Abstract

We propose a feasible and efficient scheme to generate N-atom W-class states in spatially separated cavities without using any classical driving pulses. We adopt the model in which the couplings between different atoms are mediated only by virtual excitations of the cavity and fiber fields, so the scheme is insensitive to the cavity decay and fiber photon leakage. We carry out both theoretical investigation in a decoherence-free subspace and numerical calculation accounting for decoherence due to the atomic spontaneous emission as well as the decay of cavity and fiber modes. The theoretical and numerical results agree in the large atom-cavity detuning regime. Our scheme proves to be useful in scalable distributed quantum networks.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  26. 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]
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    [CrossRef]
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    [CrossRef]
  29. T. Findakly and B. Chen, “Single-mode integrated optical 1×N star coupler,” Appl. Phys. Lett. 40, 549–550 (1982).
    [CrossRef]
  30. H. Feng, E. H. Li, and K. Tada, “Analysis of X-intersecting waveguide switches with a large branching angles ranging from 2° to 12°,” Jpn. J. Appl. Phys. 36, 5136–5142 (1997).
    [CrossRef]
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  32. C. Dragone, C. H. Henry, I. P. Kaminow, and R. C. Kistler, “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
    [CrossRef]
  33. 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]
  34. A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
    [CrossRef]
  35. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
    [CrossRef]
  36. S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
    [CrossRef]
  37. J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67, 033806 (2003).
    [CrossRef]
  38. F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
    [CrossRef]

2012 (1)

L. T. Shen, H. Z. Wu, and Z. B. Yang, “Distributed phase-covariant cloning with atomic ensembles via quantum Zeno dynamics,” Eur. Phys. J. D 66, 123–127 (2012).
[CrossRef]

2010 (2)

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]

W. Cui, E. Chitambar, and H. K. Lo, “Optimal entanglement transformations among N-qubit W-class states,” Phys. Rev. A 82, 062314 (2010).
[CrossRef]

2009 (3)

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef]

X. W. Wang, G. J. Yang, Y. H. Su, and M. Xie, “Simple schemes for quantum information processing with W-type entanglement,” Quant. Info. Proc. 8, 431–442 (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)

H. Z. Wu, Z. B. Yang, W. J. Su, Z. R. Zhong, and J. M. Huang, “Quantum information splitting based on current cavity QED techniques,” Commun. Theor. Phys. 49, 1165–1168 (2008).
[CrossRef]

J. Song, Y. Xia, and H. S. Song, “Quantum nodes for W-state generation in noisy channels,” Phys. Rev. A 78, 024302 (2008).
[CrossRef]

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[CrossRef]

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 (3)

J. Song, Y. Xia, H. S. Song, J. L. Guo, and J. Nie, “Quantum computation and entangled-state generation through adiabatic evolution in two distant cavities,” Europhys. Lett. 80, 60001 (2007).
[CrossRef]

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]

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[CrossRef]

2006 (3)

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

S. B. Zheng, “Splitting quantum information via W states,” Phys. Rev. A 74, 054303 (2006).
[CrossRef]

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

2005 (2)

N. B. An, “Cavity-catalyzed deterministic generation of maximal entanglement between nonidentical atoms,” Phys. Lett. A 344, 77–83 (2005).
[CrossRef]

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

2004 (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).
[CrossRef]

2003 (3)

A. Sen(De), U. Sen, M. Wiésniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
[CrossRef]

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

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

2002 (1)

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

2001 (2)

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef]

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

2000 (2)

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

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

1999 (1)

D. Gottesmanand and I. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature 402, 390–393 (1999).
[CrossRef]

1998 (1)

1997 (2)

H. Feng, E. H. Li, and K. Tada, “Analysis of X-intersecting waveguide switches with a large branching angles ranging from 2° to 12°,” Jpn. J. Appl. Phys. 36, 5136–5142 (1997).
[CrossRef]

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

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, 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]

1992 (1)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (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. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1143 (1990).
[CrossRef]

1989 (1)

C. Dragone, C. H. Henry, I. P. Kaminow, and R. C. Kistler, “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[CrossRef]

1982 (1)

T. Findakly and B. Chen, “Single-mode integrated optical 1×N star coupler,” Appl. Phys. Lett. 40, 549–550 (1982).
[CrossRef]

1964 (1)

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

Agarwal, G. S.

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef]

Agrawal, P.

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

An, N. B.

N. B. An, “Cavity-catalyzed deterministic generation of maximal entanglement between nonidentical atoms,” Phys. Lett. A 344, 77–83 (2005).
[CrossRef]

Auffeves, A.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

Bastin, T.

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef]

Becher, C.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

Bell, J. S.

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

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, 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]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[CrossRef]

Bertet, P.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

Blatt, R.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

Bose, S.

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

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, 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. J.

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef]

Brune, M.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

Buck, J. R.

J. R. Buck and H. J. Kimble, “Optimal 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]

Carmichael, H. J.

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[CrossRef]

Chen, B.

T. Findakly and B. Chen, “Single-mode integrated optical 1×N star coupler,” Appl. Phys. Lett. 40, 549–550 (1982).
[CrossRef]

Chitambar, E.

W. Cui, E. Chitambar, and H. K. Lo, “Optimal entanglement transformations among N-qubit W-class states,” Phys. Rev. A 82, 062314 (2010).
[CrossRef]

Chuang, I.

D. Gottesmanand and I. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature 402, 390–393 (1999).
[CrossRef]

Cirac, J. I.

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

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, 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]

Cui, W.

W. Cui, E. Chitambar, and H. K. Lo, “Optimal entanglement transformations among N-qubit W-class states,” Phys. Rev. A 82, 062314 (2010).
[CrossRef]

Dimer, F.

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[CrossRef]

Dragone, C.

C. Dragone, C. H. Henry, I. P. Kaminow, and R. C. Kistler, “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[CrossRef]

Dür, W.

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

Ekert, A. K.

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

Eschner, J.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

Estienne, B.

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[CrossRef]

Feng, H.

H. Feng, E. H. Li, and K. Tada, “Analysis of X-intersecting waveguide switches with a large branching angles ranging from 2° to 12°,” Jpn. J. Appl. Phys. 36, 5136–5142 (1997).
[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]

Findakly, T.

T. Findakly and B. Chen, “Single-mode integrated optical 1×N star coupler,” Appl. Phys. Lett. 40, 549–550 (1982).
[CrossRef]

Goh, K. W.

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

Gordon, K. J.

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]

Gottesmanand, D.

D. Gottesmanand and I. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature 402, 390–393 (1999).
[CrossRef]

Greenberger, D. M.

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

Guo, G. C.

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

Guo, J. L.

J. Song, Y. Xia, H. S. Song, J. L. Guo, and J. Nie, “Quantum computation and entangled-state generation through adiabatic evolution in two distant cavities,” Europhys. Lett. 80, 60001 (2007).
[CrossRef]

Hao, X. Y.

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]

Haroche, S.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

Henry, C. H.

C. Dragone, C. H. Henry, I. P. Kaminow, and R. C. Kistler, “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[CrossRef]

Horne, M.

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

Huang, J. M.

H. Z. Wu, Z. B. Yang, W. J. Su, Z. R. Zhong, and J. M. Huang, “Quantum information splitting based on current cavity QED techniques,” Commun. Theor. Phys. 49, 1165–1168 (2008).
[CrossRef]

Joo, J.

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, 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]

Kaminow, I. P.

C. Dragone, C. H. Henry, I. P. Kaminow, and R. C. Kistler, “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[CrossRef]

Kaszlikowski, D.

A. Sen(De), U. Sen, M. Wiésniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
[CrossRef]

Kim, J.

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Kimble, H. J.

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[CrossRef]

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

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

Kippenberg, T. J.

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

Kistler, R. C.

C. Dragone, C. H. Henry, I. P. Kaminow, and R. C. Kistler, “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[CrossRef]

Kreuter, A.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

Lamata, L.

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef]

Leibfried, D.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

Li, E. H.

H. Feng, E. H. Li, and K. Tada, “Analysis of X-intersecting waveguide switches with a large branching angles ranging from 2° to 12°,” Jpn. J. Appl. Phys. 36, 5136–5142 (1997).
[CrossRef]

Li, F. L.

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]

Lo, H. K.

W. Cui, E. Chitambar, and H. K. Lo, “Optimal entanglement transformations among N-qubit W-class states,” Phys. Rev. A 82, 062314 (2010).
[CrossRef]

Lü, X. Y.

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]

Maioli, P.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

Mancini, S.

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

Mundt, A. B.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

Nie, J.

J. Song, Y. Xia, H. S. Song, J. L. Guo, and J. Nie, “Quantum computation and entangled-state generation through adiabatic evolution in two distant cavities,” Europhys. Lett. 80, 60001 (2007).
[CrossRef]

Nori, F.

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]

Oh, S.

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Osnaghi, S.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

Park, Y. J.

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Parkins, A. S.

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[CrossRef]

Pati, A.

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

Pellizzari, T.

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

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, 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]

Raimond, J. M.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

Raussendorf, R.

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef]

Schmidt-Kaler, F.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

Sen, U.

A. Sen(De), U. Sen, M. Wiésniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
[CrossRef]

Sen(De), A.

A. Sen(De), U. Sen, M. Wiésniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
[CrossRef]

Serafini, A.

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

Shen, L. T.

L. T. Shen, H. Z. Wu, and Z. B. Yang, “Distributed phase-covariant cloning with atomic ensembles via quantum Zeno dynamics,” Eur. Phys. J. D 66, 123–127 (2012).
[CrossRef]

Shimony, A.

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

Si, L. G.

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]

Solano, E.

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef]

Song, H. S.

J. Song, Y. Xia, and H. S. Song, “Quantum nodes for W-state generation in noisy channels,” Phys. Rev. A 78, 024302 (2008).
[CrossRef]

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]

J. Song, Y. Xia, H. S. Song, J. L. Guo, and J. Nie, “Quantum computation and entangled-state generation through adiabatic evolution in two distant cavities,” Europhys. Lett. 80, 60001 (2007).
[CrossRef]

Song, J.

J. Song, Y. Xia, and H. S. Song, “Quantum nodes for W-state generation in noisy channels,” Phys. Rev. A 78, 024302 (2008).
[CrossRef]

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]

J. Song, Y. Xia, H. S. Song, J. L. Guo, and J. Nie, “Quantum computation and entangled-state generation through adiabatic evolution in two distant cavities,” Europhys. Lett. 80, 60001 (2007).
[CrossRef]

Spillane, S. M.

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

Su, W. J.

H. Z. Wu, Z. B. Yang, W. J. Su, Z. R. Zhong, and J. M. Huang, “Quantum information splitting based on current cavity QED techniques,” Commun. Theor. Phys. 49, 1165–1168 (2008).
[CrossRef]

Su, Y. H.

X. W. Wang, G. J. Yang, Y. H. Su, and M. Xie, “Simple schemes for quantum information processing with W-type entanglement,” Quant. Info. Proc. 8, 431–442 (2009).
[CrossRef]

Tada, K.

H. Feng, E. H. Li, and K. Tada, “Analysis of X-intersecting waveguide switches with a large branching angles ranging from 2° to 12°,” Jpn. J. Appl. Phys. 36, 5136–5142 (1997).
[CrossRef]

Thiel, C.

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef]

Townsend, P. D.

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]

Vahala, K. J.

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

Vidal, G.

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

von Zanthier, J.

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef]

Wang, X. W.

X. W. Wang, G. J. Yang, Y. H. Su, and M. Xie, “Simple schemes for quantum information processing with W-type entanglement,” Quant. Info. Proc. 8, 431–442 (2009).
[CrossRef]

Wiesner, S. J.

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[CrossRef]

Wiésniak, M.

A. Sen(De), U. Sen, M. Wiésniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
[CrossRef]

Wilcut, E.

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

Wootters, W.

C. H. Bennett, G. Brassard, C. Crépeau, 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]

Wu, H. Z.

L. T. Shen, H. Z. Wu, and Z. B. Yang, “Distributed phase-covariant cloning with atomic ensembles via quantum Zeno dynamics,” Eur. Phys. J. D 66, 123–127 (2012).
[CrossRef]

H. Z. Wu, Z. B. Yang, W. J. Su, Z. R. Zhong, and J. M. Huang, “Quantum information splitting based on current cavity QED techniques,” Commun. Theor. Phys. 49, 1165–1168 (2008).
[CrossRef]

Xia, Y.

J. Song, Y. Xia, and H. S. Song, “Quantum nodes for W-state generation in noisy channels,” Phys. Rev. A 78, 024302 (2008).
[CrossRef]

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]

J. Song, Y. Xia, H. S. Song, J. L. Guo, and J. Nie, “Quantum computation and entangled-state generation through adiabatic evolution in two distant cavities,” Europhys. Lett. 80, 60001 (2007).
[CrossRef]

Xie, M.

X. W. Wang, G. J. Yang, Y. H. Su, and M. Xie, “Simple schemes for quantum information processing with W-type entanglement,” Quant. Info. Proc. 8, 431–442 (2009).
[CrossRef]

Yang, C. P.

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]

Yang, G. J.

X. W. Wang, G. J. Yang, Y. H. Su, and M. Xie, “Simple schemes for quantum information processing with W-type entanglement,” Quant. Info. Proc. 8, 431–442 (2009).
[CrossRef]

Yang, X.

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]

Yang, Z. B.

L. T. Shen, H. Z. Wu, and Z. B. Yang, “Distributed phase-covariant cloning with atomic ensembles via quantum Zeno dynamics,” Eur. Phys. J. D 66, 123–127 (2012).
[CrossRef]

H. Z. Wu, Z. B. Yang, W. J. Su, Z. R. Zhong, and J. M. Huang, “Quantum information splitting based on current cavity QED techniques,” Commun. Theor. Phys. 49, 1165–1168 (2008).
[CrossRef]

Yin, Z. Q.

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]

Yuan, L. B.

Zeilinger, A.

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

Zheng, S. B.

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]

S. B. Zheng, “Splitting quantum information via W states,” Phys. Rev. A 74, 054303 (2006).
[CrossRef]

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

Zhong, Z. R.

H. Z. Wu, Z. B. Yang, W. J. Su, Z. R. Zhong, and J. M. Huang, “Quantum information splitting based on current cavity QED techniques,” Commun. Theor. Phys. 49, 1165–1168 (2008).
[CrossRef]

Zhou, L. M.

Zukowski, M.

A. Sen(De), U. Sen, M. Wiésniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
[CrossRef]

Am. J. Phys. (1)

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

Appl. Opt. (1)

Appl. Phys. Lett. (2)

T. Findakly and B. Chen, “Single-mode integrated optical 1×N star coupler,” Appl. Phys. Lett. 40, 549–550 (1982).
[CrossRef]

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]

Commun. Theor. Phys. (1)

H. Z. Wu, Z. B. Yang, W. J. Su, Z. R. Zhong, and J. M. Huang, “Quantum information splitting based on current cavity QED techniques,” Commun. Theor. Phys. 49, 1165–1168 (2008).
[CrossRef]

Eur. Phys. J. D (1)

L. T. Shen, H. Z. Wu, and Z. B. Yang, “Distributed phase-covariant cloning with atomic ensembles via quantum Zeno dynamics,” Eur. Phys. J. D 66, 123–127 (2012).
[CrossRef]

Europhys. Lett. (1)

J. Song, Y. Xia, H. S. Song, J. L. Guo, and J. Nie, “Quantum computation and entangled-state generation through adiabatic evolution in two distant cavities,” Europhys. Lett. 80, 60001 (2007).
[CrossRef]

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).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. Dragone, C. H. Henry, I. P. Kaminow, and R. C. Kistler, “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Feng, E. H. Li, and K. Tada, “Analysis of X-intersecting waveguide switches with a large branching angles ranging from 2° to 12°,” Jpn. J. Appl. Phys. 36, 5136–5142 (1997).
[CrossRef]

Nature (2)

D. Gottesmanand and I. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature 402, 390–393 (1999).
[CrossRef]

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[CrossRef]

New J. Phys. (1)

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Phys. Lett. A (1)

N. B. An, “Cavity-catalyzed deterministic generation of maximal entanglement between nonidentical atoms,” Phys. Lett. A 344, 77–83 (2005).
[CrossRef]

Phys. Rev. A (12)

W. Cui, E. Chitambar, and H. K. Lo, “Optimal entanglement transformations among N-qubit W-class states,” Phys. Rev. A 82, 062314 (2010).
[CrossRef]

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

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

A. Sen(De), U. Sen, M. Wiésniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
[CrossRef]

J. Song, Y. Xia, and H. S. Song, “Quantum nodes for W-state generation in noisy channels,” Phys. Rev. A 78, 024302 (2008).
[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]

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]

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]

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

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

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[CrossRef]

S. B. Zheng, “Splitting quantum information via W states,” Phys. Rev. A 74, 054303 (2006).
[CrossRef]

Phys. Rev. Lett. (10)

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef]

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef]

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef]

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

C. H. Bennett, G. Brassard, C. Crépeau, 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]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[CrossRef]

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

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef]

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

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

Physica (Amsterdam) (1)

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

Quant. Info. Proc. (1)

X. W. Wang, G. J. Yang, Y. H. Su, and M. Xie, “Simple schemes for quantum information processing with W-type entanglement,” Quant. Info. Proc. 8, 431–442 (2009).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Experimental setup. The black dots denote the atoms, which are trapped in N distant cavities, and these cavities are connected by a 1×N single-mode integrated optical star coupler. (b) Level configuration for each atom.

Fig. 2.
Fig. 2.

Fidelity FN versus dimensionless time (a) τ=NηNt and (b) ft, with Δ/f=Δ/ν=10 for N=3, 4, 5, and 6.

Fig. 3.
Fig. 3.

Fidelity F4 at t=π/4η4 versus Δ/f when ν/f=10.

Fig. 4.
Fig. 4.

Fidelity F4 at t=π/4η4 versus Δ/f and Δ/ν when (a) Γ/f=0.01 and γ=κ=0; (b) Γ=κ=0 and γ/f=0.3, and (c) Γ=γ=0 and κ/f=0.3.

Fig. 5.
Fig. 5.

Density plots of the fidelity F4 at t=π/4η4 versus (a) Γ/f and γ/f and (b) Γ/f and κ/f.

Equations (23)

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

H=H1+H2,
H1=l=1Nν(alb+bal),
H2=l=1Nf(alSleiΔt+Sl+aleiΔt),
cα=l=1Ntα,lal+tα,N+1b,
T=(N1N1N(N1)1N(N1)1N(N1)1N(N1)1N(N1)00N2N11(N1)(N2)1(N1)(N2)1(N1)(N2)1(N1)(N2)000N3N21(N2)(N3)1(N2)(N3)1(N2)(N3)00002313×213×2000001212×1012N12N12N12N12N12N1212N12N12N12N12N12N12N)
al=α=1N+1χl,αcα,
b=α=1N+1χN+1,αcα,
X=T1=TT.
H1=Nν(cNcNcN+1cN+1)
H2=l=1Nα=1N+1fχl,α(Sl+cαeiΔt+cαSleiΔt).
int=l=1Nα=1N+1fχl,α(Sl+cαeiΔαt+cαSleiΔαt),
Δα={Δforα=1,2,,N1Δ+Nνforα=NΔNνforα=N+1.
eff=l,m=1NξlmSl+Sm,
ξlm=f2α=1N+1χl,αχm,αΔα.
ξlm={f2N(N1Δ+ΔΔ2Nν2)=ξNforl=mf2N(1ΔΔΔ2Nν2)=ηNforlm.
|ΦN(t)=n=1NCn(N)(t)|ϕn,
iCn(N)(t)t=ξNCn(N)(t)ηNl=1;lnNCl(N)(t)
C1(N)(t)=1Nei(ξN+ηN)t(eiNηNt+N1),
C2(N)(t)=C3(N)(t)==CN(N)(t)=1Nei(ξN+ηN)t(eiNηNt1).
|ΨN=1N[(N2)|ϕ12n=2N|ϕn]
t=(2k+1)πNηN.
|Ψ4=12(|e1g2g3g4|g1e2g3g4|g1g2e3g4|g1g2g3e4).
ρ˙=i[H,ρ]l=1NΓl2(Sl+Slρ2SlρSl++ρSl+Sl)l+1Nγl2(alalρ2alρal+ρalal)κ2(bbρ2bρb+ρbb),

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