Abstract

The group velocity of light becomes superluminal in a medium with a tuned negative dispersion, using two gain peaks, for example. Inside a laser, however, the gain is constant, equaling the loss. We show here that the effective dispersion experienced by the lasing frequency is still sensitive to the spectral profile of the unsaturated gain. In particular, a dip in the gain profile leads to a superluminal group velocity for the lasing mode. The displacement sensitivity of the lasing frequency is enhanced by nearly five orders of magnitude, leading to a versatile sensor of hyper sensitivity.

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References

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  1. M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
    [CrossRef]
  2. G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
    [CrossRef]
  3. G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99(13), 133601 (2007).
    [CrossRef] [PubMed]
  4. M. S. Shahriar and M. Salit, “Application of fast-light in gravitational wave detection with interferometers and resonators,” J. Mod. Opt. 55(19), 3133–3147 (2008).
    [CrossRef]
  5. A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
    [CrossRef]
  6. R. H. Rinkleff and A. Wicht, “The concept of white light cavities using atomic phase coherence,” Phys. Scr. T 118, 85–88 (2005).
    [CrossRef]
  7. R. Fleischhaker and J. Evers, “Four wave mixing enhanced white-light cavity,” Phys. Rev. A 78(5), 051802 (2008).
    [CrossRef]
  8. H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77(3), 031801 (2008).
    [CrossRef]
  9. A. Rocco, A. Wicht, R. H. Rinkleff, and K. Danzmann, “Anomalous dispersion of transparent atomic two- and three-level ensembles,” Phys. Rev. A 66(5), 053804 (2002).
    [CrossRef]
  10. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000).
    [CrossRef] [PubMed]
  11. J. S. Toll, “Causality and the dispersion relation: logical foundation,” Phys. Rev. 104(6), 1760–1770 (1956).
    [CrossRef]
  12. H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
    [CrossRef]
  13. G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45A, 393 (1973).
  14. H. Yum, and M. S. Shahriar, “Pump-probe model for the Kramers-Kronig relations in a laser,” to appear in J. Opt. (preprint can be viewed at http://arxiv.org/abs/1003.3686 )
  15. M. O. Scully, and W. E. Lamb, Laser Physics, (Westview Press, Boulder, CO, 1974).
  16. M. O. Scully, and M. S. Zubairy, Quantum Optics, (Cambridge University Press, New York, NY, 1997).
  17. W. F. Krupke, R. J. Beach, V. K. Kanz, and S. A. Payne, “Resonance transition 795-nm rubidium laser,” Opt. Lett. 28(23), 2336–2338 (2003).
    [CrossRef] [PubMed]
  18. G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
    [CrossRef] [PubMed]

2009 (1)

2008 (4)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[CrossRef]

M. S. Shahriar and M. Salit, “Application of fast-light in gravitational wave detection with interferometers and resonators,” J. Mod. Opt. 55(19), 3133–3147 (2008).
[CrossRef]

R. Fleischhaker and J. Evers, “Four wave mixing enhanced white-light cavity,” Phys. Rev. A 78(5), 051802 (2008).
[CrossRef]

H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77(3), 031801 (2008).
[CrossRef]

2007 (2)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99(13), 133601 (2007).
[CrossRef] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

2005 (1)

R. H. Rinkleff and A. Wicht, “The concept of white light cavities using atomic phase coherence,” Phys. Scr. T 118, 85–88 (2005).
[CrossRef]

2003 (1)

2002 (1)

A. Rocco, A. Wicht, R. H. Rinkleff, and K. Danzmann, “Anomalous dispersion of transparent atomic two- and three-level ensembles,” Phys. Rev. A 66(5), 053804 (2002).
[CrossRef]

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000).
[CrossRef] [PubMed]

1997 (1)

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
[CrossRef]

1973 (1)

G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45A, 393 (1973).

1969 (1)

H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
[CrossRef]

1956 (1)

J. S. Toll, “Causality and the dispersion relation: logical foundation,” Phys. Rev. 104(6), 1760–1770 (1956).
[CrossRef]

Bambini, A.

G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45A, 393 (1973).

Beach, R. J.

Bolton, H. C.

H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
[CrossRef]

Danzmann, K.

A. Rocco, A. Wicht, R. H. Rinkleff, and K. Danzmann, “Anomalous dispersion of transparent atomic two- and three-level ensembles,” Phys. Rev. A 66(5), 053804 (2002).
[CrossRef]

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
[CrossRef]

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000).
[CrossRef] [PubMed]

Evers, J.

R. Fleischhaker and J. Evers, “Four wave mixing enhanced white-light cavity,” Phys. Rev. A 78(5), 051802 (2008).
[CrossRef]

Fleischhaker, R.

R. Fleischhaker and J. Evers, “Four wave mixing enhanced white-light cavity,” Phys. Rev. A 78(5), 051802 (2008).
[CrossRef]

Fleischhauer, M.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
[CrossRef]

Gopal, V.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Kanz, V. K.

Krupke, W. F.

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000).
[CrossRef] [PubMed]

Messall, M.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Miiller, G.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
[CrossRef]

Pati, G. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[CrossRef] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[CrossRef]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99(13), 133601 (2007).
[CrossRef] [PubMed]

Payne, S. A.

Rinkleff, R. H.

R. H. Rinkleff and A. Wicht, “The concept of white light cavities using atomic phase coherence,” Phys. Scr. T 118, 85–88 (2005).
[CrossRef]

A. Rocco, A. Wicht, R. H. Rinkleff, and K. Danzmann, “Anomalous dispersion of transparent atomic two- and three-level ensembles,” Phys. Rev. A 66(5), 053804 (2002).
[CrossRef]

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
[CrossRef]

Rocco, A.

A. Rocco, A. Wicht, R. H. Rinkleff, and K. Danzmann, “Anomalous dispersion of transparent atomic two- and three-level ensembles,” Phys. Rev. A 66(5), 053804 (2002).
[CrossRef]

Salit, K.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[CrossRef] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[CrossRef]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99(13), 133601 (2007).
[CrossRef] [PubMed]

Salit, M.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[CrossRef] [PubMed]

M. S. Shahriar and M. Salit, “Application of fast-light in gravitational wave detection with interferometers and resonators,” J. Mod. Opt. 55(19), 3133–3147 (2008).
[CrossRef]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[CrossRef]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99(13), 133601 (2007).
[CrossRef] [PubMed]

Scully, M.

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
[CrossRef]

Shahriar, M. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[CrossRef] [PubMed]

M. S. Shahriar and M. Salit, “Application of fast-light in gravitational wave detection with interferometers and resonators,” J. Mod. Opt. 55(19), 3133–3147 (2008).
[CrossRef]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[CrossRef]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99(13), 133601 (2007).
[CrossRef] [PubMed]

Toll, J. S.

J. S. Toll, “Causality and the dispersion relation: logical foundation,” Phys. Rev. 104(6), 1760–1770 (1956).
[CrossRef]

Tripathi, R.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Troup, G. J.

G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45A, 393 (1973).

H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
[CrossRef]

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000).
[CrossRef] [PubMed]

Wicht, A.

R. H. Rinkleff and A. Wicht, “The concept of white light cavities using atomic phase coherence,” Phys. Scr. T 118, 85–88 (2005).
[CrossRef]

A. Rocco, A. Wicht, R. H. Rinkleff, and K. Danzmann, “Anomalous dispersion of transparent atomic two- and three-level ensembles,” Phys. Rev. A 66(5), 053804 (2002).
[CrossRef]

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
[CrossRef]

Wu, H.

H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77(3), 031801 (2008).
[CrossRef]

Xiao, M.

H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77(3), 031801 (2008).
[CrossRef]

J. Mod. Opt. (1)

M. S. Shahriar and M. Salit, “Application of fast-light in gravitational wave detection with interferometers and resonators,” J. Mod. Opt. 55(19), 3133–3147 (2008).
[CrossRef]

Nature (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000).
[CrossRef] [PubMed]

Opt. Commun. (2)

A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, and R. H. Rinkleff, “White-light cavities, atomic phase coherence, and gravitational wave detectors,” Opt. Commun. 134(1-6), 431–439 (1997).
[CrossRef]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Philos. Mag. (1)

H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
[CrossRef]

Phys. Lett. (1)

G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45A, 393 (1973).

Phys. Rev. (1)

J. S. Toll, “Causality and the dispersion relation: logical foundation,” Phys. Rev. 104(6), 1760–1770 (1956).
[CrossRef]

Phys. Rev. A (4)

R. Fleischhaker and J. Evers, “Four wave mixing enhanced white-light cavity,” Phys. Rev. A 78(5), 051802 (2008).
[CrossRef]

H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77(3), 031801 (2008).
[CrossRef]

A. Rocco, A. Wicht, R. H. Rinkleff, and K. Danzmann, “Anomalous dispersion of transparent atomic two- and three-level ensembles,” Phys. Rev. A 66(5), 053804 (2002).
[CrossRef]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A 75(5), 053807 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. 99(13), 133601 (2007).
[CrossRef] [PubMed]

Phys. Scr. T (1)

R. H. Rinkleff and A. Wicht, “The concept of white light cavities using atomic phase coherence,” Phys. Scr. T 118, 85–88 (2005).
[CrossRef]

Other (3)

H. Yum, and M. S. Shahriar, “Pump-probe model for the Kramers-Kronig relations in a laser,” to appear in J. Opt. (preprint can be viewed at http://arxiv.org/abs/1003.3686 )

M. O. Scully, and W. E. Lamb, Laser Physics, (Westview Press, Boulder, CO, 1974).

M. O. Scully, and M. S. Zubairy, Quantum Optics, (Cambridge University Press, New York, NY, 1997).

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Figures (4)

Fig. 1
Fig. 1

Real part of the steady-state susceptibility for the combined absorbing and amplifying media (solid line), and the conventional gain medium (dashed line). The inset shows an expanded view of the solid line in the main figure

Fig. 2
Fig. 2

Sensitivity enhancement associated with Eq. (2). The inset (a) shows R in Eq. (2) in an expanded view (solid line), and its value in the linear limit (dotted line). The inset (b) is an expanded view of R with a linear vertical scale.

Fig. 3
Fig. 3

Illustration of relation between L−L0 and ν−ν0 for |ν−ν0|/2π<80MHz. Dotted line shows the behavior for an empty cavity. The inset shows an expanded view for |ν−ν0|/2π<100kHz.

Fig. 4
Fig. 4

Energy levels for (a) 795-nm Rb laser to produce broadband gain, (b) Raman depletion to induce narrowband absorption dip. (c) Schematics of the experimental set-up to realize a superluminal laser: PBS, polarizing beam splitter; BS, beam splitter; AOM, acousto-optic modulator. Note that the superluminal laser is the same as the Raman pump. The scheme shown is for 85Rb atoms. The broadband gain is produced by side-pumping with a diode laser array.

Equations (5)

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

ν + φ ˙ = Ω χ ( E , ν ) 2 ν
E ˙ = ν E 2 Q χ ( E , ν ) E 2 ν
R = 1 / [ 1 + χ 2 + ν 2 d χ d ν ]
χ = G e Γ e 2 ϑ e + G i Γ i 2 ϑ i
χ = 2 G e ( ν ν 0 ) Γ e ϑ e 2 G i ( ν ν 0 ) Γ i ϑ i

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