Abstract

No instrument is able to measure directly the quantum entanglement of a system. However, both theory and experiment, following the well-known Bell inequality, reveal the existence of the entanglement phenomenon in quantum mechanics. To examine the characterization of quantum entanglement, here we present a two-site cavity system, in which each cavity contains a Λ-type three-level atom and the two sites are identical and coupled with each other. We investigate and calculate the bipartite entanglement entropy of the system for the ground states. For photons of different types, corresponding to the two ground states of the atom, we investigate the correlations and violation of the Bell inequality.

© 2017 Chinese Laser Press

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References

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  1. J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1, 195–200 (1964).
  2. S. Freedman and J. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28, 938–941 (1972).
    [Crossref]
  3. E. Fry and R. Thompson, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 37, 465–468 (1976).
    [Crossref]
  4. A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
    [Crossref]
  5. A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
    [Crossref]
  6. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10  km apart,” Phys. Rev. Lett. 81, 3563–3566 (1998).
    [Crossref]
  7. G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
    [Crossref]
  8. L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
    [Crossref]
  9. Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A 83, 013825 (2011).
    [Crossref]
  10. E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).
    [Crossref]
  11. E. K. Irish, “Ground-state entanglement in a coupled-cavity model,” Phys. Rev. A 80, 043825 (2009).
    [Crossref]
  12. Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
    [Crossref]
  13. J. F. Huang, J. Q. Liao, and C. P. Sun, “Photon blockade induced by atoms with Rydberg coupling,” Phys. Rev. A 87, 023822 (2013).
    [Crossref]
  14. T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
    [Crossref]
  15. F. Badshah, S. Qamar, and M. Paternostro, “Dynamics of interacting Dicke model in a coupled-cavity array,” Phys. Rev. A 90, 033813 (2014).
    [Crossref]
  16. L. Tan, Y. Q. Zhang, and W. M. Liu, “Quantum phase transitions for two coupled cavities with dipole-interaction atoms,” Phys. Rev. A 84, 063816 (2011).
    [Crossref]
  17. S. Zeeb, C. Noh, A. S. Parkins, and H. J. Carmichael, “Superradiant decay and dipole-dipole interaction of distant atoms in a two-way cascaded cavity QED system,” Phys. Rev. A 91, 023829 (2015).
    [Crossref]
  18. A. C. Ji, Q. Sun, X. C. Xie, and W. M. Liu, “Josephson effect for photons in two weakly linked microcavities,” Phys. Rev. Lett. 102, 023602 (2009).
    [Crossref]
  19. R. Qi, X. L. Yu, Z. B. Li, and W. M. Liu, “Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps,” Phys. Rev. Lett. 102, 185301 (2009).
    [Crossref]
  20. A. C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).
    [Crossref]
  21. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
    [Crossref]
  22. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
    [Crossref]

2015 (2)

S. Zeeb, C. Noh, A. S. Parkins, and H. J. Carmichael, “Superradiant decay and dipole-dipole interaction of distant atoms in a two-way cascaded cavity QED system,” Phys. Rev. A 91, 023829 (2015).
[Crossref]

T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
[Crossref]

2014 (2)

F. Badshah, S. Qamar, and M. Paternostro, “Dynamics of interacting Dicke model in a coupled-cavity array,” Phys. Rev. A 90, 033813 (2014).
[Crossref]

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

2013 (1)

J. F. Huang, J. Q. Liao, and C. P. Sun, “Photon blockade induced by atoms with Rydberg coupling,” Phys. Rev. A 87, 023822 (2013).
[Crossref]

2012 (1)

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

2011 (2)

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A 83, 013825 (2011).
[Crossref]

L. Tan, Y. Q. Zhang, and W. M. Liu, “Quantum phase transitions for two coupled cavities with dipole-interaction atoms,” Phys. Rev. A 84, 063816 (2011).
[Crossref]

2009 (3)

E. K. Irish, “Ground-state entanglement in a coupled-cavity model,” Phys. Rev. A 80, 043825 (2009).
[Crossref]

A. C. Ji, Q. Sun, X. C. Xie, and W. M. Liu, “Josephson effect for photons in two weakly linked microcavities,” Phys. Rev. Lett. 102, 023602 (2009).
[Crossref]

R. Qi, X. L. Yu, Z. B. Li, and W. M. Liu, “Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps,” Phys. Rev. Lett. 102, 185301 (2009).
[Crossref]

2008 (2)

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).
[Crossref]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[Crossref]

2007 (1)

A. C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).
[Crossref]

1998 (2)

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10  km apart,” Phys. Rev. Lett. 81, 3563–3566 (1998).
[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

1982 (1)

A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

1981 (1)

A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

1976 (1)

E. Fry and R. Thompson, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 37, 465–468 (1976).
[Crossref]

1972 (1)

S. Freedman and J. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28, 938–941 (1972).
[Crossref]

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

1964 (1)

J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1, 195–200 (1964).

Aspect, A.

A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

Badshah, F.

F. Badshah, S. Qamar, and M. Paternostro, “Dynamics of interacting Dicke model in a coupled-cavity array,” Phys. Rev. A 90, 033813 (2014).
[Crossref]

Bell, J. S.

J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1, 195–200 (1964).

Brendel, J.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10  km apart,” Phys. Rev. Lett. 81, 3563–3566 (1998).
[Crossref]

Brunner, N.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Carmichael, H. J.

S. Zeeb, C. Noh, A. S. Parkins, and H. J. Carmichael, “Superradiant decay and dipole-dipole interaction of distant atoms in a two-way cascaded cavity QED system,” Phys. Rev. A 91, 023829 (2015).
[Crossref]

Cavalcanti, D.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Chang, D. E.

T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
[Crossref]

Chang, Y.

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A 83, 013825 (2011).
[Crossref]

Cirac, J. I.

T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
[Crossref]

Clauser, J.

S. Freedman and J. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28, 938–941 (1972).
[Crossref]

Clauser, J. F.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Freedman, S.

S. Freedman and J. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28, 938–941 (1972).
[Crossref]

Fry, E.

E. Fry and R. Thompson, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 37, 465–468 (1976).
[Crossref]

Gisin, N.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10  km apart,” Phys. Rev. Lett. 81, 3563–3566 (1998).
[Crossref]

Gong, Z. R.

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A 83, 013825 (2011).
[Crossref]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[Crossref]

Grangier, P.

A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Horne, M. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Huang, J. F.

J. F. Huang, J. Q. Liao, and C. P. Sun, “Photon blockade induced by atoms with Rydberg coupling,” Phys. Rev. A 87, 023822 (2013).
[Crossref]

Irish, E. K.

E. K. Irish, “Ground-state entanglement in a coupled-cavity model,” Phys. Rev. A 80, 043825 (2009).
[Crossref]

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).
[Crossref]

Jennewein, T.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Ji, A. C.

A. C. Ji, Q. Sun, X. C. Xie, and W. M. Liu, “Josephson effect for photons in two weakly linked microcavities,” Phys. Rev. Lett. 102, 023602 (2009).
[Crossref]

A. C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).
[Crossref]

Kim, M. S.

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).
[Crossref]

Li, Y.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

Li, Z. B.

R. Qi, X. L. Yu, Z. B. Li, and W. M. Liu, “Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps,” Phys. Rev. Lett. 102, 185301 (2009).
[Crossref]

Liao, J. Q.

J. F. Huang, J. Q. Liao, and C. P. Sun, “Photon blockade induced by atoms with Rydberg coupling,” Phys. Rev. A 87, 023822 (2013).
[Crossref]

Liu, W. M.

L. Tan, Y. Q. Zhang, and W. M. Liu, “Quantum phase transitions for two coupled cavities with dipole-interaction atoms,” Phys. Rev. A 84, 063816 (2011).
[Crossref]

A. C. Ji, Q. Sun, X. C. Xie, and W. M. Liu, “Josephson effect for photons in two weakly linked microcavities,” Phys. Rev. Lett. 102, 023602 (2009).
[Crossref]

R. Qi, X. L. Yu, Z. B. Li, and W. M. Liu, “Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps,” Phys. Rev. Lett. 102, 185301 (2009).
[Crossref]

A. C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).
[Crossref]

Liu, Y. X.

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[Crossref]

Noh, C.

S. Zeeb, C. Noh, A. S. Parkins, and H. J. Carmichael, “Superradiant decay and dipole-dipole interaction of distant atoms in a two-way cascaded cavity QED system,” Phys. Rev. A 91, 023829 (2015).
[Crossref]

Nori, F.

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[Crossref]

Ogden, C. D.

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).
[Crossref]

Parkins, A. S.

S. Zeeb, C. Noh, A. S. Parkins, and H. J. Carmichael, “Superradiant decay and dipole-dipole interaction of distant atoms in a two-way cascaded cavity QED system,” Phys. Rev. A 91, 023829 (2015).
[Crossref]

Paternostro, M.

F. Badshah, S. Qamar, and M. Paternostro, “Dynamics of interacting Dicke model in a coupled-cavity array,” Phys. Rev. A 90, 033813 (2014).
[Crossref]

Pironio, S.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Qamar, S.

F. Badshah, S. Qamar, and M. Paternostro, “Dynamics of interacting Dicke model in a coupled-cavity array,” Phys. Rev. A 90, 033813 (2014).
[Crossref]

Qi, R.

R. Qi, X. L. Yu, Z. B. Li, and W. M. Liu, “Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps,” Phys. Rev. Lett. 102, 185301 (2009).
[Crossref]

Roger, G.

A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47, 460–463 (1981).
[Crossref]

Scarani, V.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Shi, T.

T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
[Crossref]

Shimony, A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Simon, C.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Sun, C. P.

J. F. Huang, J. Q. Liao, and C. P. Sun, “Photon blockade induced by atoms with Rydberg coupling,” Phys. Rev. A 87, 023822 (2013).
[Crossref]

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A 83, 013825 (2011).
[Crossref]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[Crossref]

Sun, Q.

A. C. Ji, Q. Sun, X. C. Xie, and W. M. Liu, “Josephson effect for photons in two weakly linked microcavities,” Phys. Rev. Lett. 102, 023602 (2009).
[Crossref]

Tan, L.

L. Tan, Y. Q. Zhang, and W. M. Liu, “Quantum phase transitions for two coupled cavities with dipole-interaction atoms,” Phys. Rev. A 84, 063816 (2011).
[Crossref]

Thompson, R.

E. Fry and R. Thompson, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 37, 465–468 (1976).
[Crossref]

Tittel, W.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10  km apart,” Phys. Rev. Lett. 81, 3563–3566 (1998).
[Crossref]

Wang, Z. H.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

Wehner, S.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Weihs, G.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Weinfurter, H.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Xie, X. C.

A. C. Ji, Q. Sun, X. C. Xie, and W. M. Liu, “Josephson effect for photons in two weakly linked microcavities,” Phys. Rev. Lett. 102, 023602 (2009).
[Crossref]

A. C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).
[Crossref]

Yu, X. L.

R. Qi, X. L. Yu, Z. B. Li, and W. M. Liu, “Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps,” Phys. Rev. Lett. 102, 185301 (2009).
[Crossref]

Zbinden, H.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10  km apart,” Phys. Rev. Lett. 81, 3563–3566 (1998).
[Crossref]

Zeeb, S.

S. Zeeb, C. Noh, A. S. Parkins, and H. J. Carmichael, “Superradiant decay and dipole-dipole interaction of distant atoms in a two-way cascaded cavity QED system,” Phys. Rev. A 91, 023829 (2015).
[Crossref]

Zeilinger, A.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Zhang, P.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

Zhang, Y. Q.

L. Tan, Y. Q. Zhang, and W. M. Liu, “Quantum phase transitions for two coupled cavities with dipole-interaction atoms,” Phys. Rev. A 84, 063816 (2011).
[Crossref]

Zhou, D. L.

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

Zhou, L.

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[Crossref]

Phys. Rev. A (9)

Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A 83, 013825 (2011).
[Crossref]

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).
[Crossref]

E. K. Irish, “Ground-state entanglement in a coupled-cavity model,” Phys. Rev. A 80, 043825 (2009).
[Crossref]

Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[Crossref]

J. F. Huang, J. Q. Liao, and C. P. Sun, “Photon blockade induced by atoms with Rydberg coupling,” Phys. Rev. A 87, 023822 (2013).
[Crossref]

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Figures (12)

Fig. 1.
Fig. 1. Schematic configuration of the two-site coupled-cavity system. The system is composed of two harmonic resonators and two Λ-type three-level atoms. For the atom, |e represents the excitation state, and |H and |V are the degenerate ground states of the atom.
Fig. 2.
Fig. 2. Entropies in the ground states as a function of detuning and hopping strength. Parameter values are gV=0.5gH, where gH=1 is set as the basic unit throughout this paper.
Fig. 3.
Fig. 3. Probabilities for the purely atomic states in the ground states.
Fig. 4.
Fig. 4. Probabilities for the intersect states, one atom being in the excited state in one cavity, while a photon is in its eigenstate in the other cavity, in the ground states.
Fig. 5.
Fig. 5. Probabilities for the intersect states, two excitations being in the same cavity, in the ground states.
Fig. 6.
Fig. 6. Probabilities for the all-photon states.
Fig. 7.
Fig. 7. Probabilities of the intersect states: (a) one atom excited in one cavity and one H-polarized photon excited in the other cavity, (b) one atom excited in one cavity and one V-polarized photon excited in the other cavity, (c) one atom and one H-polarized photon excited in the same cavity, and (d) one atom and one V-polarized photon excited in the same cavity.
Fig. 8.
Fig. 8. Probability distribution of the H-polarized photons under the small hopping limit. Parameter values are gH=2gV and A=0.01gH.
Fig. 9.
Fig. 9. Bipartite entanglement under the small hopping limit. Parameter values are gH=2gV and A=0.01gH.
Fig. 10.
Fig. 10. Probability distribution of the eigenstates in the one-site subsystem. The inset shows the total probability for the three eigenstates. Parameter values are gH=2gV and A=0.01gH.
Fig. 11.
Fig. 11. Bipartite entanglement under the large hopping limit. Parameter values are gH=2gV and A=10gH.
Fig. 12.
Fig. 12. Dependence of S=MxNα+MxNβ+MyNαMyNβ on the detuning Δ. The solid curves show the results calculated in the classical manner, while the dashed curves are the results calculated in the quantum manner. From top to bottom, and from left to right, panels (a)–(i) correspond to the results calculated for directions α=0,π/4,π/2,3π/4,π,5π/4,3π/2,7π/4, and 2π, respectively. The gray lines are the gridlines of ±2,±22. Parameters are gH=2gV and A=0.01gH.

Equations (33)

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H^c=ωcj=1,2s=H,Va^j,sa^j,s+As=H,V(a^1,sa^2,s+a^1,sa^2,s),
H^a=ωaj=1,2|ejej|,
H^i=j=1,2s=H,V(gsa^j,s|sjej|+gsa^j,s|ejsj|).
|ϕc1=|2H|0V|He|0H|0V|He,
|ϕc21=|1H|1V|He|0H|0V|Ve,
|ϕc22=|1H|1V|Ve|0H|0V|He,
|ϕc3=|1H|0V|He|1H|0V|He,
|ϕc41=|1H|0V|He|0H|1V|Ve,
|ϕc42=|1H|0V|Ve|0H|1V|He,
|ϕc5=|0H|2V|Ve|0H|0V|Ve,
|ϕc61=|0H|1V|He|1H|0V|Ve,
|ϕc62=|0H|1V|Ve|1H|0V|He,
|ϕc7=|0H|1V|Ve|0H|1V|Ve,
|ϕc8=|0H|0V|He|2H|0V|He,
|ϕc91=|0H|0V|He|1H|1V|Ve,
|ϕc92=|0H|0V|Ve|1H|1V|He,
|ϕc10=|0H|0V|Ve|0H|2V|Ve.
|ϕa=|0H|0V|ee|0H|0V|ee.
|ϕi1=|1H|0V|ee|0H|0V|He,
|ϕi2=|0H|1V|ee|0H|0V|Ve,
|ϕi3=|0H|0V|ee|1H|0V|He,
|ϕi4=|0H|0V|ee|0H|1V|Ve,
|ϕi5=|1H|0V|He|0H|0V|ee,
|ϕi6=|0H|1V|Ve|0H|0V|ee,
|ϕi7=|0H|0V|He|1H|0V|ee,
|ϕi8=|0H|0V|Ve|0H|1V|ee.
H^=(000A00000000000gH00000000000A00A00000000gH00000000000A00A000000gV0000000A000000000A000000gH0gH0000A000000000A000000gHgV00000A000000000A0000000000000000000A000000gV0000000A000000000A0000000000000A000000000A0000gV00gH00000000A000000A0000gV0gV00000A00000000000000000gH00000A00A0000000000000gV000000A00A0000000000000gH000000000A000000000000gV000000000000002Δ00gHgVgHgV00gH0gV000000000000Δ0A000000gH0000gV000000000Δ0A0000000gH0000gV00000gHA0Δ000000000gH0000gV0000gV0A0Δ0000000gHgV000000000gH0000Δ0A000000000gHgV0000gV00000Δ0A0000000000gHgV0000000A0Δ0000000000000gHgV000000A0Δ),
M^0=(100000000),M^1=(000010000),M^2=(000000001).
Pm=ψ|E^mE^m|ψ,
S=MxNα+MxNβ+MyNαMyNβ2.
Mx=My=(100010001).
Nα=(cosα,sinα)·(Mx,My),
Nβ=(cosβ,sinβ)·(Mx,My).

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