Abstract

I propose an electromagnetically induced phase grating based on the giant Kerr nonlinearity of an atomic medium under electromagnetically induced transparency. The atomic phase grating behaves similarly to an ideal sinusoidal phase grating, and it is capable of producing a π phase excursion across a weak probe beam along with high transmissivity. The grating is created with arbitrarily weak fields, and diffraction efficiencies as high as 30% are predicted.

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References

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  1. K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
    [CrossRef] [PubMed]
  2. H. Schmidt and A. Imamoglu, Opt. Lett. 21, 1936 (1996).
    [CrossRef] [PubMed]
  3. H. Y. Ling, Y.-Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
    [CrossRef]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  5. M. Mitsunaga and N. Imoto, Phys. Rev. A 59, 4773 (1999).
    [CrossRef]
  6. G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
    [CrossRef]
  7. A. W. Brown and M. Xiao, Opt. Lett. 30, 699 (2005).
    [CrossRef] [PubMed]
  8. H. S. Kang and Y. F. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
    [CrossRef] [PubMed]
  9. R. D. Cowan, The Theory of Atomic Structure and Spectra, (University of California Press, 1981), p. 640.
  10. W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
    [CrossRef] [PubMed]

2005 (1)

2003 (1)

H. S. Kang and Y. F. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

2002 (1)

G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
[CrossRef]

1999 (1)

M. Mitsunaga and N. Imoto, Phys. Rev. A 59, 4773 (1999).
[CrossRef]

1998 (1)

H. Y. Ling, Y.-Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

1996 (1)

1993 (1)

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

1991 (1)

K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

1981 (1)

R. D. Cowan, The Theory of Atomic Structure and Spectra, (University of California Press, 1981), p. 640.

1968 (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Boller, K. J.

K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

Brown, A. W.

Cardoso, G. C.

G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
[CrossRef]

Cowan, R. D.

R. D. Cowan, The Theory of Atomic Structure and Spectra, (University of California Press, 1981), p. 640.

Davis, K. B.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Harris, S. E.

K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

Imamoglu, A.

H. Schmidt and A. Imamoglu, Opt. Lett. 21, 1936 (1996).
[CrossRef] [PubMed]

K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

Imoto, N.

M. Mitsunaga and N. Imoto, Phys. Rev. A 59, 4773 (1999).
[CrossRef]

Joffe, M. A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Kang, H. S.

H. S. Kang and Y. F. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

Ketterle, W.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Li, Y. -Q.

H. Y. Ling, Y.-Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

Ling, H. Y.

H. Y. Ling, Y.-Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

Martin, A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Mitsunaga, M.

M. Mitsunaga and N. Imoto, Phys. Rev. A 59, 4773 (1999).
[CrossRef]

Pritchard, D. E.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Schmidt, H.

Tabosa, J. W. R.

G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
[CrossRef]

Xiao, M.

A. W. Brown and M. Xiao, Opt. Lett. 30, 699 (2005).
[CrossRef] [PubMed]

H. Y. Ling, Y.-Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

Zhu, Y. F.

H. S. Kang and Y. F. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (3)

H. Y. Ling, Y.-Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

M. Mitsunaga and N. Imoto, Phys. Rev. A 59, 4773 (1999).
[CrossRef]

G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

H. S. Kang and Y. F. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Other (2)

R. D. Cowan, The Theory of Atomic Structure and Spectra, (University of California Press, 1981), p. 640.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (3)

Fig. 1
Fig. 1

(a) The atomic model. An open four-level atom interacting with three laser beams: probe ( Ω p ) , coupling ( Ω c ) and signal ( Ω ) . (b) Sketch of the probe- and signal-beam spatial configuration with respect to the atomic sample showing the zeroth and first diffraction orders.

Fig. 2
Fig. 2

(a) The amplitude (dashed black line) and phase (solid red line) of the transmission function T ( x ) plotted over two space periods for α L / 2 = 0.14 . (b) Cross section of the diffraction pattern for the transmission function shown in (a). The inset shows the diffraction pattern when σ ( x ) 0 .

Fig. 3
Fig. 3

(a) First-order diffracted intensity as a function of signal detuning for different interaction lengths and Ω / Ω c = 4 . (b) First-order diffracted intensity as a function of the ratio Ω / Ω c for L = 160 ζ and Δ = 285 γ c . In both cases, sin   θ 1 = 0.25 .  

Equations (5)

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Re [ χ ] = K 2 ( Ω / Ω c ) 2 Δ 4 Δ 2 + [ γ c + γ d ( Ω / Ω c ) 2 ] 2 ,
Im [ χ ] = K γ c ( Ω / Ω c ) 2 + γ d ( Ω / Ω c ) 4 4 Δ 2 + [ γ c + γ d ( Ω / Ω c ) 2 ] 2 ,
E p z = ( α / 2 + i σ ) E p .
T ( x ) = e α ( x ) L / 2 e i σ ( x ) L .
I p ( θ ) = | J ( θ ) | 2 sin 2 ( N π Λ   sin   θ / λ ) N 2 sin 2 ( π Λ   sin   θ / λ ) ,

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