Abstract

Radiative renormalization has been used to deduce and describe electromagnetically induced transparency succinctly in four-wave mixing for both one and two strong fields. We find both additive and nested renormalization terms and give a prescription for obtaining renormalized expressions starting from perturbation theory solutions. The advantages of using a second strong field are also discussed.

© 1993 Optical Society of America

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References

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  1. K.-J. Boller, A. Imamoğlu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991); S. E. Harris, J. E. Field, A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
    [CrossRef] [PubMed]
  2. K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991); Phys. Rev. A 45, 5152 (1992).
    [CrossRef] [PubMed]
  3. O. Blum, P. J. Harshman, T. K. Gustafson, P. L. Kelley, Phys. Rev. A 47, 5165 (1993), and references therein.
    [CrossRef] [PubMed]

1993

O. Blum, P. J. Harshman, T. K. Gustafson, P. L. Kelley, Phys. Rev. A 47, 5165 (1993), and references therein.
[CrossRef] [PubMed]

1991

K.-J. Boller, A. Imamoğlu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991); S. E. Harris, J. E. Field, A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991); Phys. Rev. A 45, 5152 (1992).
[CrossRef] [PubMed]

Blum, O.

O. Blum, P. J. Harshman, T. K. Gustafson, P. L. Kelley, Phys. Rev. A 47, 5165 (1993), and references therein.
[CrossRef] [PubMed]

Boller, K.-J.

K.-J. Boller, A. Imamoğlu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991); S. E. Harris, J. E. Field, A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Gustafson, T. K.

O. Blum, P. J. Harshman, T. K. Gustafson, P. L. Kelley, Phys. Rev. A 47, 5165 (1993), and references therein.
[CrossRef] [PubMed]

Hakuta, K.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991); Phys. Rev. A 45, 5152 (1992).
[CrossRef] [PubMed]

Harris, S. E.

K.-J. Boller, A. Imamoğlu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991); S. E. Harris, J. E. Field, A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Harshman, P. J.

O. Blum, P. J. Harshman, T. K. Gustafson, P. L. Kelley, Phys. Rev. A 47, 5165 (1993), and references therein.
[CrossRef] [PubMed]

Imamoglu, A.

K.-J. Boller, A. Imamoğlu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991); S. E. Harris, J. E. Field, A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Kelley, P. L.

O. Blum, P. J. Harshman, T. K. Gustafson, P. L. Kelley, Phys. Rev. A 47, 5165 (1993), and references therein.
[CrossRef] [PubMed]

Marmet, L.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991); Phys. Rev. A 45, 5152 (1992).
[CrossRef] [PubMed]

Stoicheff, B. P.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991); Phys. Rev. A 45, 5152 (1992).
[CrossRef] [PubMed]

Phys. Rev. A

O. Blum, P. J. Harshman, T. K. Gustafson, P. L. Kelley, Phys. Rev. A 47, 5165 (1993), and references therein.
[CrossRef] [PubMed]

Phys. Rev. Lett.

K.-J. Boller, A. Imamoğlu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991); S. E. Harris, J. E. Field, A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991); Phys. Rev. A 45, 5152 (1992).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Energy-level diagram for the upconversion process proposed in Ref. 1. (a) Assumed energy-level configuration, where the fields at ωb and ωc are possibly strong, (b) The lowest-order nonlinear process in terms of double-sided Feynman diagrams.

Fig. 2
Fig. 2

Single-strong-field case (|fb| weak, |fc| strong): Plot of the ratio of the characteristic absorption length to the characteristic conversion length, labs/l4-w, for (a) the radiatively renormalized response and (b) the radiatively renormalized response divided by the perturbation theory limit. These are plotted as a function of δωb and |fc| with |fb| = 2 × 10−5, δωa = δωc = 0, and Γ = Γ21 = Γ31 = Γ41/10.

Fig. 3
Fig. 3

Two-strong-field case (|fb| and |fc| strong): Plot of the ratio of the characteristic absorption length of the characteristic conversion length, labs/l4-w, for (a) the radiatively renormalized response and (b) the radiatively renormalized response divided by the perturbation theory limit. These are plotted as a function of δωa and |fc| with |fb| = 2, δωb = δωc = 0, and the dephasing constants as in Fig. 2.

Equations (4)

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ρ 31 = ( Ω a Ω b D a b D a + Ω d Ω c * D d D a b ) ρ 11 ( | Ω b | 2 D a D a b + | Ω c | 2 D a b D d ) ρ 31 .
ρ 31 = 1 D ˜ a b ( Ω a Ω b D a + Ω d Ω c * D d ) ρ 11 ,
ρ 41 = i D d ( Ω c ρ 31 + Ω d ρ 11 ) .
ρ 41 = i D ˆ d ( Ω a Ω b Ω c D ˆ a b D a Ω d ) ,

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