Abstract

We demonstrate the simultaneous propagation of slow- and fast-light optical pulses in a four-wave mixing scheme using warm potassium vapor. We show that when the system is tuned such that the input probe pulses exhibit slow-light group velocities and the generated pulses propagate with negative group velocities, the information velocity in the medium is nonetheless constrained to propagate at, or less than, c. These results demonstrate that the transfer and copying of information on optical pulses to those with negative group velocities obeys information causality, in a manner that is reminiscent of a classical version of the no-cloning theorem. Additionally, these results support the fundamental concept that points of non-analyticity on optical pulses correspond to carriers of new information.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  37. B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” European Phys. J. D - Atomic, Molecular Opt. Phys. 23, 125–141 (2003).
  38. R. T. Glasser, U. Vogl, and P. D. Lett, “Stimulated generation of superluminal light pulses via four-wave mixing,” Phys. Rev. Lett. 108, 173902 (2012).
    [Crossref] [PubMed]
  39. R. T. Glasser, U. Vogl, and P. D. Lett, “Demonstration of images with negative group velocities,” Opt. Express 20, 13702–13710 (2012).
    [Crossref] [PubMed]
  40. Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
    [Crossref] [PubMed]

2016 (6)

B. P. Abbott and et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

B. Macke and B. Ségard, “Simultaneous slow and fast light involving the Faraday effect,” Phys. Rev. A 94, 043801 (2016).
[Crossref]

A. H. Dorrah and M. Mojahedi, “Nonanalytic pulse discontinuities as carriers of information,” Phys. Rev. A 93, 013823 (2016).
[Crossref]

H. Amano and M. Tomita, “Influence of finite bandwidth on the propagation of information in fast- and slow-light media,” Phys. Rev. A 93, 063854 (2016).
[Crossref]

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13, 015205 (2016).
[Crossref]

2014 (2)

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

M. Tomita, H. Amano, S. Masegi, and A. I. Talukder, “Direct observation of a pulse peak using a peak-removed Gaussian optical pulse in a superluminal medium,” Phys. Rev. Lett. 112, 093903 (2014).
[Crossref] [PubMed]

2013 (1)

R. Suzuki and M. Tomita, “Causal propagation of nonanalytical points in fast- and slow-light media,” Phys. Rev. A 88, 053822 (2013).
[Crossref]

2012 (2)

R. T. Glasser, U. Vogl, and P. D. Lett, “Stimulated generation of superluminal light pulses via four-wave mixing,” Phys. Rev. Lett. 108, 173902 (2012).
[Crossref] [PubMed]

R. T. Glasser, U. Vogl, and P. D. Lett, “Demonstration of images with negative group velocities,” Opt. Express 20, 13702–13710 (2012).
[Crossref] [PubMed]

2011 (1)

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, “Causal information velocity in fast and slow pulse propagation in an optical ring resonator,” Phys. Rev. A 84, 043843 (2011).
[Crossref]

2009 (1)

R. W. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908–1915 (2009).
[Crossref]

2008 (2)

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Observation of simultaneous fast and slow light,” Phys. Rev. A 77, 053816 (2008).
[Crossref]

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (3)

H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep. 436, 1–69 (2006).
[Crossref]

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys.: Condensed Matter 18, 3117–3126 (2006).

L. Masanes, A. Acin, and N. Gisin, “General properties of nonsignaling theories,” Phys. Rev. A 73, 012112 (2006).
[Crossref]

2005 (1)

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “Fast causal information transmission in a medium with a slow group velocity,” Phys. Rev. Lett. 94, 053902 (2005).
[Crossref] [PubMed]

2004 (2)

D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. M. Hickmann, “Fast light, slow light, and phase singularities: a connection to ceneralized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[Crossref]

M. C. Parker and S. D. Walker, “Information transfer and Landauer’s principle,” Opt. Commun. 229, 23–27 (2004).
[Crossref]

2003 (3)

B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” European Phys. J. D - Atomic, Molecular Opt. Phys. 23, 125–141 (2003).

G. Nimtz, “On superluminal tunneling,” Prog. Quantum Electron. 27, 417–450 (2003).
[Crossref]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ’fast-light’ optical medium,” Nature 425, 695–698 (2003).
[Crossref] [PubMed]

2002 (1)

C. de Carvalho and H. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
[Crossref]

2001 (1)

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001).
[Crossref] [PubMed]

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref] [PubMed]

1998 (1)

J. Garrison, M. Mitchell, R. Chiao, and E. Bolda, “Superluminal signals: causal loop paradoxes revisited,” Phys. Rev. A 245, 19–25 (1998).

1994 (1)

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).
[Crossref] [PubMed]

1982 (1)

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[Crossref]

1972 (1)

J. C. Hafele and R. E. Keating, “Around-the-world atomic clocks: predicted relativistic time gains,” Science 177, 166–168 (1972).
[Crossref] [PubMed]

1938 (1)

1905 (1)

A. Einstein, “Zur Elektrodynamik bewegter Körper,” Annalen der Physik 322, 891–921 (1905).
[Crossref]

1898 (1)

H. A. Lorentz, “Simplified theory of electrical and optical phenomena in moving systems,” Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 1, 427–442 (1898).

1887 (1)

A. A. Michelson and E. W. Morley, “On the Relative Motion of the Earth and of the Luminiferous Ether,” Sidereal Messenger 6, 306–310 (1887).

1865 (1)

J. C. Maxwell, “A Dynamical Theory of the Electromagnetic Field,” Philosophical Trans. Royal Soc. London 155, 459–512 (1865).
[Crossref]

Abbott, B. P.

B. P. Abbott and et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Acin, A.

L. Masanes, A. Acin, and N. Gisin, “General properties of nonsignaling theories,” Phys. Rev. A 73, 012112 (2006).
[Crossref]

Amano, H.

H. Amano and M. Tomita, “Influence of finite bandwidth on the propagation of information in fast- and slow-light media,” Phys. Rev. A 93, 063854 (2016).
[Crossref]

M. Tomita, H. Amano, S. Masegi, and A. I. Talukder, “Direct observation of a pulse peak using a peak-removed Gaussian optical pulse in a superluminal medium,” Phys. Rev. Lett. 112, 093903 (2014).
[Crossref] [PubMed]

Arimondo, E.

Asano, M.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Bianucci, P.

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Observation of simultaneous fast and slow light,” Phys. Rev. A 77, 053816 (2008).
[Crossref]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys.: Condensed Matter 18, 3117–3126 (2006).

Bliokh, K. Y.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Bliokh, Y. P.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Bolda, E.

J. Garrison, M. Mitchell, R. Chiao, and E. Bolda, “Superluminal signals: causal loop paradoxes revisited,” Phys. Rev. A 245, 19–25 (1998).

Boyd, R. W.

R. W. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908–1915 (2009).
[Crossref]

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys.: Condensed Matter 18, 3117–3126 (2006).

Boyer, V.

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Chiao, R.

J. Garrison, M. Mitchell, R. Chiao, and E. Bolda, “Superluminal signals: causal loop paradoxes revisited,” Phys. Rev. A 245, 19–25 (1998).

Chiao, R. Y.

D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. M. Hickmann, “Fast light, slow light, and phase singularities: a connection to ceneralized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[Crossref]

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001).
[Crossref] [PubMed]

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).
[Crossref] [PubMed]

Chu, S.

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[Crossref]

Clark, J. B.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

de Carvalho, C.

C. de Carvalho and H. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
[Crossref]

Dogariu, A.

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001).
[Crossref] [PubMed]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref] [PubMed]

Dorrah, A. H.

A. H. Dorrah and M. Mojahedi, “Nonanalytic pulse discontinuities as carriers of information,” Phys. Rev. A 93, 013823 (2016).
[Crossref]

Einstein, A.

A. Einstein, “Zur Elektrodynamik bewegter Körper,” Annalen der Physik 322, 891–921 (1905).
[Crossref]

Fietz, C. R.

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Observation of simultaneous fast and slow light,” Phys. Rev. A 77, 053816 (2008).
[Crossref]

Galison, P.

P. Galison, Einstein’s Clocks and Poincaré’s Maps: Empires of Time (W.W. Norton, 2003).

Garrison, J.

J. Garrison, M. Mitchell, R. Chiao, and E. Bolda, “Superluminal signals: causal loop paradoxes revisited,” Phys. Rev. A 245, 19–25 (1998).

Gauthier, D. J.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “Fast causal information transmission in a medium with a slow group velocity,” Phys. Rev. Lett. 94, 053902 (2005).
[Crossref] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ’fast-light’ optical medium,” Nature 425, 695–698 (2003).
[Crossref] [PubMed]

Gisin, N.

L. Masanes, A. Acin, and N. Gisin, “General properties of nonsignaling theories,” Phys. Rev. A 73, 012112 (2006).
[Crossref]

Glasser, R. T.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

R. T. Glasser, U. Vogl, and P. D. Lett, “Stimulated generation of superluminal light pulses via four-wave mixing,” Phys. Rev. Lett. 108, 173902 (2012).
[Crossref] [PubMed]

R. T. Glasser, U. Vogl, and P. D. Lett, “Demonstration of images with negative group velocities,” Opt. Express 20, 13702–13710 (2012).
[Crossref] [PubMed]

Glorieux, Q.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

Hafele, J. C.

J. C. Hafele and R. E. Keating, “Around-the-world atomic clocks: predicted relativistic time gains,” Science 177, 166–168 (1972).
[Crossref] [PubMed]

Hickmann, J. M.

D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. M. Hickmann, “Fast light, slow light, and phase singularities: a connection to ceneralized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[Crossref]

Hohensee, M.

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

Ikuta, R.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Imoto, N.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Ives, H. E.

Jelenkovic, B. M.

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13, 015205 (2016).
[Crossref]

Jiang, L.

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

Jones, K. M.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

Keating, R. E.

J. C. Hafele and R. E. Keating, “Around-the-world atomic clocks: predicted relativistic time gains,” Science 177, 166–168 (1972).
[Crossref] [PubMed]

Kivshar, Y. S.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Klein, M.

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

Kofman, A. G.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Krmpot, A. J.

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13, 015205 (2016).
[Crossref]

Kuzmich, A.

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001).
[Crossref] [PubMed]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref] [PubMed]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys.: Condensed Matter 18, 3117–3126 (2006).

Lett, P. D.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

R. T. Glasser, U. Vogl, and P. D. Lett, “Stimulated generation of superluminal light pulses via four-wave mixing,” Phys. Rev. Lett. 108, 173902 (2012).
[Crossref] [PubMed]

R. T. Glasser, U. Vogl, and P. D. Lett, “Demonstration of images with negative group velocities,” Opt. Express 20, 13702–13710 (2012).
[Crossref] [PubMed]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178 (2007).
[Crossref]

Li, T.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

Lorentz, H. A.

H. A. Lorentz, “Simplified theory of electrical and optical phenomena in moving systems,” Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 1, 427–442 (1898).

Lukin, M. D.

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

Macke, B.

B. Macke and B. Ségard, “Simultaneous slow and fast light involving the Faraday effect,” Phys. Rev. A 94, 043801 (2016).
[Crossref]

B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” European Phys. J. D - Atomic, Molecular Opt. Phys. 23, 125–141 (2003).

Masanes, L.

L. Masanes, A. Acin, and N. Gisin, “General properties of nonsignaling theories,” Phys. Rev. A 73, 012112 (2006).
[Crossref]

Masegi, S.

M. Tomita, H. Amano, S. Masegi, and A. I. Talukder, “Direct observation of a pulse peak using a peak-removed Gaussian optical pulse in a superluminal medium,” Phys. Rev. Lett. 112, 093903 (2014).
[Crossref] [PubMed]

Maxwell, J. C.

J. C. Maxwell, “A Dynamical Theory of the Electromagnetic Field,” Philosophical Trans. Royal Soc. London 155, 459–512 (1865).
[Crossref]

McCormick, C. F.

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178 (2007).
[Crossref]

D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. M. Hickmann, “Fast light, slow light, and phase singularities: a connection to ceneralized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[Crossref]

Michelson, A. A.

A. A. Michelson and E. W. Morley, “On the Relative Motion of the Earth and of the Luminiferous Ether,” Sidereal Messenger 6, 306–310 (1887).

Milonni, P. W.

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001).
[Crossref] [PubMed]

Mitchell, M.

J. Garrison, M. Mitchell, R. Chiao, and E. Bolda, “Superluminal signals: causal loop paradoxes revisited,” Phys. Rev. A 245, 19–25 (1998).

Mojahedi, M.

A. H. Dorrah and M. Mojahedi, “Nonanalytic pulse discontinuities as carriers of information,” Phys. Rev. A 93, 013823 (2016).
[Crossref]

Morley, E. W.

A. A. Michelson and E. W. Morley, “On the Relative Motion of the Earth and of the Luminiferous Ether,” Sidereal Messenger 6, 306–310 (1887).

Neifeld, M. A.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “Fast causal information transmission in a medium with a slow group velocity,” Phys. Rev. Lett. 94, 053902 (2005).
[Crossref] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ’fast-light’ optical medium,” Nature 425, 695–698 (2003).
[Crossref] [PubMed]

Nimtz, G.

G. Nimtz, “On superluminal tunneling,” Prog. Quantum Electron. 27, 417–450 (2003).
[Crossref]

Nori, F.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Nussenzveig, H.

C. de Carvalho and H. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
[Crossref]

Oishi, T.

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, “Causal information velocity in fast and slow pulse propagation in an optical ring resonator,” Phys. Rev. A 84, 043843 (2011).
[Crossref]

Özdemir, K.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Parker, M. C.

M. C. Parker and S. D. Walker, “Information transfer and Landauer’s principle,” Opt. Commun. 229, 23–27 (2004).
[Crossref]

Phillips, D. F.

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

Poincaré, H.

H. Poincaré, Science and Hypothesis (Science, 1905).

Popescu, S.

D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. M. Hickmann, “Fast light, slow light, and phase singularities: a connection to ceneralized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[Crossref]

Radonjic, M.

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13, 015205 (2016).
[Crossref]

Robertson, J. W.

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Observation of simultaneous fast and slow light,” Phys. Rev. A 77, 053816 (2008).
[Crossref]

Ségard, B.

B. Macke and B. Ségard, “Simultaneous slow and fast light involving the Faraday effect,” Phys. Rev. A 94, 043801 (2016).
[Crossref]

B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” European Phys. J. D - Atomic, Molecular Opt. Phys. 23, 125–141 (2003).

Shih, C.-K.

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Observation of simultaneous fast and slow light,” Phys. Rev. A 77, 053816 (2008).
[Crossref]

Shin, H.

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys.: Condensed Matter 18, 3117–3126 (2006).

Shvets, G.

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Observation of simultaneous fast and slow light,” Phys. Rev. A 77, 053816 (2008).
[Crossref]

Šibalic, N.

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13, 015205 (2016).
[Crossref]

Solli, D. R.

D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. M. Hickmann, “Fast light, slow light, and phase singularities: a connection to ceneralized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[Crossref]

Steinberg, A. M.

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).
[Crossref] [PubMed]

Stenner, M. D.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “Fast causal information transmission in a medium with a slow group velocity,” Phys. Rev. Lett. 94, 053902 (2005).
[Crossref] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ’fast-light’ optical medium,” Nature 425, 695–698 (2003).
[Crossref] [PubMed]

Stilwell, G. R.

Sultana, P.

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, “Causal information velocity in fast and slow pulse propagation in an optical ring resonator,” Phys. Rev. A 84, 043843 (2011).
[Crossref]

Suzuki, R.

R. Suzuki and M. Tomita, “Causal propagation of nonanalytical points in fast- and slow-light media,” Phys. Rev. A 88, 053822 (2013).
[Crossref]

Talukder, A. I.

M. Tomita, H. Amano, S. Masegi, and A. I. Talukder, “Direct observation of a pulse peak using a peak-removed Gaussian optical pulse in a superluminal medium,” Phys. Rev. Lett. 112, 093903 (2014).
[Crossref] [PubMed]

Tomita, M.

H. Amano and M. Tomita, “Influence of finite bandwidth on the propagation of information in fast- and slow-light media,” Phys. Rev. A 93, 063854 (2016).
[Crossref]

M. Tomita, H. Amano, S. Masegi, and A. I. Talukder, “Direct observation of a pulse peak using a peak-removed Gaussian optical pulse in a superluminal medium,” Phys. Rev. Lett. 112, 093903 (2014).
[Crossref] [PubMed]

R. Suzuki and M. Tomita, “Causal propagation of nonanalytical points in fast- and slow-light media,” Phys. Rev. A 88, 053822 (2013).
[Crossref]

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, “Causal information velocity in fast and slow pulse propagation in an optical ring resonator,” Phys. Rev. A 84, 043843 (2011).
[Crossref]

Uesugi, H.

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, “Causal information velocity in fast and slow pulse propagation in an optical ring resonator,” Phys. Rev. A 84, 043843 (2011).
[Crossref]

Vogl, U.

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

R. T. Glasser, U. Vogl, and P. D. Lett, “Stimulated generation of superluminal light pulses via four-wave mixing,” Phys. Rev. Lett. 108, 173902 (2012).
[Crossref] [PubMed]

R. T. Glasser, U. Vogl, and P. D. Lett, “Demonstration of images with negative group velocities,” Opt. Express 20, 13702–13710 (2012).
[Crossref] [PubMed]

Walker, S. D.

M. C. Parker and S. D. Walker, “Information transfer and Landauer’s principle,” Opt. Commun. 229, 23–27 (2004).
[Crossref]

Walsworth, R. L.

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

Wang, L. J.

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001).
[Crossref] [PubMed]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref] [PubMed]

Winful, H. G.

H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep. 436, 1–69 (2006).
[Crossref]

Wong, S.

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[Crossref]

Xiao, Y.

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

Yamamoto, T.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Yang, L.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Zlatkovic, B.

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13, 015205 (2016).
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European Phys. J. D - Atomic, Molecular Opt. Phys. (1)

B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” European Phys. J. D - Atomic, Molecular Opt. Phys. 23, 125–141 (2003).

J. Mod. Opt. (1)

R. W. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908–1915 (2009).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys.: Condensed Matter (1)

M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys.: Condensed Matter 18, 3117–3126 (2006).

Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings (1)

H. A. Lorentz, “Simplified theory of electrical and optical phenomena in moving systems,” Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 1, 427–442 (1898).

Laser Phys. Lett. (1)

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13, 015205 (2016).
[Crossref]

Nat. Commun. (1)

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7, 13488 (2016).
[Crossref] [PubMed]

Nat. Photonics (1)

J. B. Clark, R. T. Glasser, Q. Glorieux, U. Vogl, T. Li, K. M. Jones, and P. D. Lett, “Quantum mutual information of an entangled state propagating through a fast-light medium,” Nat. Photonics 8, 515–519 (2014).
[Crossref]

Nature (2)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “The speed of information in a ’fast-light’ optical medium,” Nature 425, 695–698 (2003).
[Crossref] [PubMed]

Opt. Commun. (1)

M. C. Parker and S. D. Walker, “Information transfer and Landauer’s principle,” Opt. Commun. 229, 23–27 (2004).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Philosophical Trans. Royal Soc. London (1)

J. C. Maxwell, “A Dynamical Theory of the Electromagnetic Field,” Philosophical Trans. Royal Soc. London 155, 459–512 (1865).
[Crossref]

Phys. Rep. (2)

C. de Carvalho and H. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
[Crossref]

H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep. 436, 1–69 (2006).
[Crossref]

Phys. Rev. A (9)

P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Observation of simultaneous fast and slow light,” Phys. Rev. A 77, 053816 (2008).
[Crossref]

R. Suzuki and M. Tomita, “Causal propagation of nonanalytical points in fast- and slow-light media,” Phys. Rev. A 88, 053822 (2013).
[Crossref]

B. Macke and B. Ségard, “Simultaneous slow and fast light involving the Faraday effect,” Phys. Rev. A 94, 043801 (2016).
[Crossref]

A. H. Dorrah and M. Mojahedi, “Nonanalytic pulse discontinuities as carriers of information,” Phys. Rev. A 93, 013823 (2016).
[Crossref]

H. Amano and M. Tomita, “Influence of finite bandwidth on the propagation of information in fast- and slow-light media,” Phys. Rev. A 93, 063854 (2016).
[Crossref]

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, “Causal information velocity in fast and slow pulse propagation in an optical ring resonator,” Phys. Rev. A 84, 043843 (2011).
[Crossref]

L. Masanes, A. Acin, and N. Gisin, “General properties of nonsignaling theories,” Phys. Rev. A 73, 012112 (2006).
[Crossref]

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).
[Crossref] [PubMed]

J. Garrison, M. Mitchell, R. Chiao, and E. Bolda, “Superluminal signals: causal loop paradoxes revisited,” Phys. Rev. A 245, 19–25 (1998).

Phys. Rev. Lett. (8)

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[Crossref]

B. P. Abbott and et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, “Fast causal information transmission in a medium with a slow group velocity,” Phys. Rev. Lett. 94, 053902 (2005).
[Crossref] [PubMed]

M. Tomita, H. Amano, S. Masegi, and A. I. Talukder, “Direct observation of a pulse peak using a peak-removed Gaussian optical pulse in a superluminal medium,” Phys. Rev. Lett. 112, 093903 (2014).
[Crossref] [PubMed]

D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. M. Hickmann, “Fast light, slow light, and phase singularities: a connection to ceneralized weak values,” Phys. Rev. Lett. 92, 043601 (2004).
[Crossref]

A. Kuzmich, A. Dogariu, L. J. Wang, P. W. Milonni, and R. Y. Chiao, “Signal velocity, causality, and quantum noise in superluminal light pulse propagation,” Phys. Rev. Lett. 86, 3925–3929 (2001).
[Crossref] [PubMed]

R. T. Glasser, U. Vogl, and P. D. Lett, “Stimulated generation of superluminal light pulses via four-wave mixing,” Phys. Rev. Lett. 108, 173902 (2012).
[Crossref] [PubMed]

Y. Xiao, M. Klein, M. Hohensee, L. Jiang, D. F. Phillips, M. D. Lukin, and R. L. Walsworth, “Slow light beam splitter,” Phys. Rev. Lett. 101, 043601 (2008).
[Crossref] [PubMed]

Prog. Quantum Electron. (1)

G. Nimtz, “On superluminal tunneling,” Prog. Quantum Electron. 27, 417–450 (2003).
[Crossref]

Science (1)

J. C. Hafele and R. E. Keating, “Around-the-world atomic clocks: predicted relativistic time gains,” Science 177, 166–168 (1972).
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Sidereal Messenger (1)

A. A. Michelson and E. W. Morley, “On the Relative Motion of the Earth and of the Luminiferous Ether,” Sidereal Messenger 6, 306–310 (1887).

Other (3)

H. Poincaré, Science and Hypothesis (Science, 1905).

P. Galison, Einstein’s Clocks and Poincaré’s Maps: Empires of Time (W.W. Norton, 2003).

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

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Figures (6)

Fig. 1
Fig. 1 Spacetime diagrams for information flow between two causally connected events through (a) free space and (b) a simultaneously fast- and slow-light medium of length L. In both cases, the black dotted line represents information flow. The red and blue lines in (b) correspond to optical pulses with group velocities which are slow (vg < c) and fast (negative, vg < 0), respectively.
Fig. 2
Fig. 2 Depiction of the four-wave mixing copier. The probe input is seeded with an input pulse (shown in red), and the process generates a copy of the input (blue). The arrival times of the pulses are compared with a reference of the speed of light in air (black). The inset shows an energy level diagram which summarizes the four-wave mixing process. The hyperfine ground state splitting in potassium is ΔHFS = 462 MHz.
Fig. 3
Fig. 3 Simultaneous slow and fast light. (a) Normalized intensities of detected pulses when the medium is tuned so that the probe and conjugate pulses are delayed and advanced, respectively, with respect to the reference pulse. (b) Relative (center-of-mass) advancement and calculated distortion as a function of spatial position over the conjugate mode. Pulses are advanced for x < 0, delayed for x > 0 and travel approximately at c near x = 0. The inset shows a normalized intensity image of the conjugate mode, with the dotted line indicating the position of the iris used in the measurement.
Fig. 4
Fig. 4 Arrival of new information in simultaneously slow- and fast-light media. (a) Normalized pulse intensities when the new information is placed on the leading edge of the pulse. The probe and conjugate modes are delayed and advanced by 14% and 5%, respectively. (b) Normalized pulse intensities when the new information is placed on the trailing edge of the pulse. The delay and advancement are 11% and 8%, respectively. In both (a) and (b), the discontinuity is displaced from the peak of the input pulse by τ/2, τ/4 or coincident with the peak (bottom row). Example pulses without the (approximately) non-analytic point are shown in the top row.
Fig. 5
Fig. 5 Information transfer in the unity gain regime. (Top) Pulse intensities when the probe is strongly absorbed and the effective total gain is 0.94 ± 0.13. The inset displays the pulses normalized to the reference peak intensity, revealing that the conjugate channel is virtually dispersion-free and and probe is delayed by 26%. New information is placed on the leading edge of the input pulse, either τ/2 away from the reference peak (middle) or at the peak (bottom). The information signal is barely visible on the probe, whereas the relative signal intensity on the conjugate is nearly one, thus demonstrating information transfer to the conjugate.
Fig. 6
Fig. 6 Information velocity and fast light. (a) Normalized pulse intensities for various pump detunings, with the discontinuity placed on the trailing edges of the pulses. Due to pulse reshaping, fast light is associated with a reduction in the intensity of the information signal, for both the probe and conjugate pulses. (b) Center-of-mass advancements and arrival times of the information signal, for the probe and conjugate data shown in (a). The COM shifts are shown in solid lines for the probe (red) and conjugate (blue), and the dashed-dotted lines correspond to the relative arrival times of τsig, the information signal. Despite the group velocity advancements, both information signals always travels slower than the reference.

Tables (1)

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Table 1 Experimental parameters

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