Abstract

We investigate the interplay between the two components of the four-wave mixing (FWM) beams in a ladder-type three-level atomic system. The interplay, including the shift and splitting of the two FWM beams and their intensity modulation, depends on the frequency detuning and the angles as well as the powers of the pump fields. The x-directional splitting due to the cross-phase modulation and y-directional splitting because of electromagnetically induced gratings of FWM beams are investigated. Both the theoretical and experimental results exhibit that the spatial separation and the number of the FWM signals can be well controlled by additional dressing laser beams. Such studies not only can be very useful in better understanding the formation of spatial solitons but also have potential applications in signal processing.

© 2012 Optical Society of America

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  1. G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64, 2487–2490 (1990).
    [CrossRef]
  2. J. M. Hickmann, A. S. L. Gomes, and C. Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–3550 (1992).
    [CrossRef]
  3. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408–415 (1996).
    [CrossRef]
  4. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
    [CrossRef]
  5. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
    [CrossRef]
  6. H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
    [CrossRef]
  7. A. Imamoglu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
    [CrossRef]
  8. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
    [CrossRef]
  9. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
    [CrossRef]
  10. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
    [CrossRef]
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    [CrossRef]

2011 (1)

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole solitons in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

2010 (1)

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

2009 (2)

Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. B. Li, J. P. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80, 013835 (2009).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804(2009).
[CrossRef]

2008 (1)

X.-M. Liu, “Theory and experiments for multiple four-wave-mixing processes with multi-frequency pumps in optical fibers,” Phys. Rev. A 77, 043818 (2008).
[CrossRef]

2005 (1)

2004 (1)

H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70, 061804 (2004).
[CrossRef]

2001 (5)

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82, 1847–1850 (1999).
[CrossRef]

1998 (2)

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A. 57, 1338–1344 (1998).
[CrossRef]

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[CrossRef]

1996 (1)

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408–415 (1996).
[CrossRef]

1992 (1)

J. M. Hickmann, A. S. L. Gomes, and C. Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–3550 (1992).
[CrossRef]

1990 (1)

G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64, 2487–2490 (1990).
[CrossRef]

1989 (1)

Agrawal, G. P.

G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64, 2487–2490 (1990).
[CrossRef]

Araujo, C.

J. M. Hickmann, A. S. L. Gomes, and C. Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–3550 (1992).
[CrossRef]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Chang, H.

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804(2009).
[CrossRef]

Chen, H. X.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole solitons in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

Cirac, J. I.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef]

Duan, L. M.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef]

Dunn, M. H.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408–415 (1996).
[CrossRef]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Fleischhauer, M.

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82, 1847–1850 (1999).
[CrossRef]

Fulton, D. J.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408–415 (1996).
[CrossRef]

Gomes, A. S. L.

J. M. Hickmann, A. S. L. Gomes, and C. Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–3550 (1992).
[CrossRef]

Goorskey, D.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[CrossRef]

A. Imamoglu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
[CrossRef]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hernandez, G.

H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70, 061804 (2004).
[CrossRef]

Hickmann, J. M.

J. M. Hickmann, A. S. L. Gomes, and C. Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–3550 (1992).
[CrossRef]

Imamoglu, A.

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

A. Imamoglu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
[CrossRef]

Kang, H.

H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70, 061804 (2004).
[CrossRef]

Li, C. B.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole solitons in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804(2009).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. B. Li, J. P. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80, 013835 (2009).
[CrossRef]

Li, Y. Q.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A. 57, 1338–1344 (1998).
[CrossRef]

Ling, H. Y.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A. 57, 1338–1344 (1998).
[CrossRef]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

Liu, X.

Liu, X.-M.

X.-M. Liu, “Theory and experiments for multiple four-wave-mixing processes with multi-frequency pumps in optical fibers,” Phys. Rev. A 77, 043818 (2008).
[CrossRef]

Lu, C.

Lu, F.

Lu, K. Q.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole solitons in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Lukin, M. D.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef]

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82, 1847–1850 (1999).
[CrossRef]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Matsko, A. B.

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82, 1847–1850 (1999).
[CrossRef]

Moseley, R. R.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408–415 (1996).
[CrossRef]

Ng, J.

Nie, Z. Q.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole solitons in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804(2009).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. B. Li, J. P. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80, 013835 (2009).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, and M. Xiao, Coherent Control of Four-Wave Mixing (Springer, 2010).

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Scully, M. O.

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82, 1847–1850 (1999).
[CrossRef]

Shepherd, S.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408–415 (1996).
[CrossRef]

Sinclair, B. D.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408–415 (1996).
[CrossRef]

Song, J. P.

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804(2009).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. B. Li, J. P. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80, 013835 (2009).
[CrossRef]

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Wang, H.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

Wang, Z. G.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole solitons in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Xiao, M.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole solitons in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. B. Li, J. P. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80, 013835 (2009).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804(2009).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A. 57, 1338–1344 (1998).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, and M. Xiao, Coherent Control of Four-Wave Mixing (Springer, 2010).

Yamamoto, Y.

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

Yang, X.

Yuan, C. Z.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Zhang, Y. P.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole solitons in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804(2009).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. B. Li, J. P. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80, 013835 (2009).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, and M. Xiao, Coherent Control of Four-Wave Mixing (Springer, 2010).

Zheng, H. B.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804(2009).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. B. Li, J. P. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80, 013835 (2009).
[CrossRef]

Zhou, X.

Zhu, Y. F.

H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70, 061804 (2004).
[CrossRef]

Zoller, P.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Two FWM processes to generate EF1 and EF2 in a ladder-type three-level atomic system. (b) and (c) Spatial geometry for the laser beams in the experiment. The scale gives the angle value of the corresponding position in the heat-pipe oven.

Fig. 2.
Fig. 2.

Images of EF1 or EF2 versus the power of the pump fields at an optical depth of 6.35×106. (a) EF1 versus P1 when E2 and E2 are blocked: (a1) Transverse section profile. (a2) Images with Δ1=30GHz and Δθ1=0.15°. (a3) Images with Δ1=20GHz and Δθ1=0. (b) EF2 versus P2 when E1 and E1 are blocked. E2 and E2 are set (b1) at Δθ2=0.15° with Δ2=15GHz and (b2) at Δθ2=0 with Δ2=10GHz. (c) EF1 versus P2 when E1 and E1 are set (c1) at Δθ1=0.15° with Δ1=25GHz and Δ2=25GHz and (c2) at Δθ1=0 with Δ1=20GHz and Δ2=20GHz. (c3) EF2 versus P1 when E2 and E2 are set at Δθ1=0 with Δ1=15GHz and Δ2=15GHz. The curves of the left column are the experimental results and those of the right column are the calculated beam profiles. The horizontal coordinate is x(mm) for EF1 and y(mm) for EF2. The vertical coordinate is the FWM beam profile.

Fig. 3.
Fig. 3.

Images of EF1 or EF2 versus the angle between the corresponding two pump fields at an optical depth of 6.35×106. (a) EF1 versus Δθ1 when both E2 and E2 are blocked with (a1) Δ1=25GHz and (a2) Δ1=50GHz. (b1) EF1 versus Δθ2 with Δ1=20GHz and Δ2=20GHz when E1 and E1 are set at Δθ1=0. (b2) EF2 versus Δθ1 with Δ1=25GHz and Δ2=25GHz when E2 and E2 are set at Δθ2=0.15. (b3) E3 versus Δθ1. The condition is similar to that of (b2). (c) EF1 versus Δθ1 with Δ120GHz and Δ2=20GHZ: (c1) both E1 and E2 off, (c2) only E2 on, (c3) both E2 and E2 on. The setup of the right columns is as those in Fig. 2.

Fig. 4.
Fig. 4.

(a1) Curve of EF1 signal intensity versus Δ1. (a2) Images of EF1 beam versus Δ1. (a3) Images of EF2 beam versus Δ1 with Δθ1=0.075 and both E2 and E2 blocked. (b1), (b2) Intensity curves or (b3), (b4) images of EF2 signal intensity versus Δ2 with Δθ2=0.075. In (b1) and (b3), both E1 and E1 are on; in (b2) and (b4), both E1 and E1 are off. (c1) Intensity curve and (c2) images of EF1 signal versus Δ2 with Δθ1=0. All the cases are at an optical depth of 6.35×106.

Fig. 5.
Fig. 5.

For the images in (a), (b), and (c), from bottom to top, the optical depth is 6.35×106, 9.97×106, 1.54×107, and 2.33×107 successively. The vertical axis label (n) is the splitting number of the FWM beam. (a) Images of EF2 versus Δθ1 with Δ1=20GHz, Δ2=20GHz, and Δθ2=0.15. (b) Power dependence of the dressing effect of E2 on EF1 beams with Δθ1=0 at Δ1=25GHz and Δ2=25GHz. (c) Power dependence of the dressing effect of E1 on EF2 beams when Δθ2=0.15 at Δ1=20GHz and Δ2=20GHz. The above panels are the splitting number of FWM (square dots) and the fitted curve versus different optical depth.

Equations (4)

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u3(x,y,z)zi2k3[2u3(x,y,z)x2+2u3(x,y,z)y2]=ik02[(2n01)+iχI(1)+n2S1|u3(x,y,z)|2+n2X1|u1(x,y,z)|2+n2X2|u2(x,y,z)|2]u3(x,y,z),
uF1(x,y,z)zi2k3[2uF1(x,y,z)x2+2uF1(x,y,z)y2]=ik02[(2n01)+iχI(1)+n2S2|uF1(x,y,z)|2+n2X3|u1(x,y,z)|2cos2(πξ/Λ)+n2X4|u2(x,y,z)|2]uF1(x,y,z),
uF2(x,y,z)zi2k3[2uF2(x,y,z)x2+2uF2(x,y,z)y2]=ik02[(2n01)+iχI(1)+n2S3|uF2(x,y,z)|2+n2X5|u1(x,y,z)|2+n2X6|u2(x,y,z)|2cos2(πξ/Λ)]uF2(x,y,z),
I3,F1,F2(x,y,z)=u3,F1,F22(x,y,0){exp[((x2+y2)/2)]+exp[((xx0)2(yy0)2)/2]}2×cos2ϕNL.

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