Abstract

The influence of a repump laser on a nearly degenerate four-wave-mixing (ND-FWM) spectrum was investigated. We found the amplitude and the line shape of the NDFWM depended strongly on the detuning of the repump field. A five-peak structure was observed, and at some certain repump detuning a dip appeared at the central peak. A rough analysis was proposed to explain this effect.

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References

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  1. Optical Phase Conjugation, R.Fisher, ed. (Academic, 1983).
  2. P. F. Liao, D. M. Bloom, and N. P. Economou, "cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813-815 (1978).
    [CrossRef]
  3. D. Bloch, R. K. Raj, K. S. Peng, and M. Ducloy, "Dispersive character and directional anisotropy of saturated susceptibilities in resonant backward four-wave mixing," Phys. Rev. Lett. 49, 719-722 (1982).
    [CrossRef]
  4. G. Grynberg, M. Pinard, and P. Verkerk, "Saturation in degenerate four wave mixing: the dressed-atom approach," Opt. Commun. 50, 261-264 (1984).
    [CrossRef]
  5. M. Oria, D. Bloch, M. Fichet, and M. Ducloy, "Efficient phase-conjugation of a cw low-power laser diode in a short Cs vapor-cell at 852nm," Opt. Lett. 14, 1082-1084 (1989).
    [CrossRef] [PubMed]
  6. J. Liu and D. G. Steel, "High-resolution four-wave-mixing spectroscopy of collision-induced narrow resonances in Doppler-broadened systems," Phys. Rev. A 38, 4639-4646 (1988).
    [CrossRef] [PubMed]
  7. A. Lezama, G. C. Cardoso, and J. W. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2000).
    [CrossRef]
  8. J. Lin, A. I. Rubiera, and Y. F. Zhu, "Nearly degenerate four-wave mixing with bichromatic laser fields in a Rb atomic system," Phys. Rev. A 52, 4882-4885 (1995).
    [CrossRef] [PubMed]
  9. R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, "Four-wave parametric interactions in a strongly driven two-level system," Phys. Rev. A 24, 411-423 (1981).
    [CrossRef]
  10. D. G. Steel and J. T. Remillard, "Resonant nearly degenerate backward four-wave mixing in open and closed systems," Phys. Rev. A 36, 4330-4337 (1987).
    [CrossRef] [PubMed]
  11. P. R. Berman, D. G. Steel, G. Khitrova, and J. Liu, "Effects of radiative decay in four-wave-mixing spectroscopy: narrow resonances produced by nonconservation of population, alignment, and orientation," Phys. Rev. A 38,252-262 (1988).
    [CrossRef] [PubMed]
  12. Y. F. Zhu, T. N. Wasserlauf, and P. Sanchez, "Effect of optical pumping and Raman scattering on the degenerate four-wave mixing in coherently pumped rubidium atoms," Phys. Rev. A 55, 668-672 (1997).
    [CrossRef]

2000

A. Lezama, G. C. Cardoso, and J. W. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2000).
[CrossRef]

1997

Y. F. Zhu, T. N. Wasserlauf, and P. Sanchez, "Effect of optical pumping and Raman scattering on the degenerate four-wave mixing in coherently pumped rubidium atoms," Phys. Rev. A 55, 668-672 (1997).
[CrossRef]

1995

J. Lin, A. I. Rubiera, and Y. F. Zhu, "Nearly degenerate four-wave mixing with bichromatic laser fields in a Rb atomic system," Phys. Rev. A 52, 4882-4885 (1995).
[CrossRef] [PubMed]

1989

1988

J. Liu and D. G. Steel, "High-resolution four-wave-mixing spectroscopy of collision-induced narrow resonances in Doppler-broadened systems," Phys. Rev. A 38, 4639-4646 (1988).
[CrossRef] [PubMed]

P. R. Berman, D. G. Steel, G. Khitrova, and J. Liu, "Effects of radiative decay in four-wave-mixing spectroscopy: narrow resonances produced by nonconservation of population, alignment, and orientation," Phys. Rev. A 38,252-262 (1988).
[CrossRef] [PubMed]

1987

D. G. Steel and J. T. Remillard, "Resonant nearly degenerate backward four-wave mixing in open and closed systems," Phys. Rev. A 36, 4330-4337 (1987).
[CrossRef] [PubMed]

1984

G. Grynberg, M. Pinard, and P. Verkerk, "Saturation in degenerate four wave mixing: the dressed-atom approach," Opt. Commun. 50, 261-264 (1984).
[CrossRef]

1982

D. Bloch, R. K. Raj, K. S. Peng, and M. Ducloy, "Dispersive character and directional anisotropy of saturated susceptibilities in resonant backward four-wave mixing," Phys. Rev. Lett. 49, 719-722 (1982).
[CrossRef]

1981

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, "Four-wave parametric interactions in a strongly driven two-level system," Phys. Rev. A 24, 411-423 (1981).
[CrossRef]

1978

P. F. Liao, D. M. Bloom, and N. P. Economou, "cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813-815 (1978).
[CrossRef]

Berman, P. R.

P. R. Berman, D. G. Steel, G. Khitrova, and J. Liu, "Effects of radiative decay in four-wave-mixing spectroscopy: narrow resonances produced by nonconservation of population, alignment, and orientation," Phys. Rev. A 38,252-262 (1988).
[CrossRef] [PubMed]

Bloch, D.

M. Oria, D. Bloch, M. Fichet, and M. Ducloy, "Efficient phase-conjugation of a cw low-power laser diode in a short Cs vapor-cell at 852nm," Opt. Lett. 14, 1082-1084 (1989).
[CrossRef] [PubMed]

D. Bloch, R. K. Raj, K. S. Peng, and M. Ducloy, "Dispersive character and directional anisotropy of saturated susceptibilities in resonant backward four-wave mixing," Phys. Rev. Lett. 49, 719-722 (1982).
[CrossRef]

Bloom, D. M.

P. F. Liao, D. M. Bloom, and N. P. Economou, "cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813-815 (1978).
[CrossRef]

Boyd, R. W.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, "Four-wave parametric interactions in a strongly driven two-level system," Phys. Rev. A 24, 411-423 (1981).
[CrossRef]

Cardoso, G. C.

A. Lezama, G. C. Cardoso, and J. W. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2000).
[CrossRef]

Ducloy, M.

M. Oria, D. Bloch, M. Fichet, and M. Ducloy, "Efficient phase-conjugation of a cw low-power laser diode in a short Cs vapor-cell at 852nm," Opt. Lett. 14, 1082-1084 (1989).
[CrossRef] [PubMed]

D. Bloch, R. K. Raj, K. S. Peng, and M. Ducloy, "Dispersive character and directional anisotropy of saturated susceptibilities in resonant backward four-wave mixing," Phys. Rev. Lett. 49, 719-722 (1982).
[CrossRef]

Economou, N. P.

P. F. Liao, D. M. Bloom, and N. P. Economou, "cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813-815 (1978).
[CrossRef]

Fichet, M.

Grynberg, G.

G. Grynberg, M. Pinard, and P. Verkerk, "Saturation in degenerate four wave mixing: the dressed-atom approach," Opt. Commun. 50, 261-264 (1984).
[CrossRef]

Harter, D. J.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, "Four-wave parametric interactions in a strongly driven two-level system," Phys. Rev. A 24, 411-423 (1981).
[CrossRef]

Khitrova, G.

P. R. Berman, D. G. Steel, G. Khitrova, and J. Liu, "Effects of radiative decay in four-wave-mixing spectroscopy: narrow resonances produced by nonconservation of population, alignment, and orientation," Phys. Rev. A 38,252-262 (1988).
[CrossRef] [PubMed]

Lezama, A.

A. Lezama, G. C. Cardoso, and J. W. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2000).
[CrossRef]

Liao, P. F.

P. F. Liao, D. M. Bloom, and N. P. Economou, "cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813-815 (1978).
[CrossRef]

Lin, J.

J. Lin, A. I. Rubiera, and Y. F. Zhu, "Nearly degenerate four-wave mixing with bichromatic laser fields in a Rb atomic system," Phys. Rev. A 52, 4882-4885 (1995).
[CrossRef] [PubMed]

Liu, J.

P. R. Berman, D. G. Steel, G. Khitrova, and J. Liu, "Effects of radiative decay in four-wave-mixing spectroscopy: narrow resonances produced by nonconservation of population, alignment, and orientation," Phys. Rev. A 38,252-262 (1988).
[CrossRef] [PubMed]

J. Liu and D. G. Steel, "High-resolution four-wave-mixing spectroscopy of collision-induced narrow resonances in Doppler-broadened systems," Phys. Rev. A 38, 4639-4646 (1988).
[CrossRef] [PubMed]

Narum, P.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, "Four-wave parametric interactions in a strongly driven two-level system," Phys. Rev. A 24, 411-423 (1981).
[CrossRef]

Oria, M.

Peng, K. S.

D. Bloch, R. K. Raj, K. S. Peng, and M. Ducloy, "Dispersive character and directional anisotropy of saturated susceptibilities in resonant backward four-wave mixing," Phys. Rev. Lett. 49, 719-722 (1982).
[CrossRef]

Pinard, M.

G. Grynberg, M. Pinard, and P. Verkerk, "Saturation in degenerate four wave mixing: the dressed-atom approach," Opt. Commun. 50, 261-264 (1984).
[CrossRef]

Raj, R. K.

D. Bloch, R. K. Raj, K. S. Peng, and M. Ducloy, "Dispersive character and directional anisotropy of saturated susceptibilities in resonant backward four-wave mixing," Phys. Rev. Lett. 49, 719-722 (1982).
[CrossRef]

Raymer, M. G.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, "Four-wave parametric interactions in a strongly driven two-level system," Phys. Rev. A 24, 411-423 (1981).
[CrossRef]

Remillard, J. T.

D. G. Steel and J. T. Remillard, "Resonant nearly degenerate backward four-wave mixing in open and closed systems," Phys. Rev. A 36, 4330-4337 (1987).
[CrossRef] [PubMed]

Rubiera, A. I.

J. Lin, A. I. Rubiera, and Y. F. Zhu, "Nearly degenerate four-wave mixing with bichromatic laser fields in a Rb atomic system," Phys. Rev. A 52, 4882-4885 (1995).
[CrossRef] [PubMed]

Sanchez, P.

Y. F. Zhu, T. N. Wasserlauf, and P. Sanchez, "Effect of optical pumping and Raman scattering on the degenerate four-wave mixing in coherently pumped rubidium atoms," Phys. Rev. A 55, 668-672 (1997).
[CrossRef]

Steel, D. G.

P. R. Berman, D. G. Steel, G. Khitrova, and J. Liu, "Effects of radiative decay in four-wave-mixing spectroscopy: narrow resonances produced by nonconservation of population, alignment, and orientation," Phys. Rev. A 38,252-262 (1988).
[CrossRef] [PubMed]

J. Liu and D. G. Steel, "High-resolution four-wave-mixing spectroscopy of collision-induced narrow resonances in Doppler-broadened systems," Phys. Rev. A 38, 4639-4646 (1988).
[CrossRef] [PubMed]

D. G. Steel and J. T. Remillard, "Resonant nearly degenerate backward four-wave mixing in open and closed systems," Phys. Rev. A 36, 4330-4337 (1987).
[CrossRef] [PubMed]

Tabosa, J. W.

A. Lezama, G. C. Cardoso, and J. W. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2000).
[CrossRef]

Verkerk, P.

G. Grynberg, M. Pinard, and P. Verkerk, "Saturation in degenerate four wave mixing: the dressed-atom approach," Opt. Commun. 50, 261-264 (1984).
[CrossRef]

Wasserlauf, T. N.

Y. F. Zhu, T. N. Wasserlauf, and P. Sanchez, "Effect of optical pumping and Raman scattering on the degenerate four-wave mixing in coherently pumped rubidium atoms," Phys. Rev. A 55, 668-672 (1997).
[CrossRef]

Zhu, Y. F.

Y. F. Zhu, T. N. Wasserlauf, and P. Sanchez, "Effect of optical pumping and Raman scattering on the degenerate four-wave mixing in coherently pumped rubidium atoms," Phys. Rev. A 55, 668-672 (1997).
[CrossRef]

J. Lin, A. I. Rubiera, and Y. F. Zhu, "Nearly degenerate four-wave mixing with bichromatic laser fields in a Rb atomic system," Phys. Rev. A 52, 4882-4885 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett.

P. F. Liao, D. M. Bloom, and N. P. Economou, "cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813-815 (1978).
[CrossRef]

Opt. Commun.

G. Grynberg, M. Pinard, and P. Verkerk, "Saturation in degenerate four wave mixing: the dressed-atom approach," Opt. Commun. 50, 261-264 (1984).
[CrossRef]

Opt. Lett.

Phys. Rev. A

J. Liu and D. G. Steel, "High-resolution four-wave-mixing spectroscopy of collision-induced narrow resonances in Doppler-broadened systems," Phys. Rev. A 38, 4639-4646 (1988).
[CrossRef] [PubMed]

A. Lezama, G. C. Cardoso, and J. W. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2000).
[CrossRef]

J. Lin, A. I. Rubiera, and Y. F. Zhu, "Nearly degenerate four-wave mixing with bichromatic laser fields in a Rb atomic system," Phys. Rev. A 52, 4882-4885 (1995).
[CrossRef] [PubMed]

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, "Four-wave parametric interactions in a strongly driven two-level system," Phys. Rev. A 24, 411-423 (1981).
[CrossRef]

D. G. Steel and J. T. Remillard, "Resonant nearly degenerate backward four-wave mixing in open and closed systems," Phys. Rev. A 36, 4330-4337 (1987).
[CrossRef] [PubMed]

P. R. Berman, D. G. Steel, G. Khitrova, and J. Liu, "Effects of radiative decay in four-wave-mixing spectroscopy: narrow resonances produced by nonconservation of population, alignment, and orientation," Phys. Rev. A 38,252-262 (1988).
[CrossRef] [PubMed]

Y. F. Zhu, T. N. Wasserlauf, and P. Sanchez, "Effect of optical pumping and Raman scattering on the degenerate four-wave mixing in coherently pumped rubidium atoms," Phys. Rev. A 55, 668-672 (1997).
[CrossRef]

Phys. Rev. Lett.

D. Bloch, R. K. Raj, K. S. Peng, and M. Ducloy, "Dispersive character and directional anisotropy of saturated susceptibilities in resonant backward four-wave mixing," Phys. Rev. Lett. 49, 719-722 (1982).
[CrossRef]

Other

Optical Phase Conjugation, R.Fisher, ed. (Academic, 1983).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup. P, polarizer; BS, 50/50 beam splitter; D, photodiode detector. The angle between the probe and the pump beam was about 4 mrad . The diameters of the probe and the pump beam were about 1 mm . After passing the vapor cell the forward pump beam was reflected back to form the backward pump beam and overlapped with the forward pump beam. The pump and probe beams were 795 nm lasers tuned near the 5 S 1 2 ( F = 2 ) 5 P 1 2 ( F = 3 ) transition of Rb 85 with detuning Δ and δ, respectively. The repump beam was a 780 nm laser tuned near the 5 S 1 2 ( F = 3 ) 5 P 3 2 manifold with detuning Δ r . Δ r is the detuning from the 5 S 1 2 ( F = 3 ) 5 P 3 2 ( F = 2 ) transition.

Fig. 2
Fig. 2

NDFWM spectrum without a repump beam. The pump detuning is Δ = 115 MHz . δ is the relative detuning from the frequency of the central peak.

Fig. 3
Fig. 3

Peak positions of three NDFWM resonances versus pump detuning Δ.

Fig. 4
Fig. 4

NDFWM spectrum with the repump field turned on and various repump detuning Δ r . From (a) to (j) the repump detuning Δ r amounts 205 , 132 , 79 , 60 , 15 , 93 , 122 , 163 , 168 , and 317 MHz , respectively.

Fig. 5
Fig. 5

Simple two-level system γ 1 and γ 2 are the total decay rates of level 1 and 2, respectively. γ 2 1 is the decay rate from 2 to 1.

Fig. 6
Fig. 6

Calculated NDFWM spectrum based on Eq. (5) with different parameters. (a) Δ = 50 , γ 1 = 3 , γ 2 = 6 , γ p h = 3 , γ 2 1 = 6 . (b) Δ = 50 , γ 1 = 3 , γ 2 = 0.1 , γ p h = 3 , γ 2 1 = 6 . (c) is the same as (a), but the spectrum was integrated over velocity distribution; (d) is the same as (b) but the spectrum was integrated over velocity distribution.

Equations (6)

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i ( t + v ) ρ = [ H 0 , ρ ] + [ V , ρ ] i 2 [ Γ , ρ ] + i d ρ d t s p + i d ρ d t p h + i Λ ,
i ( t + v ) ρ 11 = ( V 12 ρ 21 c . c ) i γ 1 ρ 11 + i γ 2 1 ρ 22 + i λ 1 ,
i ( t + v ) ρ 22 = ( V 12 ρ 21 c . c ) i γ 2 ρ 22 + i λ 2 ,
i ( t + v ) ρ 12 = ω 0 ρ 12 + ( V 12 ρ 22 ρ 11 V 21 ) i γ p h T ρ 12 ,
P ( 3 ) = N 0 μ 12 4 Ω f Ω b Ω p * e i [ ( ω δ ) t + k p r ] 1 ( Δ δ ) k p v + i γ p h T × ( 1 R δ Δ k v + i γ 1 + 1 + R δ Δ k v + i γ 2 ) [ 1 Δ + k f v + i γ 12 + 1 ( δ + Δ ) k p v + i γ 12 ] + c.c. ,
( ρ 11 ρ 22 ) e q = λ 1 γ 1 λ 2 γ 2 ( 1 γ 2 1 γ 1 ) .

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