Abstract

We propose a scheme to achieve the entanglement of N photon modes (frequency modes) with perfectly efficient ultraslow multiwave mixing in a cold atomic medium. In addition, the method provides an efficient approach to realizing frequency tunability.

© 2004 Optical Society of America

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References

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  1. M. G. Payne and L. Deng, Phys. Rev. Lett. 91, 123602 (2003).
    [CrossRef]
  2. A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
    [CrossRef]
  3. E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
    [CrossRef] [PubMed]
  4. P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
    [CrossRef] [PubMed]
  5. M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
    [CrossRef] [PubMed]
  6. C. P. Sun, Y. Li, and X. F. Liu, Phys. Rev. Lett. 91, 147903 (2003).
    [CrossRef]
  7. M. Nielsen and I. Chuang, Quantum Computation and Quantum Communication (Cambridge U. Press, Cambridge, England, 2000).
  8. W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
    [CrossRef]
  9. S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
    [CrossRef]
  10. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5099 (2000).

2003

M. G. Payne and L. Deng, Phys. Rev. Lett. 91, 123602 (2003).
[CrossRef]

C. P. Sun, Y. Li, and X. F. Liu, Phys. Rev. Lett. 91, 147903 (2003).
[CrossRef]

2001

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef] [PubMed]

2000

M. Nielsen and I. Chuang, Quantum Computation and Quantum Communication (Cambridge U. Press, Cambridge, England, 2000).

W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
[CrossRef]

M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5099 (2000).

1999

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

1995

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Bertet, P.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

Brune, M.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

Chuang, I.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Communication (Cambridge U. Press, Cambridge, England, 2000).

Cirac, J. I.

W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Deng, L.

M. G. Payne and L. Deng, Phys. Rev. Lett. 91, 123602 (2003).
[CrossRef]

Dür, W.

W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5099 (2000).

Haroche, S.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

Harris, S. E.

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

Hau, L. V.

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

Imamoglu, A.

M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef] [PubMed]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef] [PubMed]

Li, Y.

C. P. Sun, Y. Li, and X. F. Liu, Phys. Rev. Lett. 91, 147903 (2003).
[CrossRef]

Liu, X. F.

C. P. Sun, Y. Li, and X. F. Liu, Phys. Rev. Lett. 91, 147903 (2003).
[CrossRef]

Lukin, M. D.

M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5099 (2000).

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef] [PubMed]

Nielsen, M.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Communication (Cambridge U. Press, Cambridge, England, 2000).

Nogues, G.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

Osnaghi, S.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

Payne, M. G.

M. G. Payne and L. Deng, Phys. Rev. Lett. 91, 123602 (2003).
[CrossRef]

Raimond, J. M.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

Rauschenbeutel, A.

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

Sun, C. P.

C. P. Sun, Y. Li, and X. F. Liu, Phys. Rev. Lett. 91, 147903 (2003).
[CrossRef]

Vidal, G.

W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Zeilinger, A.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Nature

E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001).
[CrossRef] [PubMed]

Phys. Rev. A

A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 64, 050301 (2001).
[CrossRef]

W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Phys. Rev. Lett.

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5099 (2000).

M. G. Payne and L. Deng, Phys. Rev. Lett. 91, 123602 (2003).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

C. P. Sun, Y. Li, and X. F. Liu, Phys. Rev. Lett. 91, 147903 (2003).
[CrossRef]

Other

M. Nielsen and I. Chuang, Quantum Computation and Quantum Communication (Cambridge U. Press, Cambridge, England, 2000).

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Figures (1)

Fig. 1
Fig. 1

Three-level lifetime-broadened atomic system coupled with a quantized probe field Eˆp1ωp1 and a strong classically treated cw N-mode control field Ωc1,ωc1;Ωc2,ωc2;;ΩcN,ωcN. The probe field frequency ωp1 and the control field frequency ωc1 are such that the exact two-photon resonance between atomic levels |1 and |3 is achieved. The complex detunings are defined as dpj=δpj+iγ (j=1,2,,N), where δpj and γ2=2γ are the detunings from level |2 and the decay rate of level |2, respectively.

Equations (14)

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Eˆpj+z+1cEˆpj+t=iκ12D12Sˆpj, j=1,2,,N,
Sˆpj=-D12dpjEˆpj+-ΩcjdpjRˆ3,
Rˆ3t=-iD12j=1NΩcjdpjEˆpj+-ij=1NΩcj2dpjRˆ3.
Zˆpj+z-iωcZˆpj+=iκ12ωd-D+dΩcj2/dpjZˆpj++dkjΩcjΩck/dpkZˆpk+D-ωddpj,
Zˆ=expiηGZˆ0,
j=1Nd˜ξdj2+djD˜-ω˜d˜=1.
Eˆpj+z,t=k=1Naˆpkn=1Ncjkn expizσnPt-zVgn,
1Vgn=1c+κ12Ωc2Re1j=1N1+djξn0/D˜-2,
|Ψ=k,n=1Nc1kn expizσnPt-zVgnaˆpk|vac,
Eˆpj+z,t=CPt-zVg1k=13aˆpkMjkz,
|Ψ=CPt-zVg1[M11z|1ωp1|0ωp2|0ωp3+M12z|0ωp1|1ωp2|0ωp3+M13z|0ωp1|0ωp2|1ωp3].
|Ψ=3CPt-zVg1[|1ωp1|0ωp2|0ωp3+exp-iθ|0ωp1|1ωp2|0ωp3+expiθ|0ωp1|0ωp2|1ωp3].
|Ψ=3CPt-zVg1[|1ωp1|0ωp2|0ωp3+|0ωp1|1˜ωp2|0ωp3+|0ωp1|0ωp2|1˜ωp3],
|Ψ=s|0ωp1(|1ωp2|0ωp3±i|0ωp2|1ωp3)Pt-zVg1,

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