Abstract

We propose two schemes to one-step generate the three-particle Greenberger–Horne–Zeilinger state based on the resonant atom–cavity fields interaction. The whole process may be realized experimentally providing that simple apparatus, initial conditions, and some manipulation in principle are achieved. Finally, in the current or the near future experiment parameter, we show that the proposed schemes can maintain the state with high fidelity under the condition of atomic spontaneous emission and decay of cavity fields.

© 2012 Optical Society of America

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  3. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
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  4. M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
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    [CrossRef]
  7. V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
    [CrossRef]
  8. J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfuter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nature 403, 515–519 (2000).
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  13. J. M. Raimond, M. Brune, and S. Haroche, “Colloquium: manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
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  14. R. Miller, T. E. Northup, K. M. Bimaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
    [CrossRef]
  15. H. Walther, B. T. H. Varcoe, B. G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69, 1325–1382 (2006).
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  16. J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
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  17. J. Q. You and F. Nori, “Superconducting circuits and quantum information,” Phys. Today 58, 42–47 (2005).
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  18. D. Loss and D. P. Divincenzo, “Quantum computation with quantum dots,” Phys. Rev. A 57, 120–126 (1998).
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  20. E. Hagley, X. Maître, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche, “Generation of Einstein–Podolsky–Rosen pairs of atoms,” Phys. Rev. Lett. 79, 1–5 (1997).
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  21. A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
    [CrossRef]
  22. A. Auffeves, P. Maioli, T. Meunier, S. Gleyzes, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity,” Phys. Rev. Lett. 91, 230405 (2003).
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    [CrossRef]
  24. B. Weber, H. P. Specht, T. Müller, J. Bochmann, M. Mücke, D. L. Moehring, and G. Rempe, “Photon–photon entanglement with a single trapped atom,” Phys. Rev. Lett. 102, 030501 (2009).
    [CrossRef]
  25. C. C. Gerry, “Preparation of multiatom entangled states through dispersive atom–cavity-field interactions,” Phys. Rev. A 53, 2857–2860 (1996).
    [CrossRef]
  26. S. B. Zheng, “Simplified realization of multi-atom Greenberger–Horne–Zeilinger states with dispersive cavity QED,” Opt. Commun. 171, 77–80 (1999).
    [CrossRef]
  27. J. I. Cirac and P. Zoller, “Preparation of macroscopic superpositions in many-atom systems,” Phys. Rev. A 50, R2799–R2802 (1994).
    [CrossRef]
  28. S. B. Zheng, “Generation of multi-atom entangled states via the Raman atom-cavity-field interaction,” Chin. Phys. Lett. 7, 485–487 (1997).
    [CrossRef]
  29. M. Ikram and F. Saif, “Engineering entanglement between two cavity modes,” Phys. Rev. A 66, 014304 (2002).
    [CrossRef]
  30. C. P. Yang, “Preparation of n-qubit Greenberger–Horne–Zeilinger entangled states in cavity QED: an approach with tolerance to nonidentical qubit-cavity coupling constants,” Phys. Rev. A 83, 062302 (2011).
    [CrossRef]
  31. A. H. Khosa, R. Islam, and F. Saif, “Remote preparation of atomic and field cluster states from a pair of tri-partite GHZ states,” Chin. Phys. B 19, 040309 (2010).
    [CrossRef]
  32. C. S. Yu, X. X. Yi, and H. S. Song, “Robust preparation of Greenberger–Horne–Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
    [CrossRef]
  33. D. Gonta, S. Fritzsche, and T. Radtke, “Generation of four-partite Greenberger–Horne–Zeilinger and W states by using a high-finesse bimodal cavity,” Phys. Rev. A 77, 062312 (2008).
    [CrossRef]
  34. X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
    [CrossRef]
  35. T. Pellizzari, “Quantum networking with optical fibres,” Phys. Rev. Lett. 79, 5242–5245 (1997).
    [CrossRef]
  36. A. Zheng and J. Liu, “Generation of an N-qubit Greenberger–Horne–Zeilinger state with distant atoms in bimodal cavities,” J. Phys. B 44, 165501 (2011).
    [CrossRef]
  37. Z. B. Yang, H. Z. Wu, Y. Xia, and S. B. Zheng, “Effective dynamics for two-atom entanglement and quantum information processing by coupled cavity QED systems,” Eur. Phys. J. D 61, 737–744 (2011).
    [CrossRef]
  38. X. Y. Lü, P. J. Song, J. B. Liu, and X. Yang, “N-qubit W state of spatially separated single molecule magnets,” Opt. Express 17, 14298–14311 (2009).
    [CrossRef]
  39. X. Y. Lü, L. G. Si, X. Y. Hao, and X. Yang, “Achieving multipartite entanglement of distant atoms through selective photon emission and absorption processes,” Phys. Rev. A 79, 052330 (2009).
    [CrossRef]
  40. S. B. Zheng, “One-step synthesis of multiatom Greenberger–Horne–Zeilinger states,” Phys. Rev. Lett. 87, 230404 (2001).
    [CrossRef]
  41. J. Lee, J. Park, S. M. Lee, H. W. Lee, and A. H. Khosa, “Scalable cavity-QED-based scheme of generating entanglement of atoms and of cavity fields,” Phys. Rev. A 77, 032327 (2008).
    [CrossRef]
  42. A. Biswas and G. S. Agarwal, “Transfer of an unknown quantum state, quantum networks and memory,” Phys. Rev. A 70, 022323 (2004).
    [CrossRef]
  43. Z. Li, J. Jin, and C. Yu, “Probing quantum entanglement, quantum discord, classical correlation and the quantum state without disturbing them,” Phys. Rev. A 83, 012317 (2011).
    [CrossRef]
  44. S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deleglise, S. Osnaghi, M. Brune, J. M. Raimond, S. Haroche, E. Jacques, P. Bosland, and B. Visentin, “Ultrahigh finesse Fabry–Pérot superconducting resonator,” Appl. Phys. Lett. 90, 164101 (2007).
    [CrossRef]
  45. M. Knap, E. Arrigoni, and W. Lindern, “Spectral properties of coupled cavity arrays in one dimension,” Phys. Rev. B 81, 104303 (2010).
    [CrossRef]
  46. D. Rossini and R. Fazio, “Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities,” Phys. Rev. Lett. 99, 186401 (2007).
    [CrossRef]
  47. E. K. Irish, “Ground-state entanglement in a coupled-cavity model,” Phys. Rev. A 80, 043825 (2009).
    [CrossRef]
  48. J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).
    [CrossRef]
  49. J. Song, X. D. Sun, Y. Xia, and H. S. Song, “Efficient creation of continuous-variable entanglement for two atomic ensembles in coupled cavities,” Phys. Rev. A 83, 052309 (2011).
    [CrossRef]
  50. C. D. Ogden, E. K. Irish, and M. S. Kim, “Dynamics in a coupled-cavity array,” Phys. Rev. A 78, 063805 (2008).
    [CrossRef]
  51. Z. Q. Yi and F. L. Li, “Multiatom and resonant interaction scheme for quantum state transfer and logical gates between two remote cavities via an optical fiber,” Phys. Rev. A 75, 012324 (2007).
    [CrossRef]
  52. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
    [CrossRef]

2011 (5)

C. P. Yang, “Preparation of n-qubit Greenberger–Horne–Zeilinger entangled states in cavity QED: an approach with tolerance to nonidentical qubit-cavity coupling constants,” Phys. Rev. A 83, 062302 (2011).
[CrossRef]

A. Zheng and J. Liu, “Generation of an N-qubit Greenberger–Horne–Zeilinger state with distant atoms in bimodal cavities,” J. Phys. B 44, 165501 (2011).
[CrossRef]

Z. B. Yang, H. Z. Wu, Y. Xia, and S. B. Zheng, “Effective dynamics for two-atom entanglement and quantum information processing by coupled cavity QED systems,” Eur. Phys. J. D 61, 737–744 (2011).
[CrossRef]

Z. Li, J. Jin, and C. Yu, “Probing quantum entanglement, quantum discord, classical correlation and the quantum state without disturbing them,” Phys. Rev. A 83, 012317 (2011).
[CrossRef]

J. Song, X. D. Sun, Y. Xia, and H. S. Song, “Efficient creation of continuous-variable entanglement for two atomic ensembles in coupled cavities,” Phys. Rev. A 83, 052309 (2011).
[CrossRef]

2010 (2)

M. Knap, E. Arrigoni, and W. Lindern, “Spectral properties of coupled cavity arrays in one dimension,” Phys. Rev. B 81, 104303 (2010).
[CrossRef]

A. H. Khosa, R. Islam, and F. Saif, “Remote preparation of atomic and field cluster states from a pair of tri-partite GHZ states,” Chin. Phys. B 19, 040309 (2010).
[CrossRef]

2009 (4)

B. Weber, H. P. Specht, T. Müller, J. Bochmann, M. Mücke, D. L. Moehring, and G. Rempe, “Photon–photon entanglement with a single trapped atom,” Phys. Rev. Lett. 102, 030501 (2009).
[CrossRef]

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

X. Y. Lü, P. J. Song, J. B. Liu, and X. Yang, “N-qubit W state of spatially separated single molecule magnets,” Opt. Express 17, 14298–14311 (2009).
[CrossRef]

X. Y. Lü, L. G. Si, X. Y. Hao, and X. Yang, “Achieving multipartite entanglement of distant atoms through selective photon emission and absorption processes,” Phys. Rev. A 79, 052330 (2009).
[CrossRef]

2008 (4)

J. Lee, J. Park, S. M. Lee, H. W. Lee, and A. H. Khosa, “Scalable cavity-QED-based scheme of generating entanglement of atoms and of cavity fields,” Phys. Rev. A 77, 032327 (2008).
[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).
[CrossRef]

C. D. Ogden, E. K. Irish, and M. S. Kim, “Dynamics in a coupled-cavity array,” Phys. Rev. A 78, 063805 (2008).
[CrossRef]

D. Gonta, S. Fritzsche, and T. Radtke, “Generation of four-partite Greenberger–Horne–Zeilinger and W states by using a high-finesse bimodal cavity,” Phys. Rev. A 77, 062312 (2008).
[CrossRef]

2007 (4)

C. S. Yu, X. X. Yi, and H. S. Song, “Robust preparation of Greenberger–Horne–Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
[CrossRef]

Z. Q. Yi and F. L. Li, “Multiatom and resonant interaction scheme for quantum state transfer and logical gates between two remote cavities via an optical fiber,” Phys. Rev. A 75, 012324 (2007).
[CrossRef]

D. Rossini and R. Fazio, “Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities,” Phys. Rev. Lett. 99, 186401 (2007).
[CrossRef]

S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deleglise, S. Osnaghi, M. Brune, J. M. Raimond, S. Haroche, E. Jacques, P. Bosland, and B. Visentin, “Ultrahigh finesse Fabry–Pérot superconducting resonator,” Appl. Phys. Lett. 90, 164101 (2007).
[CrossRef]

2006 (2)

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

H. Walther, B. T. H. Varcoe, B. G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69, 1325–1382 (2006).
[CrossRef]

2005 (2)

J. Q. You and F. Nori, “Superconducting circuits and quantum information,” Phys. Today 58, 42–47 (2005).
[CrossRef]

R. Miller, T. E. Northup, K. M. Bimaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

2004 (2)

X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
[CrossRef]

A. Biswas and G. S. Agarwal, “Transfer of an unknown quantum state, quantum networks and memory,” Phys. Rev. A 70, 022323 (2004).
[CrossRef]

2003 (1)

A. Auffeves, P. Maioli, T. Meunier, S. Gleyzes, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity,” Phys. Rev. Lett. 91, 230405 (2003).
[CrossRef]

2002 (1)

M. Ikram and F. Saif, “Engineering entanglement between two cavity modes,” Phys. Rev. A 66, 014304 (2002).
[CrossRef]

2001 (4)

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A 64, 050301 (2001).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

J. M. Raimond, M. Brune, and S. Haroche, “Colloquium: manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

S. B. Zheng, “One-step synthesis of multiatom Greenberger–Horne–Zeilinger states,” Phys. Rev. Lett. 87, 230404 (2001).
[CrossRef]

2000 (3)

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfuter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nature 403, 515–519 (2000).
[CrossRef]

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

1999 (4)

S. B. Zheng, “Simplified realization of multi-atom Greenberger–Horne–Zeilinger states with dispersive cavity QED,” Opt. Commun. 171, 77–80 (1999).
[CrossRef]

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[CrossRef]

A. Karlsson, M. Koashi, and N. Imoto, “Quantum entanglement for secret sharing and secret splitting,” Phys. Rev. A 59, 162–168 (1999).
[CrossRef]

R. Cleve, D. Gottesman, and H. K. Lo, “How to share a quantum secret,” Phys. Rev. Lett. 83, 648–651 (1999).
[CrossRef]

1998 (1)

D. Loss and D. P. Divincenzo, “Quantum computation with quantum dots,” Phys. Rev. A 57, 120–126 (1998).
[CrossRef]

1997 (3)

S. B. Zheng, “Generation of multi-atom entangled states via the Raman atom-cavity-field interaction,” Chin. Phys. Lett. 7, 485–487 (1997).
[CrossRef]

T. Pellizzari, “Quantum networking with optical fibres,” Phys. Rev. Lett. 79, 5242–5245 (1997).
[CrossRef]

E. Hagley, X. Maître, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche, “Generation of Einstein–Podolsky–Rosen pairs of atoms,” Phys. Rev. Lett. 79, 1–5 (1997).
[CrossRef]

1996 (2)

C. C. Gerry, “Preparation of multiatom entangled states through dispersive atom–cavity-field interactions,” Phys. Rev. A 53, 2857–2860 (1996).
[CrossRef]

V. Bužek and M. Hillery, “Quantum copying: beyond the no-cloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).
[CrossRef]

1995 (1)

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef]

1994 (1)

J. I. Cirac and P. Zoller, “Preparation of macroscopic superpositions in many-atom systems,” Phys. Rev. A 50, R2799–R2802 (1994).
[CrossRef]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

1992 (1)

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computer,” Proc. R. Soc. Lond. A 439, 553–558(1992).
[CrossRef]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

1990 (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1143 (1990).
[CrossRef]

1964 (1)

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

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Agarwal, G. S.

A. Biswas and G. S. Agarwal, “Transfer of an unknown quantum state, quantum networks and memory,” Phys. Rev. A 70, 022323 (2004).
[CrossRef]

Angelakis, D. G.

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).
[CrossRef]

Arrigoni, E.

M. Knap, E. Arrigoni, and W. Lindern, “Spectral properties of coupled cavity arrays in one dimension,” Phys. Rev. B 81, 104303 (2010).
[CrossRef]

Auffeves, A.

A. Auffeves, P. Maioli, T. Meunier, S. Gleyzes, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity,” Phys. Rev. Lett. 91, 230405 (2003).
[CrossRef]

Becker, T.

H. Walther, B. T. H. Varcoe, B. G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69, 1325–1382 (2006).
[CrossRef]

Bell, J. S.

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

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Bernu, J.

S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deleglise, S. Osnaghi, M. Brune, J. M. Raimond, S. Haroche, E. Jacques, P. Bosland, and B. Visentin, “Ultrahigh finesse Fabry–Pérot superconducting resonator,” Appl. Phys. Lett. 90, 164101 (2007).
[CrossRef]

Bertet, P.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A 64, 050301 (2001).
[CrossRef]

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

Berthiaume, A.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[CrossRef]

Bimaum, K. M.

R. Miller, T. E. Northup, K. M. Bimaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Biswas, A.

A. Biswas and G. S. Agarwal, “Transfer of an unknown quantum state, quantum networks and memory,” Phys. Rev. A 70, 022323 (2004).
[CrossRef]

Boca, A.

R. Miller, T. E. Northup, K. M. Bimaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Bochmann, J.

B. Weber, H. P. Specht, T. Müller, J. Bochmann, M. Mücke, D. L. Moehring, and G. Rempe, “Photon–photon entanglement with a single trapped atom,” Phys. Rev. Lett. 102, 030501 (2009).
[CrossRef]

Boozer, A. D.

R. Miller, T. E. Northup, K. M. Bimaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Bose, S.

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).
[CrossRef]

Bosland, P.

S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deleglise, S. Osnaghi, M. Brune, J. M. Raimond, S. Haroche, E. Jacques, P. Bosland, and B. Visentin, “Ultrahigh finesse Fabry–Pérot superconducting resonator,” Appl. Phys. Lett. 90, 164101 (2007).
[CrossRef]

Bouwmeester, D.

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfuter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nature 403, 515–519 (2000).
[CrossRef]

Brandão, F. G. S. L.

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Brune, M.

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C. D. Ogden, E. K. Irish, and M. S. Kim, “Dynamics in a coupled-cavity array,” Phys. Rev. A 78, 063805 (2008).
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S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deleglise, S. Osnaghi, M. Brune, J. M. Raimond, S. Haroche, E. Jacques, P. Bosland, and B. Visentin, “Ultrahigh finesse Fabry–Pérot superconducting resonator,” Appl. Phys. Lett. 90, 164101 (2007).
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X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
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[CrossRef]

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J. Lee, J. Park, S. M. Lee, H. W. Lee, and A. H. Khosa, “Scalable cavity-QED-based scheme of generating entanglement of atoms and of cavity fields,” Phys. Rev. A 77, 032327 (2008).
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M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
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S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deleglise, S. Osnaghi, M. Brune, J. M. Raimond, S. Haroche, E. Jacques, P. Bosland, and B. Visentin, “Ultrahigh finesse Fabry–Pérot superconducting resonator,” Appl. Phys. Lett. 90, 164101 (2007).
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[CrossRef]

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[CrossRef]

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

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[CrossRef]

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A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A 64, 050301 (2001).
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D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1143 (1990).
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J. Song, X. D. Sun, Y. Xia, and H. S. Song, “Efficient creation of continuous-variable entanglement for two atomic ensembles in coupled cavities,” Phys. Rev. A 83, 052309 (2011).
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C. S. Yu, X. X. Yi, and H. S. Song, “Robust preparation of Greenberger–Horne–Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
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J. Song, X. D. Sun, Y. Xia, and H. S. Song, “Efficient creation of continuous-variable entanglement for two atomic ensembles in coupled cavities,” Phys. Rev. A 83, 052309 (2011).
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C. S. Yu, X. X. Yi, and H. S. Song, “Robust preparation of Greenberger–Horne–Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
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Figures (7)

Fig. 1.
Fig. 1.

Sketch of the setup of the proposed scheme for generating three-particle GHZ states.

Fig. 2.
Fig. 2.

Sketch map of a three-level atom interacting with cavity field.

Fig. 3.
Fig. 3.

(a) Maximum value of fidelity of realizing the GHZ state versus v and g when assuming g=1, gt8; (b) Fidelity of the GHZ state with different v versus time gt when g=1.4.

Fig. 4.
Fig. 4.

Sketch of the setup of the proposed scheme for generating three-particle GHZ states in two cavities.

Fig. 5.
Fig. 5.

Fidelity of realizing the GHZ states versus gt and v.

Fig. 6.
Fig. 6.

Fidelities of realizing the GHZ state versus X and Y axes, denoting decay rates κ and τ, respectively (choosing parameters 0<gt<8, g=1, g=1.4g and (a) v=0.48, (b) v=0.73, (c) v=1.68).

Fig. 7.
Fig. 7.

Fidelities of realizing the GHZ state versus X and Y axes, denoting decay rates κ and τ, respectively (choosing parameters g=1, g=1.4g and (a) gt=1.58, (b) gt=4.74, (c) gt=7.90).

Equations (9)

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

HG1=g2fa2|e2f2|+g2ga3|e2g2|+g1a1|e1f1|+g3a4|e3g3|+v(a1a2++a3a4+)+H.C,
it|ψ(t)=HG1|ψ(t).
HG2=g2fa1|e2f2|+g2ga2|e2g2|+g1a1|e1f1|+g3a3|e3g3|+H.C.
HG1con=[ga2|e2f2|+ga3|e2g2|+ga1|e1f1|+ga4|e3f3|+v(a1a2++a3a4+)+H.C]ii=14κiai+aiij3τj|ejej|,
HG2con=(ga1|e2f2|+ga2|e2g2|+ga1|e1f1|+ga2|e3g3|+H.C)ii=12κiai+aiij3τj|ejej|,
ρ˙ac1=i[HG1con,ρac1],
ρ˙ac2=i[HG2con,ρac2],
HG1=g(a1N=1M|e1Nf1N|+a4N=1M|e3Ng3N|)+g(a2|e2f2|+a3|e2g2|)+v(a1a2++a3a4+)+H.C.
HG2=g(a1|e2f2|+a2|e2g2|)+g(a1N=1M|e1Nf1N|+a2N=1M|e3Ng3N|)+H.C.,

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