Abstract

We conduct theoretical studies on the effects of various parameters on generation of multipartite continuous-variable entanglement via atomic spin wave induced by the strong coupling and probe fields in the Λ-type electromagnetically induced transparency configuration in a realistic atomic ensemble by using the Heisenberg-Langevin formalism. It is shown that the increase of the atomic density and/or Rabi frequencies of the scattering fields, as well as the decrease of the coherence decay rate of the lower doublet would strengthen the degree of multipartite entanglement. This provides a clear evidence that the creation of multicolor multipartite entangled narrow-band fields to any desired number with a long correlation time can be achieved conveniently by using atomic spin wave in an atomic ensemble with large optical depth, which may find interesting applications in quantum information processing and quantum networks.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  27. L. M. Duan, G. Giedke, J. I. Cirac, P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84(12), 2722–2725 (2000).
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  28. C. F. McCormick, V. Boyer, E. Arimondo, P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
    [CrossRef] [PubMed]
  29. C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
    [CrossRef]
  30. R. Zhang, S. R. Garner, L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103(23), 233602 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  32. P. van Loock, S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).
  33. P. van Loock, A. Furusawa, “Detecting genuine multipartite continuous- variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
    [CrossRef]
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    [CrossRef]

2013 (1)

X. H. Yang, Y. Y. Zhou, M. Xiao, “Entangler via electromagnetically induced transparency with an atomic ensemble,” Sci. Rep. 3, 3479–3483 (2013).
[PubMed]

2012 (2)

X. H. Yang, J. T. Sheng, U. Khadka, M. Xiao, “Generation of correlated and anticorrelated multiple fields via atomic spin coherence,” Phys. Rev. A 85(1), 013824 (2012).
[CrossRef]

X. H. Yang, Y. Y. Zhou, M. Xiao, “Generation of multipartite continuous- variable entanglement via atomic spin wave,” Phys. Rev. A 85(5), 052307 (2012).
[CrossRef]

2010 (1)

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

2009 (3)

H. Wu, M. Xiao, “Bright correlated twin beams from an atomic ensemble in the optical cavity,” Phys. Rev. A 80(6), 063415 (2009).
[CrossRef]

R. Zhang, S. R. Garner, L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103(23), 233602 (2009).
[CrossRef] [PubMed]

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

2008 (3)

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[CrossRef]

V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (3)

M. K. Olsen, A. S. Bradley, “Asymmetric polychromatic tripartite entanglement from interlinked χ(2) parametric interactions,” Phys. Rev. A 74(6), 063809 (2006).
[CrossRef]

K. I. Harada, T. Kanbashi, M. Mitsunaga, K. Motomura, “Competition between electromagnetically induced transparency and stimulated Raman scattering,” Phys. Rev. A 73(1), 013807 (2006).
[CrossRef]

G. S. Agarwal, T. N. Dey, D. J. Gauthier, “Competition between electromagnetically induced transparency and Raman processes,” Phys. Rev. A 74(4), 043805 (2006).
[CrossRef]

2005 (2)

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, S. E. Harris, “Generation of Paired Photons with Controllable Waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[CrossRef] [PubMed]

M. Fleischhauer, A. Imamoglu, J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

2004 (1)

V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, F. Narducci, “Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor,” Phys. Rev. A 70(5), 053811 (2004).
[CrossRef]

2003 (5)

P. van Loock, A. Furusawa, “Detecting genuine multipartite continuous- variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
[CrossRef]

F. Le Kien, A. Patnaik, K. Hakuta, “Multiorder coherent Raman scattering of a quantum probe field,” Phys. Rev. A 68(6), 063803 (2003).
[CrossRef]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

2001 (2)

L. M. Duan, M. D. Lukin, J. I. Cirac, P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[CrossRef] [PubMed]

2000 (3)

P. van Loock, S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).

L. M. Duan, G. Giedke, J. I. Cirac, P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84(12), 2722–2725 (2000).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, S. E. Harris, “Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Lambda System,” Phys. Rev. Lett. 84(23), 5308–5311 (2000).
[CrossRef] [PubMed]

1997 (1)

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

1996 (1)

E. Arimondo, “V Coherent Population Trapping in Laser Spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[CrossRef]

1995 (2)

M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche, “Measurement of Dispersive Properties of Electromagnetically Induced Transparency in Rubidium Atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[CrossRef] [PubMed]

M. Fleischhauer, T. Richter, “Pulse matching and correlation of phase fluctuations in Λ systems,” Phys. Rev. A 51(3), 2430–2442 (1995).
[CrossRef] [PubMed]

Agarwal, G. S.

G. S. Agarwal, T. N. Dey, D. J. Gauthier, “Competition between electromagnetically induced transparency and Raman processes,” Phys. Rev. A 74(4), 043805 (2006).
[CrossRef]

André, A.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

Aoki, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

Arimondo, E.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

C. F. McCormick, V. Boyer, E. Arimondo, P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[CrossRef] [PubMed]

E. Arimondo, “V Coherent Population Trapping in Laser Spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[CrossRef]

Balic, V.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, S. E. Harris, “Generation of Paired Photons with Controllable Waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[CrossRef] [PubMed]

Bennink, R. S.

V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, F. Narducci, “Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor,” Phys. Rev. A 70(5), 053811 (2004).
[CrossRef]

Bloch, I.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

Boca, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Boozer, A. D.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Bowen, W. P.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, F. Narducci, “Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor,” Phys. Rev. A 70(5), 053811 (2004).
[CrossRef]

Boyer, V.

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[CrossRef]

V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

C. F. McCormick, V. Boyer, E. Arimondo, P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[CrossRef] [PubMed]

Bradley, A. S.

M. K. Olsen, A. S. Bradley, “Asymmetric polychromatic tripartite entanglement from interlinked χ(2) parametric interactions,” Phys. Rev. A 74(6), 063809 (2006).
[CrossRef]

Braje, D. A.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, S. E. Harris, “Generation of Paired Photons with Controllable Waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[CrossRef] [PubMed]

Braunstein, S. L.

P. van Loock, S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).

Chou, C. W.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Cirac, J. I.

L. M. Duan, M. D. Lukin, J. I. Cirac, P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

L. M. Duan, G. Giedke, J. I. Cirac, P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84(12), 2722–2725 (2000).
[CrossRef] [PubMed]

Coudreau, T.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

Davidson, N.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

Dey, T. N.

G. S. Agarwal, T. N. Dey, D. J. Gauthier, “Competition between electromagnetically induced transparency and Raman processes,” Phys. Rev. A 74(4), 043805 (2006).
[CrossRef]

Duan, L. M.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

L. M. Duan, M. D. Lukin, J. I. Cirac, P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

L. M. Duan, G. Giedke, J. I. Cirac, P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84(12), 2722–2725 (2000).
[CrossRef] [PubMed]

Dubessy, R.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

Eisaman, M. D.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

M. Fleischhauer, T. Richter, “Pulse matching and correlation of phase fluctuations in Λ systems,” Phys. Rev. A 51(3), 2430–2442 (1995).
[CrossRef] [PubMed]

Furusawa, A.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

P. van Loock, A. Furusawa, “Detecting genuine multipartite continuous- variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
[CrossRef]

Garner, S. R.

R. Zhang, S. R. Garner, L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103(23), 233602 (2009).
[CrossRef] [PubMed]

Gauthier, D. J.

G. S. Agarwal, T. N. Dey, D. J. Gauthier, “Competition between electromagnetically induced transparency and Raman processes,” Phys. Rev. A 74(4), 043805 (2006).
[CrossRef]

Gea-Banacloche, J.

M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche, “Measurement of Dispersive Properties of Electromagnetically Induced Transparency in Rubidium Atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[CrossRef] [PubMed]

Giedke, G.

L. M. Duan, G. Giedke, J. I. Cirac, P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84(12), 2722–2725 (2000).
[CrossRef] [PubMed]

Glorieux, Q.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

Guibal, S.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

Guidoni, L.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

Hakuta, K.

F. Le Kien, A. Patnaik, K. Hakuta, “Multiorder coherent Raman scattering of a quantum probe field,” Phys. Rev. A 68(6), 063803 (2003).
[CrossRef]

Harada, K. I.

K. I. Harada, T. Kanbashi, M. Mitsunaga, K. Motomura, “Competition between electromagnetically induced transparency and stimulated Raman scattering,” Phys. Rev. A 73(1), 013807 (2006).
[CrossRef]

Harris, S. E.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, S. E. Harris, “Generation of Paired Photons with Controllable Waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, S. E. Harris, “Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Lambda System,” Phys. Rev. Lett. 84(23), 5308–5311 (2000).
[CrossRef] [PubMed]

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Hau, L. V.

R. Zhang, S. R. Garner, L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103(23), 233602 (2009).
[CrossRef] [PubMed]

Hiraoka, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Jin, S.

M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche, “Measurement of Dispersive Properties of Electromagnetically Induced Transparency in Rubidium Atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[CrossRef] [PubMed]

Kanbashi, T.

K. I. Harada, T. Kanbashi, M. Mitsunaga, K. Motomura, “Competition between electromagnetically induced transparency and stimulated Raman scattering,” Phys. Rev. A 73(1), 013807 (2006).
[CrossRef]

Khadka, U.

X. H. Yang, J. T. Sheng, U. Khadka, M. Xiao, “Generation of correlated and anticorrelated multiple fields via atomic spin coherence,” Phys. Rev. A 85(1), 013824 (2012).
[CrossRef]

Kimble, H. J.

H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
[CrossRef] [PubMed]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Knill, E.

E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[CrossRef] [PubMed]

Kolchin, P.

P. Kolchin, “Electromagnetically-induced-transparency-based paired photon generation,” Phys. Rev. A 75(3), 033814 (2007).
[CrossRef]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, S. E. Harris, “Generation of Paired Photons with Controllable Waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[CrossRef] [PubMed]

Kuhr, S.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

Kuzmich, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Laflamme, R.

E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[CrossRef] [PubMed]

Le Kien, F.

F. Le Kien, A. Patnaik, K. Hakuta, “Multiorder coherent Raman scattering of a quantum probe field,” Phys. Rev. A 68(6), 063803 (2003).
[CrossRef]

Lett, P. D.

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[CrossRef]

V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

C. F. McCormick, V. Boyer, E. Arimondo, P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[CrossRef] [PubMed]

Li, Y.

M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche, “Measurement of Dispersive Properties of Electromagnetically Induced Transparency in Rubidium Atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[CrossRef] [PubMed]

Likforman, J.-P.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

Lukin, M. D.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

L. M. Duan, M. D. Lukin, J. I. Cirac, P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

Manuszak, D.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, S. E. Harris, “Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Lambda System,” Phys. Rev. Lett. 84(23), 5308–5311 (2000).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Marino, A. M.

V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[CrossRef]

V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, F. Narducci, “Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor,” Phys. Rev. A 70(5), 053811 (2004).
[CrossRef]

McCormick, C. F.

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[CrossRef]

C. F. McCormick, V. Boyer, E. Arimondo, P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[CrossRef] [PubMed]

Merriam, A. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, S. E. Harris, “Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Lambda System,” Phys. Rev. Lett. 84(23), 5308–5311 (2000).
[CrossRef] [PubMed]

Milburn, G. J.

E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[CrossRef] [PubMed]

Mitsunaga, M.

K. I. Harada, T. Kanbashi, M. Mitsunaga, K. Motomura, “Competition between electromagnetically induced transparency and stimulated Raman scattering,” Phys. Rev. A 73(1), 013807 (2006).
[CrossRef]

Motomura, K.

K. I. Harada, T. Kanbashi, M. Mitsunaga, K. Motomura, “Competition between electromagnetically induced transparency and stimulated Raman scattering,” Phys. Rev. A 73(1), 013807 (2006).
[CrossRef]

Narducci, F.

V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, F. Narducci, “Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor,” Phys. Rev. A 70(5), 053811 (2004).
[CrossRef]

Olsen, M. K.

M. K. Olsen, A. S. Bradley, “Asymmetric polychromatic tripartite entanglement from interlinked χ(2) parametric interactions,” Phys. Rev. A 74(6), 063809 (2006).
[CrossRef]

Patnaik, A.

F. Le Kien, A. Patnaik, K. Hakuta, “Multiorder coherent Raman scattering of a quantum probe field,” Phys. Rev. A 68(6), 063803 (2003).
[CrossRef]

Phillips, D. F.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

Pooser, R. C.

V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Pugatch, R.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

Richter, T.

M. Fleischhauer, T. Richter, “Pulse matching and correlation of phase fluctuations in Λ systems,” Phys. Rev. A 51(3), 2430–2442 (1995).
[CrossRef] [PubMed]

Schnorrberger, U.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

Sharpe, S. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, S. E. Harris, “Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Lambda System,” Phys. Rev. Lett. 84(23), 5308–5311 (2000).
[CrossRef] [PubMed]

Sheng, J. T.

X. H. Yang, J. T. Sheng, U. Khadka, M. Xiao, “Generation of correlated and anticorrelated multiple fields via atomic spin coherence,” Phys. Rev. A 85(1), 013824 (2012).
[CrossRef]

Shverdin, M.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, S. E. Harris, “Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Lambda System,” Phys. Rev. Lett. 84(23), 5308–5311 (2000).
[CrossRef] [PubMed]

Stroud, C. R.

V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, F. Narducci, “Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor,” Phys. Rev. A 70(5), 053811 (2004).
[CrossRef]

Takei, N.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

Thompson, J. D.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

Trotzky, S.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

van der Wal, C. H.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

van Loock, P.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

P. van Loock, A. Furusawa, “Detecting genuine multipartite continuous- variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
[CrossRef]

P. van Loock, S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).

Wakui, K.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

Walsworth, R. L.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

Wong, V.

V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, F. Narducci, “Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor,” Phys. Rev. A 70(5), 053811 (2004).
[CrossRef]

Wu, H.

H. Wu, M. Xiao, “Bright correlated twin beams from an atomic ensemble in the optical cavity,” Phys. Rev. A 80(6), 063415 (2009).
[CrossRef]

Xiao, M.

X. H. Yang, Y. Y. Zhou, M. Xiao, “Entangler via electromagnetically induced transparency with an atomic ensemble,” Sci. Rep. 3, 3479–3483 (2013).
[PubMed]

X. H. Yang, Y. Y. Zhou, M. Xiao, “Generation of multipartite continuous- variable entanglement via atomic spin wave,” Phys. Rev. A 85(5), 052307 (2012).
[CrossRef]

X. H. Yang, J. T. Sheng, U. Khadka, M. Xiao, “Generation of correlated and anticorrelated multiple fields via atomic spin coherence,” Phys. Rev. A 85(1), 013824 (2012).
[CrossRef]

H. Wu, M. Xiao, “Bright correlated twin beams from an atomic ensemble in the optical cavity,” Phys. Rev. A 80(6), 063415 (2009).
[CrossRef]

M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche, “Measurement of Dispersive Properties of Electromagnetically Induced Transparency in Rubidium Atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[CrossRef] [PubMed]

Yang, X. H.

X. H. Yang, Y. Y. Zhou, M. Xiao, “Entangler via electromagnetically induced transparency with an atomic ensemble,” Sci. Rep. 3, 3479–3483 (2013).
[PubMed]

X. H. Yang, J. T. Sheng, U. Khadka, M. Xiao, “Generation of correlated and anticorrelated multiple fields via atomic spin coherence,” Phys. Rev. A 85(1), 013824 (2012).
[CrossRef]

X. H. Yang, Y. Y. Zhou, M. Xiao, “Generation of multipartite continuous- variable entanglement via atomic spin wave,” Phys. Rev. A 85(5), 052307 (2012).
[CrossRef]

Yin, G. Y.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, S. E. Harris, “Generation of Paired Photons with Controllable Waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, S. E. Harris, “Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Lambda System,” Phys. Rev. Lett. 84(23), 5308–5311 (2000).
[CrossRef] [PubMed]

Yonezawa, H.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

Zhang, R.

R. Zhang, S. R. Garner, L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103(23), 233602 (2009).
[CrossRef] [PubMed]

Zhou, Y. Y.

X. H. Yang, Y. Y. Zhou, M. Xiao, “Entangler via electromagnetically induced transparency with an atomic ensemble,” Sci. Rep. 3, 3479–3483 (2013).
[PubMed]

X. H. Yang, Y. Y. Zhou, M. Xiao, “Generation of multipartite continuous- variable entanglement via atomic spin wave,” Phys. Rev. A 85(5), 052307 (2012).
[CrossRef]

Zibrov, A. S.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

Zoller, P.

L. M. Duan, M. D. Lukin, J. I. Cirac, P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

L. M. Duan, G. Giedke, J. I. Cirac, P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84(12), 2722–2725 (2000).
[CrossRef] [PubMed]

Nature (4)

H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
[CrossRef] [PubMed]

E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[CrossRef] [PubMed]

L. M. Duan, M. D. Lukin, J. I. Cirac, P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (13)

M. Fleischhauer, T. Richter, “Pulse matching and correlation of phase fluctuations in Λ systems,” Phys. Rev. A 51(3), 2430–2442 (1995).
[CrossRef] [PubMed]

P. van Loock, A. Furusawa, “Detecting genuine multipartite continuous- variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
[CrossRef]

M. K. Olsen, A. S. Bradley, “Asymmetric polychromatic tripartite entanglement from interlinked χ(2) parametric interactions,” Phys. Rev. A 74(6), 063809 (2006).
[CrossRef]

X. H. Yang, J. T. Sheng, U. Khadka, M. Xiao, “Generation of correlated and anticorrelated multiple fields via atomic spin coherence,” Phys. Rev. A 85(1), 013824 (2012).
[CrossRef]

V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, F. Narducci, “Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor,” Phys. Rev. A 70(5), 053811 (2004).
[CrossRef]

K. I. Harada, T. Kanbashi, M. Mitsunaga, K. Motomura, “Competition between electromagnetically induced transparency and stimulated Raman scattering,” Phys. Rev. A 73(1), 013807 (2006).
[CrossRef]

G. S. Agarwal, T. N. Dey, D. J. Gauthier, “Competition between electromagnetically induced transparency and Raman processes,” Phys. Rev. A 74(4), 043805 (2006).
[CrossRef]

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[CrossRef]

H. Wu, M. Xiao, “Bright correlated twin beams from an atomic ensemble in the optical cavity,” Phys. Rev. A 80(6), 063415 (2009).
[CrossRef]

P. Kolchin, “Electromagnetically-induced-transparency-based paired photon generation,” Phys. Rev. A 75(3), 033814 (2007).
[CrossRef]

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[CrossRef]

F. Le Kien, A. Patnaik, K. Hakuta, “Multiorder coherent Raman scattering of a quantum probe field,” Phys. Rev. A 68(6), 063803 (2003).
[CrossRef]

X. H. Yang, Y. Y. Zhou, M. Xiao, “Generation of multipartite continuous- variable entanglement via atomic spin wave,” Phys. Rev. A 85(5), 052307 (2012).
[CrossRef]

Phys. Rev. Lett. (8)

M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche, “Measurement of Dispersive Properties of Electromagnetically Induced Transparency in Rubidium Atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[CrossRef] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, S. E. Harris, “Generation of Paired Photons with Controllable Waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[CrossRef] [PubMed]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, P. van Loock, “Experimental Creation of a Fully Inseparable Tripartite Continuous-Variable State,” Phys. Rev. Lett. 91(8), 080404 (2003).
[CrossRef] [PubMed]

R. Zhang, S. R. Garner, L. V. Hau, “Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates,” Phys. Rev. Lett. 103(23), 233602 (2009).
[CrossRef] [PubMed]

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, I. Bloch, “Electromagnetically Induced Transparency and Light Storage in an Atomic Mott Insulator,” Phys. Rev. Lett. 103(3), 033003 (2009).
[CrossRef] [PubMed]

P. van Loock, S. L. Braunstein, “Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, S. E. Harris, “Efficient Nonlinear Frequency Conversion in an All-Resonant Double- Lambda System,” Phys. Rev. Lett. 84(23), 5308–5311 (2000).
[CrossRef] [PubMed]

L. M. Duan, G. Giedke, J. I. Cirac, P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84(12), 2722–2725 (2000).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Prog. Opt. (1)

E. Arimondo, “V Coherent Population Trapping in Laser Spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Sci. Rep. (1)

X. H. Yang, Y. Y. Zhou, M. Xiao, “Entangler via electromagnetically induced transparency with an atomic ensemble,” Sci. Rep. 3, 3479–3483 (2013).
[PubMed]

Science (2)

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, M. D. Lukin, “Atomic Memory for Correlated Photon States,” Science 301(5630), 196–200 (2003).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Other (2)

D. Bouweester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, 2000).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

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Figures (7)

Fig. 1
Fig. 1

(a) The quintuple-Λ-type system of the D1 transitions in 85Rb atom coupled by the coupling (Ec), probe (Ep), and mixing (Em) fields based on the configuration in Refs [19, 21], where Ep, Ec, and Em fields all drive both |1|3 and |2|3 transitions, and the corresponding Stokes fields (E1 and E3), and anti-Stokes fields (E2 and E4) are generated through four FWM processes. (b) The equivalent configuration of (a) with the two lower states driven by the atomic spin wave S induced by the strong Ec and Ep fields in the Λ-type EIT configuration.

Fig. 2
Fig. 2

The evolution of V as a function of the Fourier frequency ω with L=0.02 , r=1× 10 -4 , n 0 =10 16 , γ 1 = γ 2 =3 , γ 0 =0.1 , ω 12 =3036 , Ω p = Ω c =600 , Ω 1 = Ω 2 =120 , Δ 2 = Δ 1 Δ=3036 , and Δ=ω in corresponding units of m and MHz, or m−1 and MHz−1.

Fig. 3
Fig. 3

The evolution of V as a function of the atomic density n0 with Δ = -ω = −150 MHz, and the other parameters are the same as those in Fig. 2.

Fig. 4
Fig. 4

The evolution of V as a function of the Rabi frequency Ω = Ω 1 = Ω 2 of the scattering field with Δ = -ω = −150 MHz, and the other parameters are the same as those in Fig. 2.

Fig. 5
Fig. 5

The evolution of V as a function of the coherence decay rate γ 0 of the lower doublet with Δ = -ω = −150 MHz, and the other parameters are the same as those in Fig. 2.

Fig. 6
Fig. 6

The evolution of V as a function of the ratio of the coupling coefficients g23/g13 with Δ = -ω = −150 MHz, and the other parameters are the same as those in Fig. 2.

Fig. 7
Fig. 7

The evolutions of the VLF correlations V12 (a), V13 (b), and V23 (c) as a function of the Fourier frequency ω with Δ = -ω, Δ3 = 2900 MHz, and Ω1 = Ω3 = 80 MHz, and the other parameters are the same as those in Fig. 2.

Equations (8)

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σ ˙ 12 (z,t)=( γ 0 +iΔ) σ 12 i g 1 a 1 (z,t) σ 23 + +i g 2 a 2 + ( z,t ) σ 13 +i Ω 1 σ 13 i Ω 2 σ 23 + + F 12 ( z,t ),
σ ˙ 13 (z,t)=[( γ 1 + γ 2 )/2i( Δ 1 Δ)] σ 13 +i g 1 a 1 (z,t)( σ 11 σ 33 )+i Ω 1 σ 12 + F 13 (z,t),
σ ˙ 23 (z,t)=[( γ 1 + γ 2 )/2i( Δ 2 +Δ)] σ 23 +i g 2 a 2 (z,t)( σ 22 σ 33 )+i Ω 2 σ 12 + + F 23 (z,t),
( t +c z ) a 1 (z,t)=i g 1 N σ 13 ,
( t +c z ) a 2 + (z,t)=i g 2 N σ 23 + ,
σ 13 = 1 γ 13 +i(ω Δ 1 +Δ) {[i g 1 ( σ 11 (0) σ 33 (0) )+ g 1 Ω 1 σ 23 +(0) i(ω+Δ)+ γ 0 ] a 1 g 2 Ω 1 σ 13 (0) i(ω+Δ)+ γ 0 a 2 + + i Ω 1 (i Ω 1 σ 13 (0) i Ω 2 σ 23 +(0) ) i(ω+Δ)+ γ 0 + i Ω 1 F 12 i(ω+Δ)+ γ 0 + F 13 },
σ 23 + = 1 γ 23 +i(ω+ Δ 2 +Δ) { g 1 Ω 2 σ 23 +(0) i(ω+Δ)+ γ 0 a 1 [ i g 2 ( σ 22 (0) σ 33 (0) ) g 2 Ω 2 * σ 13 (0) i(ω+Δ)+ γ 0 ] a 2 + i Ω 2 (i Ω 1 σ 13 (0) i Ω 2 σ 23 +(0) ) i(ω+Δ)+ γ 0 i Ω 2 F 12 i(ω+Δ)+ γ 0 + F 23 + }.
V 12 =V( x 1 + x 2 )+V( p 1 - p 2 + g 3 p 3 )<4 V 13 =V( x 1 - x 3 )+V( p 1 + g 2 p 2 + p 3 )<4 V 23 =V( x 2 + x 3 )+V( g 1 p 1 + p 2 - p 3 )<4

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