Abstract

A four-level inverted-Y scheme with an electromagnetically induced transparency (EIT) core is investigated for the enhancement of cross-Kerr effect in rubidium atoms. When detunings of the coupling and control fields are appropriately set, an enhanced EIT window is observed, and the induced phase shift of the probe field due to cross-phase modulation (XPM) is obtained by measuring the dispersive property of the probe transition. The maximal XPM phase shift is about 12° under the current experimental conditions. The experimental measurements agree well with the theoretical calculations. The enhanced XPM phase shift in such an atomic system has applications in quantum nonlinear optics and quantum information science.

© 2010 Optical Society of America

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  1. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
    [CrossRef] [PubMed]
  2. C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi,“Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
    [CrossRef] [PubMed]
  3. S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
    [CrossRef]
  4. A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319 (2005).
    [CrossRef]
  5. J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
    [CrossRef]
  6. Y. F. Xiao, S. K. Özdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Express 16, 21462–21475 (2008).
    [CrossRef] [PubMed]
  7. M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
    [CrossRef] [PubMed]
  8. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [CrossRef]
  9. Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
    [CrossRef]
  10. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [CrossRef]
  11. M. Fleischhauer, A. Imamoğlu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  12. H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
    [CrossRef] [PubMed]
  13. H. Schmidt and A. Imamoğlu, “High-speed properties of a phase-modulation scheme based on electromagnetically induced transparency,” Opt. Lett. 23, 1007–1009 (1998).
    [CrossRef]
  14. Z. B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in R87b,” Phys. Rev. Lett. 97, 063901 (2006).
    [CrossRef] [PubMed]
  15. H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
    [CrossRef] [PubMed]
  16. Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
    [CrossRef] [PubMed]
  17. S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
    [CrossRef] [PubMed]
  18. X. D. Yang, S. J. Li, C. H. Zhang, and H. Wang, “Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system,” J. Opt. Soc. Am. B 26, 1423–1434 (2009).
    [CrossRef]
  19. Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
    [CrossRef]
  20. M. Yan, E. G. Rickey, and Y. Zhu, “Suppression of two-photon absorption by quantum interference,” Phys. Rev. A 64, 043807 (2001).
    [CrossRef]
  21. C. L. Wang, A. J. Li, X. Y. Zhou, Z. H. Kang, J. Yun, and J. Y. Gao, “Investigation of spontaneously generated coherence in dressed states of R87b atoms,” Opt. Lett. 33, 687–689 (2008).
    [CrossRef] [PubMed]
  22. A. Joshi and M. Xiao, “Generalized dark-state polaritons for photon memory in multilevel atomic media,” Phys. Rev. A 71, 041801(R) (2005).
    [CrossRef]
  23. J. M. Wen, S. W. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
    [CrossRef]
  24. S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2001).
    [CrossRef]
  25. D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
    [CrossRef]
  26. K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
    [CrossRef] [PubMed]
  27. J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67, 3062–3065 (1991).
    [CrossRef] [PubMed]
  28. M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
    [CrossRef] [PubMed]
  29. W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137-1–137-12 (2005).
    [CrossRef]
  30. S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
    [CrossRef]
  31. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
    [CrossRef]

2009 (2)

2008 (5)

C. L. Wang, A. J. Li, X. Y. Zhou, Z. H. Kang, J. Yun, and J. Y. Gao, “Investigation of spontaneously generated coherence in dressed states of R87b atoms,” Opt. Lett. 33, 687–689 (2008).
[CrossRef] [PubMed]

Y. F. Xiao, S. K. Özdemir, V. Gaddam, C. H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Express 16, 21462–21475 (2008).
[CrossRef] [PubMed]

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef] [PubMed]

Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
[CrossRef]

J. M. Wen, S. W. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

2006 (4)

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

Z. B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in R87b,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef] [PubMed]

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef] [PubMed]

2005 (4)

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137-1–137-12 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoğlu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

A. Joshi and M. Xiao, “Generalized dark-state polaritons for photon memory in multilevel atomic media,” Phys. Rev. A 71, 041801(R) (2005).
[CrossRef]

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319 (2005).
[CrossRef]

2004 (3)

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

2003 (2)

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi,“Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef] [PubMed]

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

2001 (2)

M. Yan, E. G. Rickey, and Y. Zhu, “Suppression of two-photon absorption by quantum interference,” Phys. Rev. A 64, 043807 (2001).
[CrossRef]

S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2001).
[CrossRef]

2000 (1)

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef] [PubMed]

1998 (1)

1997 (2)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

1996 (1)

1995 (2)

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

1991 (2)

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67, 3062–3065 (1991).
[CrossRef] [PubMed]

Adams, C. S.

S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2001).
[CrossRef]

Artoni, M.

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi,“Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef] [PubMed]

Badger, S. D.

S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2001).
[CrossRef]

Boller, K. -J.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Cao, X. M.

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef] [PubMed]

Cataliotti, F.

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi,“Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef] [PubMed]

Chen, Y. F.

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef] [PubMed]

Corbalán, R.

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Di Giuseppe, G.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

Dong, C. H.

Du, S. W.

J. M. Wen, S. W. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

Field, J. E.

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67, 3062–3065 (1991).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoğlu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Gaddam, V.

Gao, J. Y.

Gea-Banacloche, J.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

Grangier, Ph.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Grelu, Ph.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Hahn, K. H.

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67, 3062–3065 (1991).
[CrossRef] [PubMed]

Han, Y. X.

Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
[CrossRef]

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67, 3062–3065 (1991).
[CrossRef] [PubMed]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Hood, C. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Hughes, I. G.

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
[CrossRef]

S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2001).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoğlu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef] [PubMed]

H. Schmidt and A. Imamoğlu, “High-speed properties of a phase-modulation scheme based on electromagnetically induced transparency,” Opt. Lett. 23, 1007–1009 (1998).
[CrossRef]

H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef] [PubMed]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Imoto, N.

Jin, S.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

Joshi, A.

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319 (2005).
[CrossRef]

A. Joshi and M. Xiao, “Generalized dark-state polaritons for photon memory in multilevel atomic media,” Phys. Rev. A 71, 041801(R) (2005).
[CrossRef]

Kang, H.

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

Kang, Z. H.

Kimble, H. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Lange, W.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Li, A. J.

Li, J.

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

Li, S. J.

X. D. Yang, S. J. Li, C. H. Zhang, and H. Wang, “Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system,” J. Opt. Soc. Am. B 26, 1423–1434 (2009).
[CrossRef]

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef] [PubMed]

Li, Y.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

Lin, Q.

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

Liu, Y. H.

Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
[CrossRef]

Lukin, M. D.

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef] [PubMed]

Mabuchi, H.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoğlu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Marzlin, K. P.

Z. B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in R87b,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef] [PubMed]

Munro, W. J.

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137-1–137-12 (2005).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Nemoto, K.

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137-1–137-12 (2005).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Ottaviani, C.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi,“Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef] [PubMed]

Özdemir, S. K.

Peng, K. C.

Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
[CrossRef]

Poizat, J. -Ph.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Rebic, S.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Rickey, E. G.

M. Yan, E. G. Rickey, and Y. Zhu, “Suppression of two-photon absorption by quantum interference,” Phys. Rev. A 64, 043807 (2001).
[CrossRef]

Roch, J. -F.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Rubin, M. H.

J. M. Wen, S. W. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

Sanders, B. C.

Z. B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in R87b,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef] [PubMed]

Schmidt, H.

Shapiro, H.

H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

Sinatra, A.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Smith, D. A.

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
[CrossRef]

Spiller, T. P.

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137-1–137-12 (2005).
[CrossRef]

Tombesi, P.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi,“Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef] [PubMed]

Turchette, Q. A.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Vigneron, K.

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Vitali, D.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi,“Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef] [PubMed]

Wang, C. L.

Wang, C. Y.

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef] [PubMed]

Wang, H.

X. D. Yang, S. J. Li, C. H. Zhang, and H. Wang, “Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system,” J. Opt. Soc. Am. B 26, 1423–1434 (2009).
[CrossRef]

Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
[CrossRef]

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef] [PubMed]

Wang, S. H.

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef] [PubMed]

Wang, Z. B.

Z. B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in R87b,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef] [PubMed]

Wen, J. M.

J. M. Wen, S. W. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

Xiao, J. T.

Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
[CrossRef]

Xiao, M.

Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
[CrossRef]

J. M. Wen, S. W. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

A. Joshi and M. Xiao, “Generalized dark-state polaritons for photon memory in multilevel atomic media,” Phys. Rev. A 71, 041801(R) (2005).
[CrossRef]

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319 (2005).
[CrossRef]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

Xiao, Y. F.

Xie, C. D.

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef] [PubMed]

Yan, M.

M. Yan, E. G. Rickey, and Y. Zhu, “Suppression of two-photon absorption by quantum interference,” Phys. Rev. A 64, 043807 (2001).
[CrossRef]

Yang, L.

Yang, X. D.

X. D. Yang, S. J. Li, C. H. Zhang, and H. Wang, “Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system,” J. Opt. Soc. Am. B 26, 1423–1434 (2009).
[CrossRef]

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef] [PubMed]

Yu, I. A.

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef] [PubMed]

Yun, J.

Zhang, C. H.

X. D. Yang, S. J. Li, C. H. Zhang, and H. Wang, “Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system,” J. Opt. Soc. Am. B 26, 1423–1434 (2009).
[CrossRef]

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef] [PubMed]

Zhang, Y. P.

J. M. Wen, S. W. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

Zhou, X. Y.

Zhu, Y.

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

M. Yan, E. G. Rickey, and Y. Zhu, “Suppression of two-photon absorption by quantum interference,” Phys. Rev. A 64, 043807 (2001).
[CrossRef]

Am. J. Phys. (1)

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
[CrossRef]

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

J. Phys. B (1)

S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2001).
[CrossRef]

New J. Phys. (1)

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137-1–137-12 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (9)

A. Joshi and M. Xiao, “Generalized dark-state polaritons for photon memory in multilevel atomic media,” Phys. Rev. A 71, 041801(R) (2005).
[CrossRef]

J. M. Wen, S. W. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

Y. X. Han, J. T. Xiao, Y. H. Liu, H. Wang, M. Xiao, and K. C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A 77, 023824 (2008).
[CrossRef]

M. Yan, E. G. Rickey, and Y. Zhu, “Suppression of two-photon absorption by quantum interference,” Phys. Rev. A 64, 043807 (2001).
[CrossRef]

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319 (2005).
[CrossRef]

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

Phys. Rev. Lett. (12)

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67, 3062–3065 (1991).
[CrossRef] [PubMed]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef] [PubMed]

J.-F. Roch, K. Vigneron, Ph. Grelu, A. Sinatra, J.-Ph. Poizat, and Ph. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi,“Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef] [PubMed]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef] [PubMed]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Z. B. Wang, K. P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in R87b,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef] [PubMed]

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef] [PubMed]

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[CrossRef] [PubMed]

S. J. Li, X. D. Yang, X. M. Cao, C. H. Zhang, C. D. Xie, and H. Wang, “Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system,” Phys. Rev. Lett. 101, 073602 (2008).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoğlu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Relevant energy levels of R 87 b atoms and laser excitations in the experiment.

Fig. 2
Fig. 2

Schematic of the experimental setup: λ / 2 , half-wave plate; PBS, polarizing beam splitter; PD, photodiode; M, reflecting mirror; PZT, piezoelectric transducer; M1, M2, M3, and M4 compose a Mach–Zehnder interferometer, and the experiment is performed in a post-selection regime.

Fig. 3
Fig. 3

Probe absorption as a function of the probe frequency detuning. The solid curves are the experimental results, and the dashed curves are the corresponding theoretical simulations, with parameters Ω C = 30   MHz , Ω k = 10   MHz .

Fig. 4
Fig. 4

Measured dispersion curves (solid curves) of probe transition (a) without and (b) with the control field, the XPM phase shift Φ XPM 5 ° , and the dashed curves are the corresponding theoretical simulations, with parameters Ω C = 30   MHz and Ω k = 0   MHz for (a), and Ω k = 15   MHz for (b).

Fig. 5
Fig. 5

XPM phase shift as a function of the control field intensity.

Equations (4)

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

H = ( Δ p Δ C ) | 2 2 | + Δ p | 3 3 | + ( Δ p + Δ k ) | 4 4 | [ Ω p | 3 1 | + Ω C | 3 2 | + Ω k | 4 3 | + c .c . ] .
ρ 13 = Ω p [ 1 Δ 13 Ω C 2 / Δ 12 + Ω k 2 ( Δ 13 Ω C 2 / Δ 12 ) 2 Δ 14 ] ,
χ = | μ 31 | 2 ε 0 Ω p + ρ 13 ( Δ p ) N ( v ) d v ,
Δ I d ( ω ) 2 | E R | | E P | exp [ α ( ω ) L / 2 ] cos ( φ 0 + k p n ( ω ) L ) ,

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