Abstract

The coherent propagation of four optical pulses through a multilevel resonant medium is investigated theoretically. We present a self-consistent analytic solution without steady-state or adiabatic approximations and use numerical simulations to indicate that the analytic formulas can be used as a guide in an experimental setting.

© 2009 Optical Society of America

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References

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  1. S. E. Harris, Phys. Today 50, 36 (1997).
    [CrossRef]
  2. For example, see M. V. Pack, R. M. Camacho, and J. C. Howell, Phys. Rev. A 74, 013812 (2006).
    [CrossRef]
  3. G. S. Agarwal and J. H. Eberly, Phys. Rev. A 61, 013404 (2000).
    [CrossRef]
  4. Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1998).
    [CrossRef]
  5. B. D. Clader and J. H. Eberly, Phys. Rev. A 76, 053812 (2007).
    [CrossRef]
  6. M. Fleischhauer and A. Manka, Phys. Rev. A 54, 794 (1996).
    [CrossRef] [PubMed]
  7. V. V. Kozlov and J. H. Eberly, Opt. Commun. 179, 85 (2000).
    [CrossRef]
  8. J. H. Eberly and V. V. Kozlov, Phys. Rev. Lett. 88, 243604 (2002).
    [CrossRef] [PubMed]
  9. B. D. Clader and J. H. Eberly, Phys. Rev. A 78, 033803 (2008).
    [CrossRef]
  10. F. T. Hioe, J. Opt. Soc. Am. B 6, 1245 (1989).
    [CrossRef]
  11. M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
    [CrossRef]

2008 (1)

B. D. Clader and J. H. Eberly, Phys. Rev. A 78, 033803 (2008).
[CrossRef]

2007 (1)

B. D. Clader and J. H. Eberly, Phys. Rev. A 76, 053812 (2007).
[CrossRef]

2006 (1)

For example, see M. V. Pack, R. M. Camacho, and J. C. Howell, Phys. Rev. A 74, 013812 (2006).
[CrossRef]

2002 (1)

J. H. Eberly and V. V. Kozlov, Phys. Rev. Lett. 88, 243604 (2002).
[CrossRef] [PubMed]

2000 (2)

G. S. Agarwal and J. H. Eberly, Phys. Rev. A 61, 013404 (2000).
[CrossRef]

V. V. Kozlov and J. H. Eberly, Opt. Commun. 179, 85 (2000).
[CrossRef]

1998 (1)

Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

M. Fleischhauer and A. Manka, Phys. Rev. A 54, 794 (1996).
[CrossRef] [PubMed]

1989 (1)

1981 (1)

M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and J. H. Eberly, Phys. Rev. A 61, 013404 (2000).
[CrossRef]

Camacho, R. M.

For example, see M. V. Pack, R. M. Camacho, and J. C. Howell, Phys. Rev. A 74, 013812 (2006).
[CrossRef]

Clader, B. D.

B. D. Clader and J. H. Eberly, Phys. Rev. A 78, 033803 (2008).
[CrossRef]

B. D. Clader and J. H. Eberly, Phys. Rev. A 76, 053812 (2007).
[CrossRef]

Eberly, J. H.

B. D. Clader and J. H. Eberly, Phys. Rev. A 78, 033803 (2008).
[CrossRef]

B. D. Clader and J. H. Eberly, Phys. Rev. A 76, 053812 (2007).
[CrossRef]

J. H. Eberly and V. V. Kozlov, Phys. Rev. Lett. 88, 243604 (2002).
[CrossRef] [PubMed]

V. V. Kozlov and J. H. Eberly, Opt. Commun. 179, 85 (2000).
[CrossRef]

G. S. Agarwal and J. H. Eberly, Phys. Rev. A 61, 013404 (2000).
[CrossRef]

M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer and A. Manka, Phys. Rev. A 54, 794 (1996).
[CrossRef] [PubMed]

Harris, S. E.

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

Hioe, F. T.

Howell, J. C.

For example, see M. V. Pack, R. M. Camacho, and J. C. Howell, Phys. Rev. A 74, 013812 (2006).
[CrossRef]

Konopnicki, M. J.

M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
[CrossRef]

Kozlov, V. V.

J. H. Eberly and V. V. Kozlov, Phys. Rev. Lett. 88, 243604 (2002).
[CrossRef] [PubMed]

V. V. Kozlov and J. H. Eberly, Opt. Commun. 179, 85 (2000).
[CrossRef]

Manka, A.

M. Fleischhauer and A. Manka, Phys. Rev. A 54, 794 (1996).
[CrossRef] [PubMed]

Pack, M. V.

For example, see M. V. Pack, R. M. Camacho, and J. C. Howell, Phys. Rev. A 74, 013812 (2006).
[CrossRef]

Park, Q-Han

Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1998).
[CrossRef]

Shin, H. J.

Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

V. V. Kozlov and J. H. Eberly, Opt. Commun. 179, 85 (2000).
[CrossRef]

Phys. Rev. A (7)

B. D. Clader and J. H. Eberly, Phys. Rev. A 78, 033803 (2008).
[CrossRef]

For example, see M. V. Pack, R. M. Camacho, and J. C. Howell, Phys. Rev. A 74, 013812 (2006).
[CrossRef]

G. S. Agarwal and J. H. Eberly, Phys. Rev. A 61, 013404 (2000).
[CrossRef]

Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1998).
[CrossRef]

B. D. Clader and J. H. Eberly, Phys. Rev. A 76, 053812 (2007).
[CrossRef]

M. Fleischhauer and A. Manka, Phys. Rev. A 54, 794 (1996).
[CrossRef] [PubMed]

M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

J. H. Eberly and V. V. Kozlov, Phys. Rev. Lett. 88, 243604 (2002).
[CrossRef] [PubMed]

Phys. Today (1)

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

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Figures (3)

Fig. 1
Fig. 1

Sketch of an X atom and four laser pulses labeled by their Rabi frequencies, with equal detunings Δ. The pulses are assumed short enough for the effects of all relaxation channels, such as γ 3 and γ 4 , to be ignored.

Fig. 2
Fig. 2

Evolution of nonstandard total pulse areas in a finite medium, located between the dashed vertical lines. Pulses were injected into the medium with areas θ a = 5.5 , θ b = 4.4 , θ c = 0.5 , and θ d = 0.4 . Numerical parameters: α 2 = 0.8 , β 2 = 0.2 , and τ = 2.1 T 2 * .

Fig. 3
Fig. 3

Evolution of nonstandard pulse shapes in a finite medium, with numerical parameters described in Fig. 2, is shown by focusing on pulses a and c. The analytic formulas predict that the Rabi frequencies will be equal at Z 0 .

Equations (20)

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E a ( z , t ) = E a ( z , t ) e i ( k a z ω a t ) + c.c. ,
i ρ T = [ H , ρ ] ,
H = 2 ( 0 0 Ω a * Ω b * 0 0 Ω c * Ω d * Ω a Ω c 2 Δ 0 Ω b Ω d 0 2 Δ ) .
Ω a Z = i μ ρ 31 , Ω b Z = i μ ρ 41 ,
Ω c Z = i μ ρ 32 , Ω d Z = i μ ρ 42 ,
H Z = μ 2 [ W , ρ ] .
Ω a ( T , Z ) = Ω b ( T , Z ) = Ω c ( T , Z ) = Ω d ( T , Z ) = 0 ,
Ω a ( Z , T ) = cos u e α 2 ( κ + i δ ) Z Ω ( Z , T ) ,
Ω b ( Z , T ) = sin u e α 2 ( κ + i δ ) Z Ω ( Z , T ) ,
Ω c ( Z , T ) = cos u e β 2 ( κ + i δ ) Z Ω ( Z , T ) ,
Ω d ( Z , T ) = sin u e β 2 ( κ + i δ ) Z Ω ( Z , T ) .
Ω ( Z , T ) = 2 τ exp [ D ( Z ) ] sech [ D ( Z ) T τ ] .
κ + i δ = μ 2 τ d Δ F ( Δ ) Δ i τ ,
θ a ( Z ) = 2 π cos u e α 2 Z e D ( Z ) ,
θ b ( Z ) = 2 π sin u e α 2 Z e D ( Z ) ,
θ c ( Z ) = 2 π cos u e β 2 Z e D ( Z ) ,
θ d ( Z ) = 2 π sin u e β 2 Z e D ( Z ) .
θ 1 ( Z ) θ a ( Z ) 2 + θ c ( Z ) 2 = 2 π cos u ,
θ 2 ( Z ) θ b ( Z ) 2 + θ d ( Z ) 2 = 2 π sin u ,
Θ ( Z ) θ 1 ( Z ) 2 + θ 2 ( Z ) 2 = 2 π .

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