Abstract

We propose a scheme to deterministically generate Greenberger–Horne–Zeilinger states of N3 atoms trapped in spatially separated cavities connected by optical fibers. The scheme is based on the technique of fractional stimulated Raman adiabatic passage, which is a one-step technique in the sense that one needs only to wait for the desired entangled state to be generated in the stationary regime. The parametrized shapes of the Rabi frequencies of the classical fields that drive the two end atoms are chosen appropriately to realize the scheme. We also show numerically that the proposed scheme is insensitive to fluctuations of the pulses’ parameters and, at the same time, that it is robust against decoherence caused by the dissipation due to fiber decay. Moreover, a relatively high fidelity can be obtained even in the presence of cavity decay and atomic spontaneous emission.

© 2013 Optical Society of America

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    [CrossRef]
  5. Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Teleportation of an N-photon Greenberger–Horne–Zeilinger (GHZ) polarization-entangled state using linear optical elements,” J. Opt. Soc. Am. B 27, A1–A6 (2010).
    [CrossRef]
  6. K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
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  7. J. W. Pan and A. Zeilinger, “Greenberger–Horne–Zeilinger state analyzer,” Phys. Rev. A 57, 002208 (1998).
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  8. M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
    [CrossRef]
  9. W. Dur, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
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  13. G. A. Durkin, C. Simon, and D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptograph,” Phys. Rev. Lett. 88, 187902 (2002).
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  18. S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, “Improvement of frequency standards with quantum entanglement,” Phys. Rev. Lett. 79, 3865–3868(1997).
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  33. S. J. van Enk, J. I. Cirac, and P. Zoller, “Ideal quantum communication over noisy channels: a quantum optical implementation,” Phys. Rev. Lett. 78, 4293–4296 (1997).
    [CrossRef]
  34. S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, “Proposal for teleportation of an atomic state via cavity decay,” Phys. Rev. Lett. 83, 5158–5167 (1999).
    [CrossRef]
  35. S. Lloyd, M. S. Shahriar, J. H. Shapiro, and P. R. Hemmer, “Long distance, unconditional teleportation of atomic states via complete Bell state measurements,” Phys. Rev. Lett. 87, 167903 (2001).
    [CrossRef]
  36. A. S. Parkins and H. J. Kimble, “Position-momentum Einstein–Podolsky–Rosen state of distantly Separated trapped atoms,” Phys. Rev. A 61, 052104 (2000).
    [CrossRef]
  37. S. B. Zheng, “A simplified scheme for realizing Greenberger–Horne–Zeilinger states,” J. Opt.B Quantum Semiclass. Opt. 1, 534–535 (1999).
    [CrossRef]
  38. W. A. Li and L. F. Wei, “Controllable entanglement preparations between atoms in spatially-separated cavities via quantum Zeno dynamics,” Opt. Express 20, 13440–13450 (2012).
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    [CrossRef]
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    [CrossRef]
  41. U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363–5376 (1990).
    [CrossRef]
  42. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
    [CrossRef]
  43. P. Marte, P. Zoller, and J. L. Hall, “Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems,” Phys. Rev. A 44, R4118–R4121 (1991).
    [CrossRef]
  44. T. Pellizzari, “Quantum networking with optical fibers,” Phys. Rev. Lett. 79, 5242–5245 (1997).
    [CrossRef]
  45. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamic,” Phys. Rev. A 71, 013817 (2005).
    [CrossRef]
  46. J. R. Buck and H. J. Kimble, “Optimale sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67, 033806 (2003).
    [CrossRef]
  47. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
    [CrossRef]
  48. K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, “A short wavelength gigahertz clocked fiber optic quantum key distribution system,” IEEE J. Quantum Electron. 40, 900–908 (2004).
    [CrossRef]
  49. S. B. Zheng, C. P. Yang, and F. Nori, “Arbitrary control of coherent dynamics for distant qubits in a quantum network,” Phys. Rev. A 82, 042327 (2010).
    [CrossRef]

2012 (1)

2011 (2)

P. B. Li and F. L. Li, “Deterministic generation of multiparticle entanglement in a coupled cavity-fiber system,” Opt. Express 19, 1207–1216 (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]

2010 (4)

Z. B. Yang, S. Y. Ye, A. Serafini, and S. B. Zheng, “Distributed coherent manipulation of qutrits by virtual excitation processes,” J. Phys. B 43, 085506 (2010).
[CrossRef]

Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Teleportation of an N-photon Greenberger–Horne–Zeilinger (GHZ) polarization-entangled state using linear optical elements,” J. Opt. Soc. Am. B 27, A1–A6 (2010).
[CrossRef]

M. Neeley, R. C. Bialczak, M. Lenander, and E. Lucero, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

S. B. Zheng, C. P. Yang, and F. Nori, “Arbitrary control of coherent dynamics for distant qubits in a quantum network,” Phys. Rev. A 82, 042327 (2010).
[CrossRef]

2009 (3)

S. B Zheng, “Generation of Greenberger–Horne–Zeilinger states for multiple atoms trapped in separated cavities,” Eur. Phys. J. D 54, 719–722 (2009).
[CrossRef]

X. Y. Lv, 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]

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

2008 (1)

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger–Horne–Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127 (2008).
[CrossRef]

2007 (2)

Z. Q. Yin 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]

P. Kral, L. Thanopulos, and M. Shapiro, “Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79, 53–77 (2007).
[CrossRef]

2006 (1)

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

2005 (2)

D. Leibfried, E. Knill, S. Seidelin, and J. Britton, “Greation of a six-atom ‘Schrodinger cat’ state,” Nature 438, 639–642 (2005).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamic,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

2004 (3)

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, “A short wavelength gigahertz clocked fiber optic quantum key distribution system,” IEEE J. Quantum Electron. 40, 900–908 (2004).
[CrossRef]

Z. Zhao, Y. Chen, A. N. Zheng, Y. Yang, H. Briegel, and J. W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
[CrossRef]

C. P. Yang, S.-I Chu, and S. Han, “Efficient many-party controlled teleportation of multiqubit quantum information via entanglement,” Phys. Rev. A 70, 022329 (2004).
[CrossRef]

2003 (2)

J. R. Buck and H. J. Kimble, “Optimale sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67, 033806 (2003).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

2002 (1)

G. A. Durkin, C. Simon, and D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptograph,” Phys. Rev. Lett. 88, 187902 (2002).
[CrossRef]

2001 (2)

V. Scarani and N. Gisin, “Quantum communication between N partners and Bell’s inequalities,” Phys. Rev. Lett. 87, 117901 (2001).
[CrossRef]

S. Lloyd, M. S. Shahriar, J. H. Shapiro, and P. R. Hemmer, “Long distance, unconditional teleportation of atomic states via complete Bell state measurements,” Phys. Rev. Lett. 87, 167903 (2001).
[CrossRef]

2000 (3)

A. S. Parkins and H. J. Kimble, “Position-momentum Einstein–Podolsky–Rosen state of distantly Separated trapped atoms,” Phys. Rev. A 61, 052104 (2000).
[CrossRef]

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

R. J. Nelson, D. G. Cory, and S. Lloyd, “Experimental demonstration of Greenberger–Horne–Zeilinger correlations using nuclear magnetic resonance,” Phys. Rev. A 61, 022106 (2000).
[CrossRef]

1999 (5)

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

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

S. B. Zheng, “A simplified scheme for realizing Greenberger–Horne–Zeilinger states,” J. Opt.B Quantum Semiclass. Opt. 1, 534–535 (1999).
[CrossRef]

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, “Proposal for teleportation of an atomic state via cavity decay,” Phys. Rev. Lett. 83, 5158–5167 (1999).
[CrossRef]

N. V. Vitanov, K. A. Suominen, and B. W. Shore, “Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage,” J. Phys. B 32, 4535–4546 (1999).
[CrossRef]

1998 (4)

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[CrossRef]

J. W. Pan and A. Zeilinger, “Greenberger–Horne–Zeilinger state analyzer,” Phys. Rev. A 57, 002208 (1998).
[CrossRef]

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[CrossRef]

J. Preskill, “Reliable quantum computers,” Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 454, 385–410 (1998).
[CrossRef]

1997 (4)

S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, “Improvement of frequency standards with quantum entanglement,” Phys. Rev. Lett. 79, 3865–3868(1997).
[CrossRef]

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[CrossRef]

S. J. van Enk, J. I. Cirac, and P. Zoller, “Ideal quantum communication over noisy channels: a quantum optical implementation,” Phys. Rev. Lett. 78, 4293–4296 (1997).
[CrossRef]

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

1996 (3)

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[CrossRef]

D. P. DiVincenzo and P. W. Shor, “Fault-tolerant error correction with efficient quantum codes,” Phys. Rev. Lett. 77, 3260–3263 (1996).
[CrossRef]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef]

1993 (1)

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

1991 (2)

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

P. Marte, P. Zoller, and J. L. Hall, “Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems,” Phys. Rev. A 44, R4118–R4121 (1991).
[CrossRef]

1990 (2)

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363–5376 (1990).
[CrossRef]

D. M. Greenberger, M. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1142(1990).
[CrossRef]

1964 (1)

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

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

Bergmann, K.

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[CrossRef]

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results,” J. Chem. Phys. 92, 5363–5376 (1990).
[CrossRef]

Berthiaume, A.

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

Bialczak, R. C.

M. Neeley, R. C. Bialczak, M. Lenander, and E. Lucero, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Bollinger, J. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[CrossRef]

Bose, S.

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, “Proposal for teleportation of an atomic state via cavity decay,” Phys. Rev. Lett. 83, 5158–5167 (1999).
[CrossRef]

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[CrossRef]

Bouwmeester, D.

G. A. Durkin, C. Simon, and D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptograph,” Phys. Rev. Lett. 88, 187902 (2002).
[CrossRef]

Brassard, G.

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

Briegel, H.

Z. Zhao, Y. Chen, A. N. Zheng, Y. Yang, H. Briegel, and J. W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
[CrossRef]

Britton, J.

D. Leibfried, E. Knill, S. Seidelin, and J. Britton, “Greation of a six-atom ‘Schrodinger cat’ state,” Nature 438, 639–642 (2005).
[CrossRef]

Buck, J. R.

J. R. Buck and H. J. Kimble, “Optimale sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Buller, G. S.

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, “A short wavelength gigahertz clocked fiber optic quantum key distribution system,” IEEE J. Quantum Electron. 40, 900–908 (2004).
[CrossRef]

Buzek, V.

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

Chen, Y.

Z. Zhao, Y. Chen, A. N. Zheng, Y. Yang, H. Briegel, and J. W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
[CrossRef]

Chu, S.-I

C. P. Yang, S.-I Chu, and S. Han, “Efficient many-party controlled teleportation of multiqubit quantum information via entanglement,” Phys. Rev. A 70, 022329 (2004).
[CrossRef]

Cirac, J. I.

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

S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, “Improvement of frequency standards with quantum entanglement,” Phys. Rev. Lett. 79, 3865–3868(1997).
[CrossRef]

S. J. van Enk, J. I. Cirac, and P. Zoller, “Ideal quantum communication over noisy channels: a quantum optical implementation,” Phys. Rev. Lett. 78, 4293–4296 (1997).
[CrossRef]

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[CrossRef]

Cleve, R.

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

Cory, D. G.

R. J. Nelson, D. G. Cory, and S. Lloyd, “Experimental demonstration of Greenberger–Horne–Zeilinger correlations using nuclear magnetic resonance,” Phys. Rev. A 61, 022106 (2000).
[CrossRef]

Crepeau, C.

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

DiVincenzo, D. P.

D. P. DiVincenzo and P. W. Shor, “Fault-tolerant error correction with efficient quantum codes,” Phys. Rev. Lett. 77, 3260–3263 (1996).
[CrossRef]

Dur, W.

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

Durkin, G. A.

G. A. Durkin, C. Simon, and D. Bouwmeester, “Multiphoton entanglement concentration and quantum cryptograph,” Phys. Rev. Lett. 88, 187902 (2002).
[CrossRef]

Ekert, A. K.

S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, “Improvement of frequency standards with quantum entanglement,” Phys. Rev. Lett. 79, 3865–3868(1997).
[CrossRef]

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

Fernandez, V.

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, “A short wavelength gigahertz clocked fiber optic quantum key distribution system,” IEEE J. Quantum Electron. 40, 900–908 (2004).
[CrossRef]

Gaubatz, U.

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S. B. Zheng, C. P. Yang, and F. Nori, “Arbitrary control of coherent dynamics for distant qubits in a quantum network,” Phys. Rev. A 82, 042327 (2010).
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X. Y. Lv, P. J. Song, J. B. Liu, and X. Yang, “N-qubit W state of separated single molecule magnets,” Opt. Express 17, 14298–14311 (2009).
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Z. Zhao, Y. Chen, A. N. Zheng, Y. Yang, H. Briegel, and J. W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
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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).
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Z. Zhao, Y. Chen, A. N. Zheng, Y. Yang, H. Briegel, and J. W. Pan, “Experimental demonstration of five-photon entanglement and open-destination teleportation,” Nature 430, 54–58 (2004).
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Z. B. Yang, S. Y. Ye, A. Serafini, and S. B. Zheng, “Distributed coherent manipulation of qutrits by virtual excitation processes,” J. Phys. B 43, 085506 (2010).
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J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
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Am. J. Phys. (1)

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Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger–Horne–Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127 (2008).
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S. B Zheng, “Generation of Greenberger–Horne–Zeilinger states for multiple atoms trapped in separated cavities,” Eur. Phys. J. D 54, 719–722 (2009).
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IEEE J. Quantum Electron. (1)

K. J. Gordon, V. Fernandez, P. D. Townsend, and G. S. Buller, “A short wavelength gigahertz clocked fiber optic quantum key distribution system,” IEEE J. Quantum Electron. 40, 900–908 (2004).
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J. Chem. Phys. (1)

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J. Opt. Soc. Am. B (1)

J. Opt.B Quantum Semiclass. Opt. (1)

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Figures (7)

Fig. 1.
Fig. 1.

Three atoms (a1, a2, and a3), each of which has one excited state [|ek (k=1,2,3)] and three ground states (|gLk, |g0k, and |gRk) with a tripod-type configuration are, respectively, trapped in three optical cavities (c1, c2, and c3) connected by two optical fibers (f1 and f2).

Fig. 2.
Fig. 2.

N atoms are, respectively, trapped in N cavities through N1 fibers.

Fig. 3.
Fig. 3.

Time dependence of (top) the Rabi frequencies of the driving lasers Ω1(t) and Ω3(t), (middle) the probabilities P1, P3, P5, P7, P9, and P11 of finding the system in states |ϕ1, |ϕ3, |ϕ5, |ϕ7, |ϕ9, and |ϕ11, respectively, and (bottom) the fidelity F. The parameters used are α=π/4, Ω0/g=0.1, gτ=50, and gT=80.

Fig. 4.
Fig. 4.

Density plot of the fidelity F at gt=300 as a function of gτ and gT for Ω0/g=0.1 and v/g=10. The two straight lines indicate the boundaries of the region within which the fidelity is almost 1.

Fig. 5.
Fig. 5.

Density plot of the fidelity F at gt=300 as a function of (top) Ω0/g and κ/g and (bottom) Ω0/g and γ/g.

Fig. 6.
Fig. 6.

Fidelity F as a function of κ/g and κ/g for Ω0/g=0.1, v/g=10, and gt=300.

Fig. 7.
Fig. 7.

Fidelity F as a function of κ/g and γ/g for Ω0/g=0.1, v/g=10, and gt=300.

Equations (30)

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|H=Hal+Hac+Hcf,
Hal=Ω1(t)eiφ1|e1g0|+Ω3(t)eiφ3|e3g0|+H.c.,
Hac=i=12gi,lai,l|eigL|+i=23gi,rai,r|eigR|+H.c.,
Hcf=v1b1(a1,l+a2,l)+v2b2(a2,r+a3,r)+H.c.
|Ψ()=|g0,gL,gRa1a2a3|0c1|0f1|0,0c2|0f2|0c3.
|ϕ1=|Ψ()=|g0,gL,gRa1a2a3|0c1|0f1|0,0c2|0f2|0c3,
|ϕ2=|e,gL,gRa1a2a3|0c1|0f1|0,0c2|0f2|0c3,
|ϕ3=|gL,gL,gRa1a2a3|1c1|0f1|0,0c2|0f2|0c3,
|ϕ4=|gL,gL,gRa1a2a3|0c1|1f1|0,0c2|0f2|0c3,
|ϕ5=|gL,gL,gRa1a2a3|0c1|0f1|1,0c2|0f2|0c3,
|ϕ6=|gL,e,gRa1a2a3|0c1|0f1|0,0c2|0f2|0c3,
|ϕ7=|gL,gR,gRa1a2a3|0c1|0f1|0,1c2|0f2|0c3,
|ϕ8=|gL,gR,gRa1a2a3|0c1|0f1|0,0c2|1f2|0c3,
|ϕ9=|gL,gR,gRa1a2a3|0c1|0f1|0,0c2|0f2|1c3,
|ϕ10=|gL,gR,ea1a2a3|0c1|0f1|0,0c2|0f2|0c3,
|ϕ11=|gL,gR,g0a1a2a3|0c1|0f1|0,0c2|0f2|0c3.
H=(0Ω˜1(t)000000000Ω˜1*(t)0g000000000g0v000000000v0v000000000v0g000000000g0g000000000g0v000000000v0v000000000v0g000000000g0Ω˜3(t)000000000Ω˜3*(t)0)
|Φ1(t)=G(t)4X2(t)+G2(t)[X2(t)+1]|ϕ1X(t)4X2(t)+G2(t)[X2(t)+1](|ϕ3|ϕ5+|ϕ7|ϕ9)ei(φ1+φ3)G(t)X(t)4X2(t)+G2(t)[X2(t)+1]|ϕ11,
|Ψ(t)=m=111wm(t)|Φm(t),m=111|wm(t)|2=1
limtΩ3(t)>limtΩ1(t)=0,
2Ω1(t)Ω3(t)Ω12(t)+Ω32(t)g,
limtΩ1,3(t)=0;limt[Ω1(t)/Ω3(t)]=limtX(t)=X()=const.
limt|Φ1(t)=|ghz123|0c1|0f1|0,0c2|0f2|0c3
|ghz123=1X2()+1|g0,gL,gRa1a2a3ei(φ1+φ3)X()X2()+1|gL,gR,g0a1a2a3,
Hal=Ω1(t)eiφ1|e1g0|+ΩN(t)eiφN|eNg0|+H.c.,
Hac=g[i=1N1ai,l|eigL|+i=2Nai,r|eigR|]+H.c.,
Hcf=vi=1(N1)/2[b2i1(a2i1,l+a2i,l)+b2i(a2i,r+a2i+1,r)]+H.c.
Ω1(t)=Ω0sinαe(tτ)2/T2
Ω3(t)=Ω0e(t+τ)2/T2+Ω0cosαe(tτ)2/T2.
ρ˙=i[H,ρ]f=12kf2(bfbfρ2bfρbf+ρbfbf)[i=12κi2(ai,lai,lρ2ai,lρai,l+ρai,lai,l)+i=23κi2(ai,rai,rρ2ai,rρai,r+ρai,rai,r)]i=13j=g0,gL,gRγij2(SijSijρ2SijρSij+ρSijSij),

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