Abstract

Coherent manipulation of stored images is performed at low light levels based on enhanced cross-Kerr nonlinearity in a four-level N-type electromagnetically induced transparency (EIT) system. Using intensity masks in the signal pulse, quadratic phase shifts with low nonlinear absorption can be efficiently imprinted on the Fraunhofer diffraction patterns already stored in the EIT system. Fast-Fourier-transform-based numerical simulations clearly demonstrate that the far-field images of the retrieved probe light can be flexibly modulated by applying different signal fields. Our studies could help advance the goals of nonlinear all-optical processing for spatial information coherently stored in EIT systems.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010 (1)

G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, Phys. Rev. A 81, 011401(R) (2010).

2009 (1)

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

2008 (3)

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef]

L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, Phys. Rev. A 77, 041802(R) (2008).

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef]

2006 (1)

Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef]

2003 (1)

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

2000 (1)

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef]

1999 (1)

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

1996 (1)

Beil, F.

G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, Phys. Rev. A 81, 011401(R) (2010).

Bloch, I.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

Camacho, R. M.

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef]

Chen, Y.-F.

Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef]

Davidson, N.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef]

Ding, D.

J. Wu, D. Ding, Y. Liu, Z. Zhou, B. Shi, X. Zou, and G. Guo, arXiv:1204.0955 (2012).

Firstenberg, O.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Guo, G.

J. Wu, D. Ding, Y. Liu, Z. Zhou, B. Shi, X. Zou, and G. Guo, arXiv:1204.0955 (2012).

Halfmann, T.

G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, Phys. Rev. A 81, 011401(R) (2010).

Harris, S. E.

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

Hau, L. V.

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

Heinze, G.

G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, Phys. Rev. A 81, 011401(R) (2010).

Howell, J. C.

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef]

Imamoglu, A.

Ingle, V. K.

V. K. Ingle and J. G. Proakis, Digital Signal Processing Using MATLAB V.4 (PWS Publishing Company, 1997).

Kang, H.

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

Kuhr, S.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

Liu, Y.

J. Wu, D. Ding, Y. Liu, Z. Zhou, B. Shi, X. Zou, and G. Guo, arXiv:1204.0955 (2012).

Lukin, M. D.

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef]

Proakis, J. G.

V. K. Ingle and J. G. Proakis, Digital Signal Processing Using MATLAB V.4 (PWS Publishing Company, 1997).

Pugatch, R.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef]

Ron, A.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef]

Rudolf, A.

G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, Phys. Rev. A 81, 011401(R) (2010).

Schmidt, H.

Schnorrberger, U.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

Shi, B.

J. Wu, D. Ding, Y. Liu, Z. Zhou, B. Shi, X. Zou, and G. Guo, arXiv:1204.0955 (2012).

Shuker, M.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef]

Thompson, J. D.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

Trotzky, S.

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

Vudyasetu, P. K.

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef]

Wang, C.-Y.

Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef]

Wang, S.-H.

Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef]

Wang, T.

L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, Phys. Rev. A 77, 041802(R) (2008).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

Wu, J.

J. Wu, D. Ding, Y. Liu, Z. Zhou, B. Shi, X. Zou, and G. Guo, arXiv:1204.0955 (2012).

Xiao, Y.

L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, Phys. Rev. A 77, 041802(R) (2008).

Yelin, S. F.

L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, Phys. Rev. A 77, 041802(R) (2008).

Yu, I. A.

Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef]

Zhao, L.

L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, Phys. Rev. A 77, 041802(R) (2008).

Zhou, Z.

J. Wu, D. Ding, Y. Liu, Z. Zhou, B. Shi, X. Zou, and G. Guo, arXiv:1204.0955 (2012).

Zhu, Y.

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

Zou, X.

J. Wu, D. Ding, Y. Liu, Z. Zhou, B. Shi, X. Zou, and G. Guo, arXiv:1204.0955 (2012).

Opt. Lett. (1)

Phys. Rev. A (2)

L. Zhao, T. Wang, Y. Xiao, and S. F. Yelin, Phys. Rev. A 77, 041802(R) (2008).

G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, Phys. Rev. A 81, 011401(R) (2010).

Phys. Rev. Lett. (7)

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef]

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

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

Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef]

U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, Phys. Rev. Lett. 103, 033003 (2009).
[CrossRef]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef]

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef]

Other (5)

D. A. Steck, “Rubidium 87 D Line Data,” available online at http://steck.us/alkalidata (revision 2.1.2, 12 August2009).

V. K. Ingle and J. G. Proakis, Digital Signal Processing Using MATLAB V.4 (PWS Publishing Company, 1997).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

J. Wu, D. Ding, Y. Liu, Z. Zhou, B. Shi, X. Zou, and G. Guo, arXiv:1204.0955 (2012).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Energy-level scheme of an N-type EIT system; (b) timing sequence of the light fields for phase imprinting on the stored transverse patterns (i.e., ρ21). For simplicity, we here assume that the storage time is equal to the square signal pulse duration ts.

Fig. 2.
Fig. 2.

Experimental setup. Note that a converging thin glass lens 1 of focal length f1 is placed right behind the spherical atomic gas to constitute a compound imaging system. An object is placed at a distance zo in front of the compound system. A photodetector (PD) at a distance zi behind the system can measure the retrieved probe light. Intensity-modulated signal images can be constructed at the gas by lens 2. BS, beam splitter; PBS, polarizing beam splitter.

Fig. 3.
Fig. 3.

(a) The size of the original input; (b)–(d) normalized intensity profiles at the photodetector, corresponding to cases (i)–(iii), respectively. The size of the pictures is 5×5mm2.

Equations (6)

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

Ep(x,y)=+Ep(ξ,η)h(xξ,yη)dξdη,
ρ21(x,y)=gΩcP(x,y)Ep(x,y),
ρ21(x,y,ts)=ρ21(x,y)exp[Ωs2(x,y)2Γ4iΔsts],
ϕ=Ωs2(x,y)Γ2+4Δs2Δsts,andα=Ωs2(x,y)Γ2+4Δs2Γts,
Ep(x,y)=Epr(x,y)exp(ikpr2/2f1).
Ep(μ,ν)=+Ep(x,y)h(μx,νy)dxdy,

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