Abstract

Controlling the group velocity of light is a valuable resource for quantum and classical optical processing and high performance sensor technologies. In this context, slow-light (SL) and the associated steep dispersion have been proposed to increase the sensitivity of certain types of interferometers. Here, we show that the interaction of two intensity-balanced light beams in a SL medium can be used to detect Doppler shifts with extremely high sensitivity. By using this effect in a liquid crystal light-valve, we have been able to measure Doppler shifts as low as 1 μHz with an integration time of only 1 s. The shot noise limited sensitivity inversely depends on the steepness of the beam-coupling dispersive response. This method allows for remote sensing of very slowly moving objects with a linear response over 5 orders of magnitude.

© 2013 Optical Society of America

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M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

R. W. Boyd and Z. Shi, Nature 481, 35 (2012).
[CrossRef]

2011

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

2010

K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, Nat. Photonics 4, 218 (2010).
[CrossRef]

U. Bortolozzo, S. Residori, and J. P. Huignard, Laser Photonics Rev. 4, 483 (2010).
[CrossRef]

2009

J. C. Howell, Nature 457, 798 (2009).
[CrossRef]

2008

L. Thévenaz, Nat. Photonics 2, 474 (2008).
[CrossRef]

S. Residori, U. Bortolozzo, and J. P. Huignard, Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef]

2007

Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science 318, 1748 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, Opt. Lett. 32, 915 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

2005

2004

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, Phys. Rev. Lett. 93, 243604 (2004).
[CrossRef]

G. Zhang, F. Bo, R. Dong, and J. Xu, Phys. Rev. Lett. 93, 133903 (2004).
[CrossRef]

2003

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

E. Podivilov, B. Sturman, A. Shumelyuk, and S. Odoulov, Phys. Rev. Lett. 91, 083902 (2003).
[CrossRef]

2001

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

1999

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

1993

1988

1985

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

1981

Behroozi, C. H.

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

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

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

Bo, F.

G. Zhang, F. Bo, R. Dong, and J. Xu, Phys. Rev. Lett. 93, 133903 (2004).
[CrossRef]

Bortolozzo, U.

U. Bortolozzo, S. Residori, and J. P. Huignard, Laser Photonics Rev. 4, 483 (2010).
[CrossRef]

S. Residori, U. Bortolozzo, and J. P. Huignard, Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef]

Boyd, R. W.

R. W. Boyd and Z. Shi, Nature 481, 35 (2012).
[CrossRef]

Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science 318, 1748 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, Opt. Lett. 32, 915 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

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

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2002), Vol. 43, p. 497.

Buse, K.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, Phys. Rev. Lett. 93, 243604 (2004).
[CrossRef]

Camacho, R. M.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Chan, J.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Chang, D. E.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Chang-Hasnain, C. J.

Crankshaw, S.

Cronin-Golomb, M.

Dahan, D.

Dawes, A. M. C.

Dong, R.

G. Zhang, F. Bo, R. Dong, and J. Xu, Phys. Rev. Lett. 93, 133903 (2004).
[CrossRef]

Dudley, C. C.

Dutton, Z.

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

Eichenfield, M.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Eisenstein, G.

Farsi, A.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Fraval, E.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

Fridman, M.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

Gaeta, A.

Gaeta, A. L.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science 318, 1748 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, Opt. Lett. 32, 915 (2007).
[CrossRef]

M. D. Stenner, M. A. Nedfield, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, Opt. Express 13, 9995 (2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2002), Vol. 43, p. 497.

González, M.

Ham, B. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Harris, S. E.

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

Hau, L. V.

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

Hemmer, P. R.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Herráez, M. G.

Herriau, J. P.

Hill, J. T.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Howell, J. C.

J. C. Howell, Nature 457, 798 (2009).
[CrossRef]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Huignard, J. P.

U. Bortolozzo, S. Residori, and J. P. Huignard, Laser Photonics Rev. 4, 483 (2010).
[CrossRef]

S. Residori, U. Bortolozzo, and J. P. Huignard, Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef]

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J. P. Huignard, Opt. Lett. 13, 327 (1988).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

J. P. Huignard and A. Marrakchi, Opt. Lett. 6, 622 (1981).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Imbert, B.

Jaksch, D.

K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, Nat. Photonics 4, 218 (2010).
[CrossRef]

Khoury, J.

Langford, N. K.

K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, Nat. Photonics 4, 218 (2010).
[CrossRef]

Lee, K. C.

K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, Nat. Photonics 4, 218 (2010).
[CrossRef]

Lepeshkin, N. N.

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

Lin, Q.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Longdell, J. J.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

Lorenz, V. O.

K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, Nat. Photonics 4, 218 (2010).
[CrossRef]

Lukin, M. D.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

Mallick, S.

Manson, N. B.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Marrakchi, A.

Mayer Alegre, T. P.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Moewe, M.

Musser, J. A.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Nedfield, M. A.

Nunn, J.

K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, Nat. Photonics 4, 218 (2010).
[CrossRef]

Odoulov, S.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, Phys. Rev. Lett. 93, 243604 (2004).
[CrossRef]

E. Podivilov, B. Sturman, A. Shumelyuk, and S. Odoulov, Phys. Rev. Lett. 91, 083902 (2003).
[CrossRef]

Okawachi, Y.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

J. Sharping, Y. Okawachi, and A. Gaeta, Opt. Express 13, 6092 (2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Painter, O.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Palinginis, P.

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

Podivilov, E.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, Phys. Rev. Lett. 93, 243604 (2004).
[CrossRef]

E. Podivilov, B. Sturman, A. Shumelyuk, and S. Odoulov, Phys. Rev. Lett. 91, 083902 (2003).
[CrossRef]

Rajbenbach, H.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J. P. Huignard, Opt. Lett. 13, 327 (1988).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Reim, K. F.

K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, Nat. Photonics 4, 218 (2010).
[CrossRef]

Residori, S.

U. Bortolozzo, S. Residori, and J. P. Huignard, Laser Photonics Rev. 4, 483 (2010).
[CrossRef]

S. Residori, U. Bortolozzo, and J. P. Huignard, Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef]

Ryan, V.

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Nature 472, 69 (2011).
[CrossRef]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Sedgwick, F.

Sellars, M. J.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. 95, 063601 (2005).
[CrossRef]

Shahriar, M. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, Phys. Rev. Lett. 88, 023602 (2001).
[CrossRef]

Sharping, J.

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Shcherbin, K.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, Phys. Rev. Lett. 93, 243604 (2004).
[CrossRef]

Shi, Z.

R. W. Boyd and Z. Shi, Nature 481, 35 (2012).
[CrossRef]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, Opt. Lett. 32, 915 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Shumelyuk, A.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, Phys. Rev. Lett. 93, 243604 (2004).
[CrossRef]

E. Podivilov, B. Sturman, A. Shumelyuk, and S. Odoulov, Phys. Rev. Lett. 91, 083902 (2003).
[CrossRef]

Solymar, L.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Song, K. Y.

Stenner, M. D.

Sturman, B.

A. Shumelyuk, K. Shcherbin, S. Odoulov, B. Sturman, E. Podivilov, and K. Buse, Phys. Rev. Lett. 93, 243604 (2004).
[CrossRef]

E. Podivilov, B. Sturman, A. Shumelyuk, and S. Odoulov, Phys. Rev. Lett. 91, 083902 (2003).
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Figures (4)

Fig. 1.
Fig. 1.

Two-beam interaction in a slow-light (SL) medium. Two nondegenerate light beams of the same intensity and with a slightly different frequencies, ν and ν+Δν, respectively, interact in the SL medium. The difference ΔN between the output intensities, which is measured through a balanced detection, strongly depends on the Doppler shift Δν.

Fig. 2.
Fig. 2.

Experimental setup of the two-beam coupling in a liquid crystal light-valve (LCLV). The laser beam is spatially filtered with a pinhole (Ph) and enlarged through the telescope composed of the two lenses L1 and L2. The beam-splitter (BS) is used to separate the input laser beam into two beams whose intensity and polarization are finely controlled through a polarizer (P) and a wave-plate (W). V0 is the voltage applied to the LCLV. The output beams are sent to a balanced detector composed by two photodiodes, PD1 and PD2, where their intensity difference V(t) is measured. An ultra-low noise voltage source (LP) is used to drive a piezo-electric mirror (PZT); the PZT moves at a constant speed vp.

Fig. 3.
Fig. 3.

Balanced signal as a function of the Doppler frequency shift. Close to zero the response is linear with a coefficient equal to χ=0.9324Hz1.

Fig. 4.
Fig. 4.

Measured voltage |V| as a function of the Doppler shift Δν. The dotted line and the gray region represent the photon shot noise. The continuous line is the fit of the linear part of the response.

Equations (3)

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Δνmin1|χ|hνηTP12,
ΔN=8πJ0(ρ)J1(ρ)Δντ1+(2πΔντ)2N,
χ=8πτJ0(2k0dn2I)J1(2k0dn2I),

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