Abstract

We report the experimental demonstration of the superluminal propagation of multi-spatial-mode images via four-wave mixing in hot atomic vapor, in which all spatial sub-regions propagate with negative group velocities. We investigate the spatial mode properties and temporal reshaping of the fast light images, and show large relative pulse peak advancements of up to 64 % of the input pulse width. The degree of temporal reshaping is quantified and increases as the relative pulse peak advancement increases. When optimized for image quality or pulse advancement, negative group velocities of up to vg=c880 and vg=c2180, respectively, are demonstrated when integrating temporally over the entire image. The present results are applicable to temporal cloaking devices that require strong manipulation of the dispersion relation, where one can envision temporally cloaking various spatial regions of an image for different durations. Additionally, the modes involved in a four-wave mixing process similar to the present experiment have been shown to exhibit quantum correlations and entanglement. The results presented here provide insight into how to tailor experimental tests of the behavior of these quantum correlations and entanglement in the superluminal regime.

© 2012 OSA

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  1. C. Garrett and D. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
    [CrossRef]
  2. S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
    [CrossRef]
  3. B. Ségard and B. Macke, “Observation of negative velocity pulse propagation,” Phys. Lett. 109, 213–216 (1985).
    [CrossRef]
  4. B. Ségard, B. Macke, and F. Wielonsky, “Optimal superluminal systems,” Phys. Rev. E 72, 035601 (2005).
    [CrossRef]
  5. R. Y. Chiao and P. W. Milonni, “Fast light, slow light,” Opt. Photon. News 13, 26–30 (2002).
    [CrossRef]
  6. A. M. Akulshin and R. J. McLean, “Fast light in atomic media,” J. Opt. 12, 104001 (2010).
    [CrossRef]
  7. E. L. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
    [CrossRef] [PubMed]
  8. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
    [CrossRef] [PubMed]
  9. E. E. Mikhailov, V. A. Sautenkov, I. Novikova, and G. R. Welch, “Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas,” Phys. Rev. A 69, 063808 (2004).
    [CrossRef]
  10. N. Brunner, V. Scarani, V. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93, 203902 (2004).
    [CrossRef] [PubMed]
  11. M. Gonzalez-Herraez, K.-Y. Song, and L. Thevenaz, “Optically controlled slow and fast light in optical fibers using stimulated brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
    [CrossRef]
  12. 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]
  13. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature (London) 406, 277–279 (2000).
    [CrossRef]
  14. 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]
  15. R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 178–180 (2002).
  16. R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
    [CrossRef] [PubMed]
  17. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
    [CrossRef] [PubMed]
  18. M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature (London) 481, 62 (2012).
    [CrossRef]
  19. J. P. Torres, M. Hendrych, and A. Valencia, “Angular dispersion: an enabling tool in nonlinear and quantum optics,” Adv. Opt. Photon. 2, 319–369 (2010).
    [CrossRef]
  20. P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374–378 (1994).
    [CrossRef]
  21. 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. Condens. Matter 18, 3117 (2006).
    [CrossRef]
  22. B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” Eur. Phys. J. D 23, 125–141 (2003).
    [CrossRef]
  23. R. W. Boyd, D. Gauthier, and P. Narum, “Causality in superluminal pulse propagation” in Time in Quantum Mechanics2, G. Muga, A. Ruschhaupt, and A. del Campo, eds. (Springer, 2009), pp. 175–202.
    [CrossRef]
  24. 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]
  25. V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
    [CrossRef] [PubMed]
  26. V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
    [CrossRef] [PubMed]

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]

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature (London) 481, 62 (2012).
[CrossRef]

2010 (2)

2008 (2)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

2007 (3)

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[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]

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[CrossRef] [PubMed]

2006 (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. Condens. Matter 18, 3117 (2006).
[CrossRef]

2005 (2)

M. Gonzalez-Herraez, K.-Y. Song, and L. Thevenaz, “Optically controlled slow and fast light in optical fibers using stimulated brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

B. Ségard, B. Macke, and F. Wielonsky, “Optimal superluminal systems,” Phys. Rev. E 72, 035601 (2005).
[CrossRef]

2004 (2)

E. E. Mikhailov, V. A. Sautenkov, I. Novikova, and G. R. Welch, “Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas,” Phys. Rev. A 69, 063808 (2004).
[CrossRef]

N. Brunner, V. Scarani, V. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

2003 (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” Eur. Phys. J. D 23, 125–141 (2003).
[CrossRef]

2002 (2)

R. Y. Chiao and P. W. Milonni, “Fast light, slow light,” Opt. Photon. News 13, 26–30 (2002).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 178–180 (2002).

2000 (1)

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

1994 (3)

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]

E. L. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
[CrossRef] [PubMed]

P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374–378 (1994).
[CrossRef]

1985 (1)

B. Ségard and B. Macke, “Observation of negative velocity pulse propagation,” Phys. Lett. 109, 213–216 (1985).
[CrossRef]

1982 (1)

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

1970 (1)

C. Garrett and D. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[CrossRef]

Akulshin, A. M.

A. M. Akulshin and R. J. McLean, “Fast light in atomic media,” J. Opt. 12, 104001 (2010).
[CrossRef]

Ali-Khan, I.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[CrossRef] [PubMed]

Arimondo, E.

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]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

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. Condens. Matter 18, 3117 (2006).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

Bolda, E. L.

E. L. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
[CrossRef] [PubMed]

Boyd, R. W.

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. Condens. Matter 18, 3117 (2006).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 178–180 (2002).

R. W. Boyd, D. Gauthier, and P. Narum, “Causality in superluminal pulse propagation” in Time in Quantum Mechanics2, G. Muga, A. Ruschhaupt, and A. del Campo, eds. (Springer, 2009), pp. 175–202.
[CrossRef]

Boyer, V.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[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]

Broadbent, C. J.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[CrossRef] [PubMed]

Brunner, N.

N. Brunner, V. Scarani, V. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Camacho, R. M.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[CrossRef] [PubMed]

Chiao, R. Y.

R. Y. Chiao and P. W. Milonni, “Fast light, slow light,” Opt. Photon. News 13, 26–30 (2002).
[CrossRef]

E. L. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
[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]

Dogariu, A.

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

Farsi, A.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature (London) 481, 62 (2012).
[CrossRef]

Fridman, M.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature (London) 481, 62 (2012).
[CrossRef]

Gaeta, A. L.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature (London) 481, 62 (2012).
[CrossRef]

Garrett, C.

C. Garrett and D. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[CrossRef]

Garrison, J. C.

E. L. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
[CrossRef] [PubMed]

Gauthier, D.

R. W. Boyd, D. Gauthier, and P. Narum, “Causality in superluminal pulse propagation” in Time in Quantum Mechanics2, G. Muga, A. Ruschhaupt, and A. del Campo, eds. (Springer, 2009), pp. 175–202.
[CrossRef]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 178–180 (2002).

Gisin, N.

N. Brunner, V. Scarani, V. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Glasser, R. T.

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]

Gonzalez-Herraez, M.

M. Gonzalez-Herraez, K.-Y. Song, and L. Thevenaz, “Optically controlled slow and fast light in optical fibers using stimulated brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Hendrych, M.

Howell, J. C.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[CrossRef] [PubMed]

Kolobov, M. I.

P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374–378 (1994).
[CrossRef]

Kumar, P.

P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374–378 (1994).
[CrossRef]

Kuzmich, A.

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

Legré, M.

N. Brunner, V. Scarani, V. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93, 203902 (2004).
[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. Condens. Matter 18, 3117 (2006).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

Lett, P. D.

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]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[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]

Macke, B.

B. Ségard, B. Macke, and F. Wielonsky, “Optimal superluminal systems,” Phys. Rev. E 72, 035601 (2005).
[CrossRef]

B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” Eur. Phys. J. D 23, 125–141 (2003).
[CrossRef]

B. Ségard and B. Macke, “Observation of negative velocity pulse propagation,” Phys. Lett. 109, 213–216 (1985).
[CrossRef]

Marino, A. M.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

McCormick, C. F.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[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]

McCumber, D.

C. Garrett and D. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[CrossRef]

McLean, R. J.

A. M. Akulshin and R. J. McLean, “Fast light in atomic media,” J. Opt. 12, 104001 (2010).
[CrossRef]

Mikhailov, E. E.

E. E. Mikhailov, V. A. Sautenkov, I. Novikova, and G. R. Welch, “Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas,” Phys. Rev. A 69, 063808 (2004).
[CrossRef]

Milonni, P. W.

R. Y. Chiao and P. W. Milonni, “Fast light, slow light,” Opt. Photon. News 13, 26–30 (2002).
[CrossRef]

Narum, P.

R. W. Boyd, D. Gauthier, and P. Narum, “Causality in superluminal pulse propagation” in Time in Quantum Mechanics2, G. Muga, A. Ruschhaupt, and A. del Campo, eds. (Springer, 2009), pp. 175–202.
[CrossRef]

Novikova, I.

E. E. Mikhailov, V. A. Sautenkov, I. Novikova, and G. R. Welch, “Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas,” Phys. Rev. A 69, 063808 (2004).
[CrossRef]

Okawachi, Y.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature (London) 481, 62 (2012).
[CrossRef]

Pooser, R. C.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[CrossRef] [PubMed]

Sautenkov, V. A.

E. E. Mikhailov, V. A. Sautenkov, I. Novikova, and G. R. Welch, “Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas,” Phys. Rev. A 69, 063808 (2004).
[CrossRef]

Scarani, V.

N. Brunner, V. Scarani, V. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Ségard, B.

B. Ségard, B. Macke, and F. Wielonsky, “Optimal superluminal systems,” Phys. Rev. E 72, 035601 (2005).
[CrossRef]

B. Macke and B. Ségard, “Propagation of light-pulses at a negative group-velocity,” Eur. Phys. J. D 23, 125–141 (2003).
[CrossRef]

B. Ségard and B. Macke, “Observation of negative velocity pulse propagation,” Phys. Lett. 109, 213–216 (1985).
[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. Condens. Matter 18, 3117 (2006).
[CrossRef]

Song, K.-Y.

M. Gonzalez-Herraez, K.-Y. Song, and L. Thevenaz, “Optically controlled slow and fast light in optical fibers using stimulated brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[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]

Thevenaz, L.

M. Gonzalez-Herraez, K.-Y. Song, and L. Thevenaz, “Optically controlled slow and fast light in optical fibers using stimulated brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Torres, J. P.

Valencia, A.

Vogl, U.

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]

Wang, L. J.

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

Wegmüller, V.

N. Brunner, V. Scarani, V. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93, 203902 (2004).
[CrossRef] [PubMed]

Welch, G. R.

E. E. Mikhailov, V. A. Sautenkov, I. Novikova, and G. R. Welch, “Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas,” Phys. Rev. A 69, 063808 (2004).
[CrossRef]

Wielonsky, F.

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Figures (4)

Fig. 1
Fig. 1

Schematic showing (1a) the double-lambda level scheme, (1b) the typical probe gain lineshape with probe detuning indicated, and (1c) the experimental setup. The pump beam is detuned ≈ 400 MHz to the blue of the 85Rb D1 line, with the probe blue-detuned ≈ 3.0 GHz relative to the pump. The probe’s center frequency is set to be on the blue wing of the probe gain line. After the 4WM interaction, the probe pulses are imaged onto a gated, intensified CCD camera. The pulses are able to be time-resolved down to 2.44 ns temporal bins.

Fig. 2
Fig. 2

Negative group velocity of a carrier pulse resulting in an advanced pulse peak with a spatially multi-mode image, in this case the letter “c”. The green curve is the detected probe pulse, integrated over the image, when the pump is not present. The red curve is the detected superluminal amplified probe pulse, integrated over the image, when the pump is turned on. A relative advancement of ≈ 50 ns, corresponding to a group velocity of v g = c 880, is shown. The probe pulse in this measurement was shaped with the letter c, and the arrival time was monitored with a gating width of 3 ns. The snapshots across the top of the graph show the cross section of the beam at equidistant times between 120 ns and 480 ns (top row: reference, lower row: superluminal pulse). The two insets show the full time-integrated images. The advanced image (left inset) shows distortion due to inhomogeneous gain, Kerr-lensing and leaked pump light, but the principal shape clearly persists. The superluminal pulse group velocity can be determined pixel-wise for the image, as well as integrated over the whole image. The peak gain of the unnormalized superluminal pulse is ≈ 2.1.

Fig. 3
Fig. 3

Gain (3a) and relative pulse peak advancement (3b) of the superluminal probe pulses for the input probe with a Gaussian spot. Each superpixel corresponds to a 12×12 binning of pixels on an intensified CCD camera. The pump beam is slightly elliptical, with a waist of ≈ 750μm×950μm. Relative pulse peak advancement is seen to increase from ≈ 40 ns to ≈ 100 ns from the right-hand side to the left-hand side of the probe spot. The gain also varies spatially, with the highest gain regions corresponding to the lowest relative pulse peak advancements. The ellipses correspond to the 1/e2 intensity of the detected amplified probe spots. Uncertainties in the relative pulse peak advancement are largest toward the edges of the image (≈ 10 ns), due to statistical uncertainties from a decreased signal-to-noise ratio resulting from the lower intensities. The uncertainty in the relative advancement near the inner region of the image is ≈ 3 ns, resulting from the minimum detector gating time.

Fig. 4
Fig. 4

Plot of the advanced pulse versus time when the system is optimized for maximum advancement rather than image quality. The red and green curves are the advanced pulse and reference pulse intensities integrated over the entire Gaussian spot. A pulse peak advancement of 124 ns is shown, corresponding to a relative pulse peak advancement of 64 % compared to the input pulse FWHM, and a group velocity of v g = c 2180. The gain in this case is ≈ 5, and the relative degree of reshaping is D ≈ 0.8. Ringing on the trailing edge of the advanced pulse is seen, as expected for very large relative advancements.

Equations (4)

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v g = c n g = c n ( ν ) + n ( ν ) d n ( ν ) d ν ,
D = | | E ( z + L , t ) | 2 | E ( z + L , t ) | 2 d t | E ( z , t Δ T ) | 2 | E ( z , t Δ T ) | 2 d t | d t .
T adv , = T adv τ a + τ a β
T adv , = T adv τ a τ a β .

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