Abstract

Recently a cross-phase modulation scheme that yields giant Kerr nonlinearities by use of an electromagnetically induced transparency (EIT) was proposed [Schmidt and Imamoǧlu, Opt. Lett. 21, 1936 (1996)]. We analyze the high-speed properties of this scheme for short-pulse propagation. We discuss the relevant losses in this system and show that for short pulses one-photon losses are dominant. We demonstrate that over the entire bandwidth the attainable phase shift in an EIT scheme with a quasi-cw coupling field is orders of magnitude higher than in a conventional three-level scheme or in EIT schemes, in which matched pulses are used to create the transparency.

© 1998 Optical Society of America

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References

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  1. A. Imamo?lu and S. E. Harris, Opt. Lett. 14, 1344 (1989).
    [CrossRef]
  2. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
    [CrossRef] [PubMed]
  3. K. Hakuta, L. Marmet, and B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
    [CrossRef] [PubMed]
  4. P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. Shahriar, and P. Kumar, Opt. Lett. 20, 982 (1995).
    [CrossRef]
  5. B. S. Ham, M. Shahriar, and P. Hemmer, Opt. Lett. 22, 1138 (1997).
    [CrossRef] [PubMed]
  6. H. Schmidt and A. Imamo?lu, Opt. Lett. 21, 1936 (1996).
    [CrossRef] [PubMed]
  7. S. E. Harris, Phys. Rev. Lett. 70, 552 (1993).
    [CrossRef] [PubMed]
  8. J. P. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
    [CrossRef] [PubMed]
  9. S. E. Harris and Z. Luo, Phys. Rev. A 52, R928 (1995).
    [CrossRef]

1997 (1)

1996 (1)

1995 (2)

1993 (2)

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993).
[CrossRef] [PubMed]

J. P. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

1991 (1)

K. Hakuta, L. Marmet, and B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

1989 (2)

Cronin-Golomb, M.

Donoghue, J.

Grangier, P.

J. P. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

Hakuta, K.

K. Hakuta, L. Marmet, and B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Ham, B. S.

Harris, S. E.

S. E. Harris and Z. Luo, Phys. Rev. A 52, R928 (1995).
[CrossRef]

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993).
[CrossRef] [PubMed]

A. Imamo?lu and S. E. Harris, Opt. Lett. 14, 1344 (1989).
[CrossRef]

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
[CrossRef] [PubMed]

Hemmer, P.

Hemmer, P. R.

Imamoglu, A.

Katz, D. P.

Kumar, P.

Luo, Z.

S. E. Harris and Z. Luo, Phys. Rev. A 52, R928 (1995).
[CrossRef]

Marmet, L.

K. Hakuta, L. Marmet, and B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Poizat, J. P.

J. P. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

Schmidt, H.

Shahriar, M.

Stoicheff, B. P.

K. Hakuta, L. Marmet, and B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. A (1)

S. E. Harris and Z. Luo, Phys. Rev. A 52, R928 (1995).
[CrossRef]

Phys. Rev. Lett. (4)

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, and B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993).
[CrossRef] [PubMed]

J. P. Poizat and P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Left, four-level EIT scheme in the dressed-state basis. Right, conventional XPM scheme. Solid curves, absorption profile of intermediate level; dotted curves, sketch of the probe pulse centered at κ·Δν.

Fig. 2
Fig. 2

Intensity profile of Gaussian input probe pulse after propagation through a medium with EIT and with a conventional three-level configuration.

Fig. 3
Fig. 3

Nonlinear phase shift as a function of bandwidth for fixed detuning from the resonances and absorption–length product.

Tables (1)

Tables Icon

Table 1 Proportionality of Absorption and Figure of Merit on the Bandwidth of the Probe Pulse for the Three XPM Schemes Discussed in the Text

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

αtot=8π2Nμ132λ0×Γ2Ωc2Δωb2+4Γ3Δω22Δωb2+14Γ4Ωc2Ωb2Ωc2-4Δω222Δωb2.
αtot=32π2Nμ132λ0 Γ3Δω22Ωc4.
ΦXPM=3πNLμ1324λ0 Ωb2Ωc2Δωb.
αtot=2π2Nμ132λ0 Γ3Δωa2,
ΦXPM=3πNLμ13216λ0 Ωb2Δωa2Δωb.
nc>f13f23nat,
α4πNμ132λ0 ΔνΩc2.

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