Abstract

A scheme is proposed for the preparation of Greenberger–Horne–Zeilinger states for three atoms and for teleportation of an entangled atom pair by use of the triplet in cavity QED. The cavity is only virtually excited, and thus the scheme is insensitive to the cavity field states and the cavity decay. The preparation and teleportation can be achieved in a simple way.

© 2003 Optical Society of America

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References

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  1. D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed. (Kluwer, Dordrecht, The Netherlands, 1989).
  2. D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1153 (1990).
    [CrossRef]
  3. J. I. Cirac and P. Zoller, “Preparation of macroscopic superposition in many-atom systems,” Phys. Rev. A 50, R2799–R2802 (1994).
    [CrossRef]
  4. C. C. Gerry, “Preparation of multiatom entangled states through dispersive atom–cavity–field interactions,” Phys. Rev. A 53, 2857–2860 (1996).
    [CrossRef] [PubMed]
  5. C. C. Gerry, “Preparation of a four-atom Greenberger–Horne–Zeilinger state,” Phys. Rev. A 53, 4591–4593 (1996).
    [CrossRef] [PubMed]
  6. S. B. Zheng and G.-C. Guo, “Preparation of multiatom GHZ states,” J. Mod. Opt. 44, 963–966 (1997).
    [CrossRef]
  7. S. B. Zheng, “A simplified scheme for realizing Greenberger–Horne–Zeilinger states,” J. Opt. B 1, 534–535 (1999).
    [CrossRef]
  8. E. S. Guerra and J. C. Retamal, “Realization of atomic Greenberger–Horne–Zeilinger states via cavity quantum electrodynamics,” J. Mod. Opt. 46, 295–302 (1999).
  9. G.-P. Guo, C. F. Li, J. Li, and G.-C. Guo, “Scheme for the preparation of the multi-particle entanglement in cavity QED,” quant-ph/0105123.
  10. 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] [PubMed]
  11. A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
    [CrossRef]
  12. V. N. Gorbachev and A. I. Trubilko, “Quantum teleportation of EPR pair by three-particle entanglement,” quant-ph/9906110.
  13. B. S. Shi, Y. K. Jiang, and G.-C. Guo, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (2000).
    [CrossRef]
  14. 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] [PubMed]
  15. A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
    [CrossRef]
  16. S. B. Zheng, “One-step synthesis of multiatom Greenberger–Horne–Zeilinger states,” Phys. Rev. Lett. 87, 230404 (2001).
    [CrossRef]

2001 (1)

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

2000 (3)

B. S. Shi, Y. K. Jiang, and G.-C. Guo, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (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] [PubMed]

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] [PubMed]

1999 (3)

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

E. S. Guerra and J. C. Retamal, “Realization of atomic Greenberger–Horne–Zeilinger states via cavity quantum electrodynamics,” J. Mod. Opt. 46, 295–302 (1999).

A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
[CrossRef]

1998 (1)

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

1997 (1)

S. B. Zheng and G.-C. Guo, “Preparation of multiatom GHZ states,” J. Mod. Opt. 44, 963–966 (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] [PubMed]

C. C. Gerry, “Preparation of a four-atom Greenberger–Horne–Zeilinger state,” Phys. Rev. A 53, 4591–4593 (1996).
[CrossRef] [PubMed]

1994 (1)

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

1990 (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1153 (1990).
[CrossRef]

Bertet, P.

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] [PubMed]

Bourennane, M.

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

Brune, M.

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] [PubMed]

Cirac, J. I.

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

Gerry, C. C.

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

C. C. Gerry, “Preparation of a four-atom Greenberger–Horne–Zeilinger state,” Phys. Rev. A 53, 4591–4593 (1996).
[CrossRef] [PubMed]

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1153 (1990).
[CrossRef]

Guerra, E. S.

E. S. Guerra and J. C. Retamal, “Realization of atomic Greenberger–Horne–Zeilinger states via cavity quantum electrodynamics,” J. Mod. Opt. 46, 295–302 (1999).

Guo, G.-C.

B. S. Shi, Y. K. Jiang, and G.-C. Guo, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (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] [PubMed]

S. B. Zheng and G.-C. Guo, “Preparation of multiatom GHZ states,” J. Mod. Opt. 44, 963–966 (1997).
[CrossRef]

Haroche, S.

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] [PubMed]

Horne, M. A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1153 (1990).
[CrossRef]

Jiang, Y. K.

B. S. Shi, Y. K. Jiang, and G.-C. Guo, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (2000).
[CrossRef]

Karlsson, A.

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

Mølmer, K.

A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
[CrossRef]

Nogues, G.

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] [PubMed]

Osnaghi, S.

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] [PubMed]

Raimond, J. M.

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] [PubMed]

Rauschenbeutel, A.

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] [PubMed]

Retamal, J. C.

E. S. Guerra and J. C. Retamal, “Realization of atomic Greenberger–Horne–Zeilinger states via cavity quantum electrodynamics,” J. Mod. Opt. 46, 295–302 (1999).

Shi, B. S.

B. S. Shi, Y. K. Jiang, and G.-C. Guo, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (2000).
[CrossRef]

Shimony, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1153 (1990).
[CrossRef]

Sørensen, A.

A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
[CrossRef]

Zeilinger, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1153 (1990).
[CrossRef]

Zheng, S. B.

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

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

S. B. Zheng and G.-C. Guo, “Preparation of multiatom GHZ states,” J. Mod. Opt. 44, 963–966 (1997).
[CrossRef]

Zoller, P.

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

Am. J. Phys. (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1153 (1990).
[CrossRef]

J. Mod. Opt. (2)

S. B. Zheng and G.-C. Guo, “Preparation of multiatom GHZ states,” J. Mod. Opt. 44, 963–966 (1997).
[CrossRef]

E. S. Guerra and J. C. Retamal, “Realization of atomic Greenberger–Horne–Zeilinger states via cavity quantum electrodynamics,” J. Mod. Opt. 46, 295–302 (1999).

J. Opt. B (1)

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

Phys. Lett. A (1)

B. S. Shi, Y. K. Jiang, and G.-C. Guo, “Probabilistic teleportation of two-particle entangled state,” Phys. Lett. A 268, 161–164 (2000).
[CrossRef]

Phys. Rev. A (4)

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

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

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

C. C. Gerry, “Preparation of a four-atom Greenberger–Horne–Zeilinger state,” Phys. Rev. A 53, 4591–4593 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

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] [PubMed]

A. Sørensen and K. Mølmer, “Quantum computation with ions in thermal motion,” Phys. Rev. Lett. 82, 1971–1974 (1999).
[CrossRef]

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

Science (1)

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] [PubMed]

Other (3)

D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed. (Kluwer, Dordrecht, The Netherlands, 1989).

V. N. Gorbachev and A. I. Trubilko, “Quantum teleportation of EPR pair by three-particle entanglement,” quant-ph/9906110.

G.-P. Guo, C. F. Li, J. Li, and G.-C. Guo, “Scheme for the preparation of the multi-particle entanglement in cavity QED,” quant-ph/0105123.

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Equations (22)

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H=H0+Hi,
H0=ωa+a+ω0j=1msz,j,
Hi=g j=1m(a+Sj-+asj+),
λ=ejgkn|Hi|gjgkn+1gjgkn+1|Hi|gjeknδ+ejgkn|Hi|ejekn-1ejek-1|Hi|gjekn-δ=g2δ.
He=λ(n+1)j=1m|ej,je|-n j=1m|gj,jg|+i,j=1,ijmSj+Si-,
He=λj=1m|ej,je|+i,j=1,ijmsj+si-.
|ϕ=[exp(-i6λt)+3 exp(-i2λt)+2]|egeg+[exp(-i6λt)-3 exp(-i2λt)+2]|gege+[exp(-i6λt)-1](|egge+|eegg+|ggee+|geeg).
|ϕ=exp[-i(π/3)]2 (|egeg+i3|gege).
Rˆ(θ)|e4=cos θ|g4-sin θ|e4,
Rˆ(θ)|g4=sin θ|g4+cos θ|e4.
|e432 |g4-12|e4,
|g412 |g4+32 |e4.
|ϕ=exp[-i(π/3)]4 [(|ege123+3i|geg123)|g4+3(|ege123-i|geg123)|e4].
|ϕGHZ=12 (|ege-i|geg),
|ψ12=α|ge12+β|eg12,
|ψ=½[|Ψ+(α|ge45-β|eg45)+|Ψ-(α|ge45+β|eg45)+|Φ+(β|ge45-α|eg45)+|Φ-(β|ge45+α|eg45)],
|Ψ±=12 (|gee123±i|egg123),
|Φ±=12 (|ege123±i|geg123).
|Ψ±12 (|ge12±i|eg12)|g3exp(-iλt)2 {[cos(λt)±sin(λt)]|ge12-i[sin(λt)cos(λt)]|eg12}|g3,
|Φ±12 (|eg12±i|ge12)|e3exp(-iλt)2 {[cos(λt)±sin(λt)]|eg12-i[sin(λt)cos(λt)]|ge12}|e3.
|Ψ±|geg-i|egg,
|Φ±|ege-i|gee,

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