae1||e1Bbe0|+|β|2c2c1*|e1Aae0||e0Bbe1|+αβ*|c1|2|g0Aae0||g1Bbe1|+αβ*|c2|2|g1Aae1||g0Bbe0|+αβ*c1c2*|g0Aae1||g1Bbe0|+αβ*c2c1*|g1Aae0||g0Bbe1|+βα*|c1|2|e0Aag0||e1Bbg1|+βα*|c2|2|e1Aag1||e0Bbg0|+βα*c1c2*|e0Aag1||e1Bbg0|+βα*c2c1*|e1Aag0||e0Bbg1|.
ρnnI(t)=ρnnII(t)ρnnIII(t),
|ρ14I(t)|=|ρ14II(t)||ρ14III(t)|,
|ρ23I(t)||ρ23II(t)|=|ρ23III(t)|=0.
CABI(t)=C1(t)+C2(t),
CABII(t)=C1(t),
CABIII(t)=C(t),
C1(t)=2max{0,[|ρ14I(t)|ρ22I(t)ρ33I(t)]},
C2(t)=2max{0,[|ρ23I(t)|ρ11I(t)ρ44I(t)]},
C(t)=2max{0,[|ρ14III(t)|ρ22III(t)ρ33III(t)]}.
DABJ(t)=min{D1J(t),D2J(t)},
D1J(t)=S(ρAJ)S(ρABJ)ρ11J(t)log2(ρ11J(t)ρ11J(t)+ρ22J(t))ρ22J(t)log2(ρ22J(t)ρ11J(t)+ρ22J(t))ρ44J(t)log2(ρ44J(t)ρ22J(t)+ρ44J(t))ρ22J(t)log2(ρ22J(t)ρ44J(t)+ρ22J(t))
D2J(t)=S(ρAJ)S(ρABJ)12(1+TJ)log2(1+TJ2)12(1TJ)log2(1TJ2),
ρ11I(t)=ρ11II(t)=α2L1{x1(s)+x2(s)}+β2L1{x3(s)+x4(s)}×L1{x5(s)+x6(s)+x7(s)},
ρ22I(t)=ρ22II(t)=|αc1|2L1{x4(s)}+|βc1|2L1{x3(s)+x4(s)}×L1{x8(s)+x9(s)}+|βc2|2L1{x5(s)+x6(s)+x7(s)}×L1{x10(s)},
ρ33I(t)=ρ33II(t)=ρ22I(t)|c1,2c2,1=ρ22II(t)|c1,2c2,1,
ρ44I(t)=ρ44II(t)=β2L1{x10(s)}×L1{x8(s)+x9(s)},
ρ14I(t)=ρ14II(t)=αβ*L1{x11(s)}×L1{x12(s)+x13(s)},
ρ23I(t)=|α|2c1c2*L1{x14(s)}×L1{x14*(s)}+|β|2c1c2L1{x15(s)+x16(s)}×L1{x15*(s)+x16*(s)},
ρ11III(t)=α2(|c1|4+|c2|4)L1{x1(s)+x2(s)}+α2|c1c2|2+α2|c1c2|2L1{x1(s)+x2(s)}×L1{x1(s)+x2(s)}+β2(|c1|4+|c2|4)L1{x3(s)+x4(s)}×L1{x5(s)+x6(s)+x7(s)}+β2|c1c2|2L1{x3(s)+x4(s)}×L1{x3(s)+x4(s)}+|β|2|c1c2|2L1{x5(s)+x6(s)+x7(s)}×L1{x5(s)+x6(s)+x7(s)},
ρ22III(t)=|α|2|c1|4L1{x4(s)}+|α|2|c1c2|2L1{x1(s)+x2(s)}×L1{x4(s)}+|β|2|c1|4L1{x3(s)+x4(s)}×L1{x8(s)+x9(s)}+β2|c1c2|2L1{x3(s)+x4(s)}×L1{x10(s)}+β2|c1c2|2L1{x5(s)+x6(s)+x7(s)}×L1{x8(s)+x9(s)}+β2|c2|4L1{x10(s)}×L1{x5(s)+x6(s)+x7(s)},
ρ33III(t)=ρ22III(t)|c1,2c2,1,
ρ44III(t)=α2|c1c2|2L1{x4(s)}×L1{x4(s)}+β2(|c1|4+|c2|4)L1{x10(s)}×L1{x8(s)+x9(s)}+β2|c1c2|2L1{x10(s)}×L1{x10(s)}+β2|c1c2|2L1{x8(s)+x9(s)}×L1{x8(s)+x9(s)},
ρ14III(t)=αβ(|c1|4+|c2|4)L1{x11(s)}×L1{x12(s)+x13(s)}+αβ|c1c2|2L1{x11(s)}×L1{x11(s)}+αβ|c1c2|2L1{x12(s)+x13(s)}×L1{x12(s)+x13(s)}.
x1(s)=Γ[1+s2s(s+Γ)+4Ω2]s(2s+Γ),
x2(s)=s(2s+Γ)+4Ω2(2s+Γ)[s(s+Γ)+4Ω2],
x3(s)=4ΓΩ2s(2s+Γ)[s(s+Γ)+4Ω2],
x4(s)=4Ω2(2s+Γ)[s(s+Γ)+4Ω2],
x5(s)=4Γ2Ω2[(2s+Γ)(7s+6Γ)+24Ω2]s(2s+Γ)(2s+3Γ)[s(s+Γ)+4Ω2][(s+Γ)(s+2Γ)+8Ω2],
x6(s)=4ΓΩ2[(2s+Γ)(7s+6Γ)+24Ω2](2s+Γ)(2s+3Γ)[s(s+Γ)+4Ω2][(s+Γ)(s+2Γ)+8Ω2],
x7(s)=8Ω2(2s+3Γ)[(s+Γ)(s+2Γ)+8Ω2],
x8(s)=Γ[4s4+20s3Γ+35s2Γ2+25sΓ3+6Γ4+4s(2s+Γ)Ω2+96Ω4](2s+Γ)(2s+3Γ)[s(s+Γ)+4Ω2][(s+Γ)(s+2Γ)+8Ω2],
x9(s)=(s+2Γ)(2s+3Γ)+8Ω2(2s+3Γ)[(s+Γ)(s+2Γ)+8Ω2],
x10(s)=(s+Γ)(2s+Γ)+4Ω2(2s+Γ)(s(s+Γ)+4Ω2),
x11(s)=2s+Γ2iω(siω)(2s+Γ2iω)+2Ω2,
x12(s)=Γ(2s+Γ2iω)(2s+3Γ2iω)((s+Γiω)(2s+Γ2iω)+2Ω2)16ΓΩ4((siω)(2s+Γ2iω)+2Ω2)((s+Γiω)2((2s+Γ2iω)(2s+3Γ2iω)+24Ω2)+4Ω4),
x13(s)=4s3+3Γ3+12s2(Γiω)11iΓ2ω+2Γ(6ω2+7Ω2)+4i(ω33ωΩ2)(s+Γiω)2(2s+Γ2iω)(2s+3Γ2iω)+24(s+Γiω)2Ω2+4Ω4+s(11Γ224iΓω+12(ω2+Ω2))(s+Γiω)2(2s+Γ2iω)(2s+3Γ2iω)+24(s+Γiω)2Ω2+4Ω4,
x14(s)=2iΩ(siω)(2s+Γ2iω)+2Ω2,
x15(s)=2iΓΩ(4s3+3Γ3+12s2(Γiω)11iΓ2ω6Γ(2ω2+3Ω2)+4i(ω3+5ωΩ2))((siω)(2s+Γ2iω)+2Ω2)((s+Γiω)2((2s+Γ2iω)(2s+3Γ2iω)+24Ω2)+4Ω4)2iΓΩs(11Γ224iΓω4(3ω2+5Ω2))((siω)(2s+Γ2iω)+2Ω2)((s+Γiω)2((2s+Γ2iω)(2s+3Γ2iω)+24Ω2)+4Ω4),
x16(s)=2iΩ[(s+Γiω)(2s+3Γ2iω)+2Ω2](s+Γiω)2(2s+Γ2iω)(2s+3Γ2iω)+24(s+Γiω)2Ω2+4Ω4.

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