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 Optical Society of America

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  1. D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, New York, 2000).
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    [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).
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  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," Nat. Photonics 3, 469-472 (2009).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  23. M. D. Lukin, and A. Imamoǧlu, "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]
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    [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," Nat. Photonics 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. Imamoǧlu, 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. Imamoǧlu, "Controlling photons using electromagnetically induced transparency," Nature 413, 273-276 (2001).
[CrossRef] [PubMed]

2000 (1)

M. D. Lukin, and A. Imamoǧlu, "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," Nat. Photonics 3, 469-472 (2009).
[CrossRef]

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, 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]

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]

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]

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]

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," Nat. Photonics 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. Imamoǧlu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

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]

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. Imamoǧlu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

M. D. Lukin, and A. Imamoǧlu, "Controlling photons using electromagnetically induced transparency," Nature 413, 273-276 (2001).
[CrossRef] [PubMed]

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

H. Schmidt, and A. Imamoǧlu, "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, 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]

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]

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. Imamoǧlu, "Controlling photons using electromagnetically induced transparency," Nature 413, 273-276 (2001).
[CrossRef] [PubMed]

M. D. Lukin, and A. Imamoǧlu, "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]

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. Imamoǧlu, 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," Nat. Photonics 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," Nat. Photonics 3, 469-472 (2009).
[CrossRef]

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]

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," Nat. Photonics 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," Nat. Photonics 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, 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]

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]

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," Nat. Photonics 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]

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 (2)

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," Nat. Photonics 3, 469-472 (2009).
[CrossRef]

Nature (2)

M. D. Lukin, and A. Imamoǧlu, "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]

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).
[CrossRef]

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. Imamoǧlu, "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]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoǧlu, 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)

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

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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