Abstract

Slow light based on transient spectral hole-burning is reported for emerald, Be3Al2Si6O18:Cr3+. Experiments were conducted in π polarization on the R1(±3/2) line (E2A24) at 2.2 K in zero field and low magnetic fields Bc. The hole width was strongly dependent on Bc, and this allowed us to smoothly tune the pulse delay from 40 to 154 ns between zero field and Bc=15.2mT. The latter corresponds to a group velocity of 16km/s. Slow light in conjunction with a linear filter theory can be used as a powerful and accurate technique in time-resolved spectroscopy, e.g., to determine spectral hole-widths as a function of time.

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  1. R. W. Boyd and D. J. Gauthier, ““Slow” and “fast” light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), pp. 497–530.
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    [CrossRef]
  3. R. W. Boyd, J. Mod. Opt. 56, 1908 (2009).
    [CrossRef]
  4. A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3733 (1991).
    [CrossRef]
  8. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
    [CrossRef]
  9. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
    [CrossRef]
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2012

2010

A. C. Selden, Opt. Express 18, 13204 (2010).
[CrossRef]

V. S. Zapasskii and G. G. Kozlov, Opt. Spectrosc. 109, 407 (2010).
[CrossRef]

2009

A. C. Selden, Opt. Spectrosc. 106, 881 (2009).
[CrossRef]

R. W. Boyd, J. Mod. Opt. 56, 1908 (2009).
[CrossRef]

R. Lauro, T. Chanelière, and J. L. Le Gouët, Phys. Rev. A 79, 063844 (2009).
[CrossRef]

2008

2007

A. Rebane, R. N. Shakhmuratov, P. Mégret, and J. Odeurs, Phys. Rev. A 127, 22 (2007).

2006

H. Riesen, Coord. Chem. Rev. 250, 1737 (2006).
[CrossRef]

2005

R. N. Shakhmuratov, A. Rebane, P. Mégret, and J. Odeurs, Phys. Rev. A 71, 053811 (2005).
[CrossRef]

R. Kolesov, Phys. Rev. A 72, 051801 (2005).
[CrossRef]

B. F. Hayward and H. Riesen, Phys. Chem. Chem. Phys. 7, 2579 (2005).
[CrossRef]

2004

2003

H. Riesen, Chem. Phys. Lett. 382, 578 (2003).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef]

1999

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

1995

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[CrossRef]

1992

1991

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3733 (1991).
[CrossRef]

1985

B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
[CrossRef]

1983

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

1967

S. E. Schwarz and T. Y. Tan, Appl. Phys. Lett. 10, 4 (1967).
[CrossRef]

Akulshin, A. M.

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

Barreiro, S.

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef]

Boller, K. J.

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

Boyd, R. W.

R. W. Boyd, J. Mod. Opt. 56, 1908 (2009).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef]

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

R. W. Boyd and D. J. Gauthier, ““Slow” and “fast” light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), pp. 497–530.

Budker, D.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

Carceller, I.

Chanelière, T.

R. Lauro, T. Chanelière, and J. L. Le Gouët, Phys. Rev. A 79, 063844 (2009).
[CrossRef]

Chang, S.-W.

Chang-Hasnain, C. J.

Chuang, S.-L.

Dubicki, L.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Field, J. E.

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3733 (1991).
[CrossRef]

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, ““Slow” and “fast” light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), pp. 497–530.

Hahn, J.

Hahn, K. H.

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3733 (1991).
[CrossRef]

Ham, B. S.

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[CrossRef]

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3733 (1991).
[CrossRef]

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Hayward, B. F.

B. F. Hayward and H. Riesen, Phys. Chem. Chem. Phys. 7, 2579 (2005).
[CrossRef]

Hillman, L. W.

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Hutton, D. R.

Imamolu, A.

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

Jain, M.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[CrossRef]

Kasapi, A.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[CrossRef]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Kimball, D. F.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

Kolesov, R.

R. Kolesov, Phys. Rev. A 72, 051801 (2005).
[CrossRef]

Kozlov, G. G.

V. S. Zapasskii and G. G. Kozlov, Opt. Spectrosc. 109, 407 (2010).
[CrossRef]

Krasinski, J.

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

Krauss, T. F.

T. F. Krauss, Nat. Photonics 2, 448 (2008).
[CrossRef]

Ku, P.-C.

Lauro, R.

R. Lauro, T. Chanelière, and J. L. Le Gouët, Phys. Rev. A 79, 063844 (2009).
[CrossRef]

Le Gouët, J. L.

R. Lauro, T. Chanelière, and J. L. Le Gouët, Phys. Rev. A 79, 063844 (2009).
[CrossRef]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef]

Lezama, A.

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

Li, T.

Lukin, M. D.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Macke, B.

B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
[CrossRef]

Manson, N. B.

Mégret, P.

A. Rebane, R. N. Shakhmuratov, P. Mégret, and J. Odeurs, Phys. Rev. A 127, 22 (2007).

R. N. Shakhmuratov, A. Rebane, P. Mégret, and J. Odeurs, Phys. Rev. A 71, 053811 (2005).
[CrossRef]

Nussenzveig, H. M.

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, 1972).

Odeurs, J.

A. Rebane, R. N. Shakhmuratov, P. Mégret, and J. Odeurs, Phys. Rev. A 127, 22 (2007).

R. N. Shakhmuratov, A. Rebane, P. Mégret, and J. Odeurs, Phys. Rev. A 71, 053811 (2005).
[CrossRef]

Palinginis, P.

Rebane, A.

A. Rebane, R. N. Shakhmuratov, P. Mégret, and J. Odeurs, Phys. Rev. A 127, 22 (2007).

R. N. Shakhmuratov, A. Rebane, P. Mégret, and J. Odeurs, Phys. Rev. A 71, 053811 (2005).
[CrossRef]

Rebane, A. K.

Riesen, H.

H. Riesen, A. K. Rebane, A. Szabo, and I. Carceller, Opt. Express 20, 19039 (2012).
[CrossRef]

H. Riesen, Coord. Chem. Rev. 250, 1737 (2006).
[CrossRef]

B. F. Hayward and H. Riesen, Phys. Chem. Chem. Phys. 7, 2579 (2005).
[CrossRef]

H. Riesen, Chem. Phys. Lett. 382, 578 (2003).
[CrossRef]

Rigby, N. E.

Rochester, S. M.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Schwarz, S. E.

S. E. Schwarz and T. Y. Tan, Appl. Phys. Lett. 10, 4 (1967).
[CrossRef]

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Sedgwick, F.

Segard, B.

B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
[CrossRef]

Selden, A. C.

A. C. Selden, Opt. Express 18, 13204 (2010).
[CrossRef]

A. C. Selden, Opt. Spectrosc. 106, 881 (2009).
[CrossRef]

Shakhmuratov, R. N.

A. Rebane, R. N. Shakhmuratov, P. Mégret, and J. Odeurs, Phys. Rev. A 127, 22 (2007).

R. N. Shakhmuratov, A. Rebane, P. Mégret, and J. Odeurs, Phys. Rev. A 71, 053811 (2005).
[CrossRef]

Stroud, C. R.

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

Szabo, A.

Tan, T. Y.

S. E. Schwarz and T. Y. Tan, Appl. Phys. Lett. 10, 4 (1967).
[CrossRef]

Troup, G. J.

Wang, H.

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Yashchuk, V. V.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

Yin, G. Y.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[CrossRef]

Zapasskii, V. S.

V. S. Zapasskii and G. G. Kozlov, Opt. Spectrosc. 109, 407 (2010).
[CrossRef]

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Appl. Phys. Lett.

S. E. Schwarz and T. Y. Tan, Appl. Phys. Lett. 10, 4 (1967).
[CrossRef]

Chem. Phys. Lett.

H. Riesen, Chem. Phys. Lett. 382, 578 (2003).
[CrossRef]

Coord. Chem. Rev.

H. Riesen, Coord. Chem. Rev. 250, 1737 (2006).
[CrossRef]

J. Mod. Opt.

R. W. Boyd, J. Mod. Opt. 56, 1908 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

T. F. Krauss, Nat. Photonics 2, 448 (2008).
[CrossRef]

Nature

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Opt. Commun.

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

A. C. Selden, Opt. Spectrosc. 106, 881 (2009).
[CrossRef]

V. S. Zapasskii and G. G. Kozlov, Opt. Spectrosc. 109, 407 (2010).
[CrossRef]

Phys. Chem. Chem. Phys.

B. F. Hayward and H. Riesen, Phys. Chem. Chem. Phys. 7, 2579 (2005).
[CrossRef]

Phys. Lett. A

B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
[CrossRef]

Phys. Rev. A

R. Kolesov, Phys. Rev. A 72, 051801 (2005).
[CrossRef]

R. N. Shakhmuratov, A. Rebane, P. Mégret, and J. Odeurs, Phys. Rev. A 71, 053811 (2005).
[CrossRef]

A. Rebane, R. N. Shakhmuratov, P. Mégret, and J. Odeurs, Phys. Rev. A 127, 22 (2007).

R. Lauro, T. Chanelière, and J. L. Le Gouët, Phys. Rev. A 79, 063844 (2009).
[CrossRef]

Phys. Rev. Lett.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef]

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3733 (1991).
[CrossRef]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

Other

R. W. Boyd and D. J. Gauthier, ““Slow” and “fast” light,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), pp. 497–530.

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, 1972).

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Figures (4)

Fig. 1.
Fig. 1.

Polarized absorption spectra of the R-lines in emerald at 2.2 K. The inset shows the energy level diagram for the R-lines, and the arrows indicate the π-polarized R1(±3/2) transitions used for the slow light experiments.

Fig. 2.
Fig. 2.

Slow light in the R1(±3/2) line at 2.2 K for (a) zero field and (b) Bc=15.2mT. The probe pulse in the absence of hole-burning is denoted as Ref. This pulse is also shown normalized (green dashed–dotted line) to the delayed pulse. The (red) dashed lines were calculated by the linear filter theory (see text). The inset shows schematically the pulse sequence (dashed lines) and the corresponding transmitted laser light (solid lines) for the experiment with (upper traces) and without (lower traces) a burn pulse.

Fig. 3.
Fig. 3.

Dependence of pulse delay on Bc. (1: 0.62; 2: 0.73; 3: 1.83; 4: 5.49; 5: 9.15; 6: 12.81; and 7: 15.2 mT.) The reference pulse is also shown normalized (dashed line) to the delayed pulse in Bc=15.2mT.

Fig. 4.
Fig. 4.

(a) Pulse delay (red circles) and corresponding group velocity (blue squares) as a function of Bc. The (green) solid triangles were calculated using experimental values for A, ΔA, Γhole, and the width of the pulse. The large error is due to the uncertainty in Γhole as determined by hole-burning. (b) Dependence of Γhole [used for calculations in (a)], as a function of Bc as measured by hole-burning experiments and corrected for spectral diffusion and laser jitter (green solid circles). The (red) solid triangles show the hole-width obtained from the slow light experiment. The error bars show 10× the standard deviation.

Equations (6)

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

vg=cng
ng=n+ωdndω.
Eout(ω)=G(ω)Ep(ω),
Ep(ω)=12πEp(t)exp(iωt)dt,
G(ω)=T(ω)exp[iΔΦ(ω)].
ΔΦ(ω)=1πInT(ω)ωωdω.

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