Abstract

We demonstrate in experiment an efficient cw four-wave mixing scheme with maximal intensity conversion efficiency up to 73% in a double-Λ system of hot rubidium atoms. Relevant theoretical analysis shows that this high conversion efficiency benefits greatly from the constructive interference between two four-wave mixing channels, characterized by two different space-dependent phases.

© 2010 Optical Society of America

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  1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
  2. M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
    [CrossRef] [PubMed]
  3. R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photon. 3, 103 (2009).
    [CrossRef]
  4. S. E. Harris, Phys. Today 50, 36 (1997).
    [CrossRef]
  5. E. Arimondo and G. Orriols, Nuovo Cimento. Lett. 17, 333 (1976).
    [CrossRef]
  6. H. S. Kang, G. Hernandez, and Y. F. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
    [CrossRef] [PubMed]
  7. L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
    [CrossRef] [PubMed]
  8. B. Lu, W. H. Burkett, and M. Xiao, Opt. Lett. 23, 804 (1998).
    [CrossRef]
  9. E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
    [CrossRef]
  10. A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
    [CrossRef] [PubMed]
  11. M. G. Payne and L. Deng, Phys. Rev. Lett. 91, 123602 (2003).
    [CrossRef] [PubMed]
  12. See, for instance, Eqs. (11) in M. G. Payne and L. Deng, Phys. Rev. A 65, 063806 (2002).
    [CrossRef]

2009 (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photon. 3, 103 (2009).
[CrossRef]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

2004 (1)

H. S. Kang, G. Hernandez, and Y. F. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

2003 (1)

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

2002 (2)

See, for instance, Eqs. (11) in M. G. Payne and L. Deng, Phys. Rev. A 65, 063806 (2002).
[CrossRef]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef] [PubMed]

2000 (1)

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

1999 (1)

E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
[CrossRef]

1998 (1)

1997 (1)

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

1996 (1)

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

1976 (1)

E. Arimondo and G. Orriols, Nuovo Cimento. Lett. 17, 333 (1976).
[CrossRef]

Arimondo, E.

E. Arimondo and G. Orriols, Nuovo Cimento. Lett. 17, 333 (1976).
[CrossRef]

Burkett, W. H.

Camacho, R. M.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photon. 3, 103 (2009).
[CrossRef]

Deng, L.

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

See, for instance, Eqs. (11) in M. G. Payne and L. Deng, Phys. Rev. A 65, 063806 (2002).
[CrossRef]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Hagley, E. W.

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef] [PubMed]

Harris, S. E.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Hernandez, G.

H. S. Kang, G. Hernandez, and Y. F. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

Howell, J. C.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photon. 3, 103 (2009).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Jain, M.

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Kang, H. S.

H. S. Kang, G. Hernandez, and Y. F. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

Korsunsky, E. A.

E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
[CrossRef]

Kosachiov, D. V.

E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
[CrossRef]

Kozuma, M.

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef] [PubMed]

Lu, B.

Manuszak, D.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Merriam, A. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Orriols, G.

E. Arimondo and G. Orriols, Nuovo Cimento. Lett. 17, 333 (1976).
[CrossRef]

Payne, M. G.

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

See, for instance, Eqs. (11) in M. G. Payne and L. Deng, Phys. Rev. A 65, 063806 (2002).
[CrossRef]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef] [PubMed]

Sharpe, S. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

Shverdin, M.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

Vudyasetu, P. K.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photon. 3, 103 (2009).
[CrossRef]

Xia, H.

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Xiao, M.

Yin, G. Y.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Zhu, Y. F.

H. S. Kang, G. Hernandez, and Y. F. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

Nat. Photon. (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photon. 3, 103 (2009).
[CrossRef]

Nuovo Cimento. Lett. (1)

E. Arimondo and G. Orriols, Nuovo Cimento. Lett. 17, 333 (1976).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

See, for instance, Eqs. (11) in M. G. Payne and L. Deng, Phys. Rev. A 65, 063806 (2002).
[CrossRef]

E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
[CrossRef]

Phys. Rev. Lett. (5)

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

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

H. S. Kang, G. Hernandez, and Y. F. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Diagram of a double-Λ system of Rb 87 atoms with one ground state shared by two strong coupling fields. (b) Schematic of the corresponding experimental setup. BS: beam splitter; λ / 2 : half-wave plate; PBS: polarization beam splitter.

Fig. 2
Fig. 2

Measured (solid) and calculated (dashed and dotted) FWM signal I s as a function of the coupling detuning δ 2 at two different temperatures T = 50 ° C and T = 65 ° C . Relevant parameters for Rb 87 atoms are δ s = δ 2 , δ p = δ 1 = 160 MHz , γ 2 = 10 kHz , γ 3 = 5.75 MHz , γ 4 = 6.07 MHz , Ω 1 = 72 MHz , Ω 2 = 72 MHz , κ 13 = 0.191 MHz · μm 1 , κ 14 = 0.194 MHz · μm 1 . In particular, we have Ω p = 7.1 MHz and Ω s = 0 at the cell entrance. Parameters for Rb 85 atoms can be easily inferred from those of Rb 87 atoms by suitably considering the isotope shifts. Inset, calculated signal I s versus detuning δ 2 when Rb 85 atoms are ignored. Solid and dotted curves correspond to cold atoms without Doppler broadening and hot atoms with Doppler broadening at T = 65 ° C , respectively.

Fig. 3
Fig. 3

Measured frequency conversion efficiency I s ( z = L ) / I p ( z = 0 ) as a function of the temperature T. All parameters are the same as in Fig. 2 except that δ 2 = 1.16 GHz and κ 1 i becomes larger and larger as the temperature is increased.

Equations (3)

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ρ 21 t = i ( Δ ω 1 + i γ 2 ) ρ 21 + i Ω 1 * ρ 31 + i Ω 2 * ρ 41 , ρ 31 t = i ( Δ ω p + i γ 3 ) ρ 31 + i Ω 1 ρ 21 + i Ω p , ρ 41 t = i ( Δ ω 2 + i γ 4 ) ρ 41 + i Ω 2 ρ 21 + i Ω s ,
Ω p z + 1 c Ω p t = i κ 13 ρ 31 , Ω s z + 1 c Ω s z = i κ 14 ρ 41 ,
Ω p ( z ) = κ 14 | Ω 1 | 2 κ 14 | Ω 1 | 2 + κ 13 | Ω 2 | 2 × ( Ω p ( 0 ) e i Q z + κ 13 | Ω 2 | 2 κ 14 | Ω 1 | 2 Ω p ( 0 ) e i P z ) , Ω s ( z ) = κ 14 Ω 1 * Ω 2 κ 14 | Ω 1 | 2 + κ 13 | Ω 2 | 2 × ( Ω p ( 0 ) e i Q z Ω p ( 0 ) e i P z ) ,

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