Abstract

We report on an experimental demonstration of applying the beat-note interferometer to simultaneously measure the phase and amplitude variations of light pulses after propagating through an electromagnetically induced transparency medium at femtowatt-light levels. Furthermore, we observe that the measured phase noise approaches the shot-noise level arising from the fluctuations of detected photons.

© 2010 OSA

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References

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  1. D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).
  2. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
  3. 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]
  4. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
    [Crossref] [PubMed]
  5. 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]
  6. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
    [Crossref] [PubMed]
  7. N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3, 95–98 (2009).
    [Crossref]
  8. H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
    [Crossref]
  9. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
    [Crossref]
  10. M. Fleischhauer, A. Imamoğlu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [Crossref]
  11. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
    [Crossref]
  12. H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
    [Crossref] [PubMed]
  13. S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
    [Crossref]
  14. 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] [PubMed]
  15. 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] [PubMed]
  16. Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, and I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30, 3207–3209 (2005).
    [Crossref] [PubMed]
  17. 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]
  18. 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]
  19. A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319 (2005).
    [Crossref]
  20. B. He, Y.-H. Ren, and J. A Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. At. Mol. Opt. Phys. 43, 025502 (2010).
    [Crossref]
  21. A. V. Gorshkov, J. Otterbach, E. Demler, M. Fleischhauer, and M. D. Lukin, “Photonic phase gate via an exchange of fermionic spin waves in a spin chain,” arXiv:1001.0968v2 [quant-ph] (2010).
  22. Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, “Beat-note interferometer for direct phase measurement of photonic information,” Phys. Rev. A 72, 033812 (2005).
    [Crossref]
  23. M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
    [Crossref] [PubMed]
  24. M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory,” Phys. Rev. A 74, 013812 (2006).
    [Crossref]
  25. G. F. Sinclair, “Time-dependent cross-phase-modulation in 87Rb,” Phys. Rev. A 79, 023815 (2009).
    [Crossref]

2010 (1)

B. He, Y.-H. Ren, and J. A Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. At. Mol. Opt. Phys. 43, 025502 (2010).
[Crossref]

2009 (3)

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3, 95–98 (2009).
[Crossref]

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[Crossref]

G. F. Sinclair, “Time-dependent cross-phase-modulation in 87Rb,” Phys. Rev. A 79, 023815 (2009).
[Crossref]

2008 (1)

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

2006 (2)

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]

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory,” Phys. Rev. A 74, 013812 (2006).
[Crossref]

2005 (4)

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

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, “Beat-note interferometer for direct phase measurement of photonic information,” Phys. Rev. A 72, 033812 (2005).
[Crossref]

Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, and I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30, 3207–3209 (2005).
[Crossref] [PubMed]

2004 (1)

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]

2003 (1)

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]

2001 (3)

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] [PubMed]

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] [PubMed]

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

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]

1999 (1)

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[Crossref]

1998 (1)

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)

1995 (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]

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]

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] [PubMed]

Bergou, J. A

B. He, Y.-H. Ren, and J. A Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. At. Mol. Opt. Phys. 43, 025502 (2010).
[Crossref]

Bochmann, J.

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[Crossref]

Bouwmeester, D.

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).

Camacho, R. M.

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory,” Phys. Rev. A 74, 013812 (2006).
[Crossref]

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]

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, “Beat-note interferometer for direct phase measurement of photonic information,” Phys. Rev. A 72, 033812 (2005).
[Crossref]

Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, and I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30, 3207–3209 (2005).
[Crossref] [PubMed]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

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]

Demler, E.

A. V. Gorshkov, J. Otterbach, E. Demler, M. Fleischhauer, and M. D. Lukin, “Photonic phase gate via an exchange of fermionic spin waves in a spin chain,” arXiv:1001.0968v2 [quant-ph] (2010).

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] [PubMed]

Edamatsu, K.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3, 95–98 (2009).
[Crossref]

Ekert, A. K.

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).

Englund, D.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

Faraon, A.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

Figueroa, E.

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[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] [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]

A. V. Gorshkov, J. Otterbach, E. Demler, M. Fleischhauer, and M. D. Lukin, “Photonic phase gate via an exchange of fermionic spin waves in a spin chain,” arXiv:1001.0968v2 [quant-ph] (2010).

Fushman, I.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

Gorshkov, A. V.

A. V. Gorshkov, J. Otterbach, E. Demler, M. Fleischhauer, and M. D. Lukin, “Photonic phase gate via an exchange of fermionic spin waves in a spin chain,” arXiv:1001.0968v2 [quant-ph] (2010).

Harris, S. E.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (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]

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] [PubMed]

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[Crossref]

He, B.

B. He, Y.-H. Ren, and J. A Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. At. Mol. Opt. Phys. 43, 025502 (2010).
[Crossref]

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]

Howell, J. C.

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory,” Phys. Rev. A 74, 013812 (2006).
[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, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[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]

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

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]

Kosaka, H.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3, 95–98 (2009).
[Crossref]

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]

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] [PubMed]

Liu, Y.-C.

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, “Beat-note interferometer for direct phase measurement of photonic information,” Phys. Rev. A 72, 033812 (2005).
[Crossref]

Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, and I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30, 3207–3209 (2005).
[Crossref] [PubMed]

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] [PubMed]

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

A. V. Gorshkov, J. Otterbach, E. Demler, M. Fleischhauer, and M. D. Lukin, “Photonic phase gate via an exchange of fermionic spin waves in a spin chain,” arXiv:1001.0968v2 [quant-ph] (2010).

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]

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] [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]

Matsuda, N.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3, 95–98 (2009).
[Crossref]

Mitsumori, Y.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3, 95–98 (2009).
[Crossref]

Moehring, D. L.

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[Crossref]

Mücke, M.

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[Crossref]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

Ottaviani, C.

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]

Otterbach, J.

A. V. Gorshkov, J. Otterbach, E. Demler, M. Fleischhauer, and M. D. Lukin, “Photonic phase gate via an exchange of fermionic spin waves in a spin chain,” arXiv:1001.0968v2 [quant-ph] (2010).

Pack, M. V.

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory,” Phys. Rev. A 74, 013812 (2006).
[Crossref]

Petroff, P.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

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] [PubMed]

Rebic, S.

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]

Rempe, G.

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[Crossref]

Ren, Y.-H.

B. He, Y.-H. Ren, and J. A Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. At. Mol. Opt. Phys. 43, 025502 (2010).
[Crossref]

Schmidt, H.

Shimizu, R.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3, 95–98 (2009).
[Crossref]

Sinclair, G. F.

G. F. Sinclair, “Time-dependent cross-phase-modulation in 87Rb,” Phys. Rev. A 79, 023815 (2009).
[Crossref]

Specht, H. P.

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[Crossref]

Stoltz, N.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

Tombesi, P.

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]

Tsai, Z.-H.

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, “Beat-note interferometer for direct phase measurement of photonic information,” Phys. Rev. A 72, 033812 (2005).
[Crossref]

Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, and I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30, 3207–3209 (2005).
[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]

Vitali, D.

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]

Vuckovic, J.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

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] [PubMed]

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, 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]

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, “Beat-note interferometer for direct phase measurement of photonic information,” Phys. Rev. A 72, 033812 (2005).
[Crossref]

Weber, B.

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[Crossref]

Xiao, M.

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

Yamamoto, Y.

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

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]

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, “Beat-note interferometer for direct phase measurement of photonic information,” Phys. Rev. A 72, 033812 (2005).
[Crossref]

Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, and I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30, 3207–3209 (2005).
[Crossref] [PubMed]

Zeilinger, A.

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).

J. Phys. At. Mol. Opt. Phys. (1)

B. He, Y.-H. Ren, and J. A Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. At. Mol. Opt. Phys. 43, 025502 (2010).
[Crossref]

Nat. Photonics (1)

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3, 95–98 (2009).
[Crossref]

Nature (2)

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

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] [PubMed]

Nature Photon. (1)

H. P. Specht, J. Bochmann, M. Mücke, B. Weber, E. Figueroa, D. L. Moehring, and G. Rempe, “Phase shaping of single-photon wave packets,” Nature Photon. 3, 469–472 (2009).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (5)

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory,” Phys. Rev. A 74, 013812 (2006).
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G. F. Sinclair, “Time-dependent cross-phase-modulation in 87Rb,” Phys. Rev. A 79, 023815 (2009).
[Crossref]

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, “Beat-note interferometer for direct phase measurement of photonic information,” Phys. Rev. A 72, 033812 (2005).
[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]

Phys. Rev. Lett. (7)

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

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[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. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[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] [PubMed]

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]

Phys. Today (1)

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

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

Science (1)

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320, 769–772 (2008).
[Crossref] [PubMed]

Other (3)

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

A. V. Gorshkov, J. Otterbach, E. Demler, M. Fleischhauer, and M. D. Lukin, “Photonic phase gate via an exchange of fermionic spin waves in a spin chain,” arXiv:1001.0968v2 [quant-ph] (2010).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Three-level Λ-scheme used for EIT in 87Rb D 2 line. (b) A schematic diagram of the experimental setup. BS, beam splitter; HWP, half-wave plate; QWP, quarter-wave plate; POL, polarizer; SM Fiber, single-mode fiber; AOM, acousto-optic modulator; PD, photo detector; PMT, photomultiplier tube. The 1/e diameters of probe and coupling beams are around 1 and 5 mm, respectively.

Fig. 2.
Fig. 2.

The beat-note amplitude (squares) and corresponding phase noise (circles) as a function of the peak power of probe pulse. Black and red dashed curves are fits of f = a I 1 p + b and g = p I 1 p + q , respectively. a = 6 . 22 [ mV pW ] , b = 0.88 mV, p = 0.016 [ rad · pW ] and q = 0.006 rad. The gain of PMT module is about 9 × 107 V/W.

Fig. 3.
Fig. 3.

(a) Observed EIT transmission versus probe laser detuning. The inset shows the EIT transmission window. (b) Measured phase shift of a light pulse induced by an EIT medium. Filled circles represent the peak power of light pulses below 10 fW. Red dashed lines in (a) and (b) correspond to theoretical curves calculated by Eqs. (1) and (2), respectively. The parameters for the theoretical curves in both figures are the same: 13 L = 16, γ 21 = 0.002Γ, γ 31 = 1.25Γ, Ω c = 0.31Γ, and Δ c = −0.7 MHz.

Fig. 4.
Fig. 4.

Measured phase noise versus number of average on oscilloscope. The red dashed line is a fitting curve based on equation h = α/√N + β, where α = 11.03 [rad · √N] and β = 0.009 rad.

Equations (4)

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T = exp [ n σ 13 L γ 31 4 δ 2 γ 31 + γ 21 ( Ω c 2 + γ 21 γ 31 ) ( Ω c 2 + γ 21 γ 31 4 p δ ) 2 + 4 ( p γ 21 + δ γ 31 ) 2 ] ,
φ EIT = n σ 13 L γ 31 δ ( Ω c 2 4 p δ ) p γ 21 2 ( Ω c 2 + γ 21 γ 31 4 p δ ) 2 + 4 ( p γ 21 + δ γ 31 ) 2 ,
I ref = I 0 r + I 1 r + 2 I 0 r I 1 r cos ( ω a t + φ r ) ,
I pro = I 0 p + I 1 p + 2 I 0 p I 1 p cos ( ω a t + φ p + φ ) ,

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